T I O N O F

L U
EVO TERFACE
A I R I N S 5 G
W A R D
TO

Prof. Suvra Sekhar Das

Electrical and Electronics Engineering
IIT Kharagpur
 INDEX
S. Page
No Topic No.
Week 1
1 Evolution of wireless Communication 1
2 Evolution of wireless Communication Standards From 2G to 5G 23
Evolution of wireless Communication Standards From 2G to 5G
3 (Contd.) 39
Evolution of wireless Communication Standards From 2G to 5G
4 (Contd.) 59
Evolution of wireless Communication Standards From 2G to 5G
5 (Contd.) 76
Week 2
6 Requirements and operating scenarios of 5G 98

7 Requirements and operating scenarios of 5G (contd.) 123

8 5G scenarios 143

9 Ultra reliable low latency communication 162

10 Designing 5G new radio 182
Week 3
11 Fundamental Framework for waveform analysis 199

12 Fundamental Framework for waveform analysis (contd.) 219

13 Waveform Design Aspects of 2G 231

14 Waveforms in 3G 251
15 Waveforms in 3G (contd.) 272
Week 4
16 Waveform in 4G and 5G (OFDM) 286

17 Waveform in 4G and 5G (OFDM) contd. 301

18 Waveform in 4G and 5G (OFDM) contd. 318

19 Waveform in 4G and 5G (OFDMA) 334

20 Waveform in 4G and 5G (OFDMA, SCFDMA, SCFDE ) 351

Week 5
21 Waveform in 4G and 5G (SCFDMA contd.) 377

22 Waveform in 5G 397
23 Waveform in 5G Numerology 416

24 Frame Structure in 5G NR 432

25 Numerology in 5G and adaptive subcarrier bandwidth 453
Week 6
26 Numerology in 5G (contd.) 475
27 Waveforms beyond 5G 502

28 Waveforms beyond 5G (contd.) 519

29 Waveforms beyond 5G (contd.) 537

30 Waveforms beyond 5G (contd.) 560
Week 7
31 Waveform beyond 5G (Precoded GFDM) 583

32 Comparison of waveforms 607

33 Channel models for performance evaluation (Part I) 623

34 Channel models for performance evaluation (Part II) 647

35 Channel models for performance evaluation (Part III) 674

Week 8
36 MIMO Signal Processing (Receive Diversity) 701

37 MIMO Signal Processing 723

38 MIMO Signal Processing (Capacity) 757

39 MIMO Signal Processing (Capacity & Massive MIMO) 774

40 Hybrid beamforming (mmWave) 800

 Evolution of Air Interface Towards 5G
Prof. Suvra Sekhar Das
G. S. Sanyal School of Telecommunications
Indian Institute of Technology, Kharagpur

Lecture – 01
Evolution of Wireless Communication

Welcome to the course on Evolution of Air Interface Towards 5G. This is the first
introductory lecture, so our main focus would be to lay the ground and discuss how the
course has been arranged, so that, you can prepare as well as revise some of the basic
concepts and well acquainted it what is expected from the course.

Although, there has been a introductory material lecture which provides the motivation
for the course, but since it is the first lecture it is necessary that we discuss the overall
layout as well as get into some of the historical aspects which lays the ground for the
entire course that we are going to take. Its a 20 hour course that has already been
announced and 40 lectures.

So, we have quite a bit many lectures to discuss, but at the same time we have quite a
few many different technologies to be addressed in this particular course. So, it is a great
opportunity to discuss this particular course pertaining to 5G, because 5G is almost
knocking at the door and this gives us the right opportunity and gives us time enough to
prepare when 5G is just launched in about a years time.

This particular course as has been said before is particularly suited for the advanced
engineers; especially for the research scholars pursuing a research career in the domain
of wireless communications. It is also suited for the graduate level wireless
communication students; it is also suited for the practicing engineers, especially for
wireless communications.

So, as we are iterating wireless communications the name repeatedly; as we will go

through the over overall layout of the particular course we will see what all things that
need to be prepared as we go slowly inside the details of the course curriculum. In
general this particular course requires you to have a prior knowledge about digital
communications and overview about wireless communications would also definitely be
of help.

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Although, we will discuss some of the basic essentials of wireless communications that
are needed to understand some of the things. For example, the propagation, which we
will discuss slowly; we will also require to have some knowledge about MIMO, but that
is not necessary, we will discuss the preliminaries before we get into the nitty-gritties of
the details.

5G as this course is supposed to be, is going to be very different from its earlier
predecessors. The earlier generations when it moved from 2G to 3G to 4G, and finally,
moving towards 5G, until the previous generation it was primarily about data rates as
well as spectral efficiency. Most of the technologies on air interface were designed to
provide higher and higher data rate as well as to provide better spectral efficiency.

Whereas, when we take a look at 5G, we find myriads of different technologies that are
required to come together at various levels from the physical layer, from the access layer
as well as in the network layer which are supposed to work together. There are different
scenarios and a huge variety of requirements as well as a wide variety of devices and
applications which required to be served simultaneously by one single network, which is
completely different compared to what happened in all the previous generations.

This is given rise to the development of various different technologies, which need to
work together. Our aim in this particular course is to take a look at the fundamentals
which will make 5G run. We will not specifically look at the exact standard
specification, but we will follow them as well as describe the details of how the different
fundamentals of technologies make such a huge standard come into being.

We have already said before that this particular course has already been written down in
form of a book, and we have given you the link before, I would simply like to show a
particular copy of the book which is already available, and the soft version or the e-book
is also available.

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(Refer Slide Time: 04:43)

So, most of the material that we will discuss in this particular course is already provided
in e-books, its already available in the internet, so if you just look for it, it will be
available. However, whatever lecture we discuss in this particular course would be also
made available through the slides, and whatever material we would be able to share with
you.

So, 5G is supposed to come around 2020, its not far away, and already one of the
versions of technological specification has already been prepared, and while we go
through the course, we will visit it time and time again, so that we can check about the
latest developments as well as about the fundamentals that are making those realizations
happen.

So, at this point, let us look at the course outlay, so that we can see what all things we
need to prepare, and how we will go through this particular course.

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(Refer Slide Time: 05:49)

So, we will of course, view the evolution of wireless communications in a few minutes
from now.

(Refer Slide Time: 05:55)

But before we go into it lets look at the week wise layout of the course. We will talk
about the evolution of wireless communication towards 5G initially. So, there its not in
details with the fundamentals of signal processing and so on but, however, it lays the
ground and the motivation for the 5G, so that all the things that follow after this
particular week we know why we are doing each particular thing. How the requirements

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have been set up, and how the solutions are arriving based on the initial objective that
has been set.

Then we will move on to the waveforms. Usually, this is termed as the new radio in 5G,
but we will not restrict ourselves to whatever is in the current version of the release 15 or
the new radio that has been described in 5G. But we will also go beyond that and discuss
some of the contending technologies which have been there in the scene. And however,
for some reason they were not accepted for the present version, but however they have
enough technical competence and capabilities to be considered for future generations of
communication systems.

With that, we will move ahead with the modulation formats. We will then look at the
propagation characteristics that are very important. Because when we look into 5G, it is
not just a single spectrum band, it is not just one single technology. So, hence it is
important to understand the propagation characteristics that influence the technologies
that are being proposed as well as their performance.

Its very important to understand how the signal propagates through the air medium in the
different scenarios, because the air medium presents the challenges which are overcome
by the different solutions as will be discussed in this particular course. There are several
other courses which detail the wireless communication aspects. However, it is always
important to remember that it is the propagation characteristics which influence the
design of the solutions which are aimed towards overcoming the challenges has thrown
by the wireless propagation characteristics of the particular medium.

5G is especially going to be different compared to other previous technologies because in

5G, we are going to see the new millimeter range of spectrum, which will be used in the
terrestrial communication system. So, this particular range of frequencies has certain
special characteristics which has been studied before, but when it will be used in the
terrestrial communications, there are certain disadvantages, and there are certain
advantages which will be considered in details.

And as a consequence, you will be easily able to understand how the different solutions
have been arrived at, and how the different solutions work together take advantage of the
situation rather than seeing the entire propagation characteristics as a challenge. Another
important aspect of 5G is MIMO communications, advanced level of MIMO

5
communications. MIMO communications have been present in the previous generations,
but there are certain special aspects especially like massive MIMO and beamforming.
We will spend a considerable amount of time in providing the basis for MIMO
communications, the fundamentals so that those who are not well equipped with the
understanding of MIMO should be able to catch up with the advanced concepts. And
then, we will move on to some of the important aspects which are going to drive 5G.

Thereafter, we will look at certain system level aspects that is the heterogeneous
networks because it will be a system where multiple kinds of transmitters and receivers
are going to work together and the RAN architecture is not going to be homogeneous
there will be various layers of operation. So, we will be detailing the issues that are
involved in such a system. Thereafter finally, we aim to touch upon the quality of
service, the energy aspects, as we will see slowly and how to evaluate performance of
systems under such situations.

(Refer Slide Time: 10:15)

If we take a look at the details of how we have planned the entire course the initial few
lectures would be on the standards, how things have evolved so that we get to set
ourselves on how the commercial domain of things are moving, and how technology has
been changing, and has been accepted by the industry so that, we are equipped with the
mode of thinking, and we design our solutions future solutions in a similar line.

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We will discuss the radio access technology especially the waveform part which we have
considerable number of lectures.

(Refer Slide Time: 10:49)

Then we look into the access part where there are different kinds of new access
technologies that are coming into play. We will talk about the channel models as has
been listed there we will especially look at the third generation partnership project based
models. Because, those are some of the models which have been well accepted and used
for performance evaluation of the 5th generation communication techniques.

So, it is essential that we understand the commercially usable or the models which are
more popular towards realization of practical systems. We will also discuss the
performance evaluation methodologies and what principles are followed, how things
have to be done, so that the results that we get are usable by others. It can be reusable,
reconstructed, and the results can be used for exchange between the different groups so
that its well accepted.

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(Refer Slide Time: 11:45)

We move beyond this with the different MIMO technologies as has been said earlier. We
will talk about the fundamentals. Then we will move on to the details of massive MIMO,
and beam space, and some of the other advanced concepts which are expected to be vital
for 5G communications.

(Refer Slide Time: 12:03)

Then as said about the heterogeneous networks, we intend to discuss small cell
architecture. We intend to discuss the non orthogonal multiple access as well as how
would MIMO interact with non orthogonal multiple access.

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Finally, we will get into the energy savings mode with multi objective optimization.
Because whenever we have systems into play there are various different objectives
where the whole network is supposed to meet and you have a set of parameters which
you can control in order to meet the different objectives. Now when you have all these
objectives coming together simultaneously, how does the system evaluation work out
and what all details happen, how does one objective play with the other, we will try to
look at that.

We will also look at techniques for computing the area spectral efficiency, which is a
very important aspect. Because when we are working with such technologies as 4G or
5G, its very important to analyze the area spectral efficiency, because users are
distributed over the area. Whereas, the link spectral efficiency is also important, but
finally, what plays a major role is when multiple users come together, how do you
analyze the spectral efficiency of systems analytically?

So, we will discuss some of the methods which are vital in doing this analysis. The
importance of looking at analytical methods is that it helps us to create a framework
through which we can get results quicker than typical simulation procedures. The
simulation procedures are of course essential because the models which are used for
performance analysis are usually from measurements, and they are usually not
mathematically tractable.

But, when we look at analytical approaches, we look at methods and tools as well as
models which are more analytically tractable, but then there is a difference from the
measurement models. So, we will try to present some of the ways in which these
analytical models could be used to provide results which are quite acceptable or as good
as the simulation results. Thus only helping us to save a lot of simulation time.

We will move beyond this and discuss about some of the quality of service aspects.
Because essentially the quality of service for real time traffic classically has been
provided through circuit switched network. Whereas, the modern networks are providing
these real time services such as voice and video through packet based services. Now,
how do we look at or how do we measure the quality of service of such systems, and if
we apply the admission control, how does it fit into? What are the metrics that needs to

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be looked at? So, this overall aspect of the link level as well as system level will be
discussed in this particular course.

(Refer Slide Time: 15:05)

So, moving beyond whatever we said it is very important that we look at from where we
started. Because, when we look at today, we are standing at the door of 5G, things have
changed really really very very fast over the past few decades.

Today the new generation is almost not aware of how things have started, but I find it
very important to look back into the past, at least for the initial few minutes so that, at
least we get back to the basics whenever it is necessary. And its very important, I
consider once again that we find out if there is anything from the past which is still
influencing our 5G technologies which will soon be able to find out.

So, at this point, we will try to look at some of the historical aspects, although it is quite
well known that most of you know about these, but I find that it is very important that we
pay our tribute to the great founders of wireless communication technology on whose
shoulders we stand. And, maybe some of the facts that we discuss, could be new to some
of us. So, with this lets get into some of the facts that we already know or maybe new to
some of us.

10
(Refer Slide Time: 16:29)

So, we know that, Morse developed the telegraph system, and which is one of the very
early communication systems. But an important fact, again most of the things are from
internet resources, some of the references are given here. Again a fact in wiki, which I
found very interesting at this point of time is what, Morse wrote a letter to a friend as has
been there in this particular slide, where he describes that even he had to fight in those
years to be established as the sole inventor of electromagnetic telegraph.

So, what it clearly means is that, whenever an invention happens simultaneously many
people across the world work on some of the things, and there has been always a war, a
fight on claiming the first. So, although that’s not the main message, but this is also an
important message, which I consider and I wish to share with all the researchers of
wireless communications of the future.

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(Refer Slide Time: 17:25)

Next, we all know the famous Maxwell equations, and this was the genesis of wireless
communication. So, whenever we think of wireless communications, we can never start
without paying a tribute to the great Maxwell, because of whom we are finally, seeing
the entire set of developments of wireless communications.

(Refer Slide Time: 17:47)

The next important stage as you all know was due to Hertz who demonstrated the
existence of electromagnetic waves. And then started a flurry of demonstrations of
wireless communications, and today we are again at the forefront of 5G.

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(Refer Slide Time: 18:03)

At this point, it is essential that we look at one of the important contributors to the
development of wireless communications, and this was Sir Jagadish Chandra Bose, and
he demonstrated the first experiment of wireless communications around 1894-95 in
Calcutta. And a very interesting fact which I would like to point out and some of you
may have already known is that he used the millimeter range of wavelength of
microwaves in order to demonstrate the particular experiment.

Now, what is important is that this particular frequency is again becoming one of the
fundamental spectrum bands where 5G is expected to work. So, this is more than 100
years ago this particular technology was used for wireless communication. And we are
back again going to use this particular spectrum for communication into 5G. So, this
particular image and the scientist plays a very vital role even though it was 100 and year
more than 100 years back it is very much relevant for 5G.

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(Refer Slide Time: 19:17)

Marconi is does not require any mention and one of the biggest contributions in that he
did was long distance wireless telephony. So, when we look at 5G today that is going to
come, it is expected to encompass not only terrestrial and small distance communication,
in fact, it is expected to encompass even satellite communications.

So whereas, in 4G, it was more restricted to terrestrial communications, in 5G we are not

only going to have very short distance communications, ultra reliable communications,
but also we will be having very very large distance communications if not inter-
terrestrial probably the next generations would be able to have some methodologies
through which these could also be done. Again, we what we are seeing is that although
these inventions were made more than 100 years ago, they are still somehow relevant for
the modern generation.

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(Refer Slide Time: 20:09)

Its important that we recognize the contributions by Tesla and amongst the various
contributions that he mentioned would like to focus on the wireless side wireless
communication or aspect. So, one of the last statements that’s written in the particular
slide, again it is taken from internet resources, its clearly states that around 1898. I mean
nearly 1900, he had developed a coherer-based radio control which he dubbed the
teleautomation and it was used to demonstrate a boat could be maneuvered using remote
control.

So, again whatever we are seeing today that remote controlled application especially
UAVs and others are already demonstrated more than 100 years ago. Of course, what we
have today is much more advanced technology, super level of control, which has been
contributed by the by the development over the last 100 years. The method of wireless
distribution of electricity today we are having wireless charging. So, again the
philosophical concepts were there, but it took a long time before it could be made of use
to the general public which will again form one of the basis for future generation
communication systems.

15
(Refer Slide Time: 21:25)

This is an interesting personality whom I would like to bring forward probably it is

usually missed out when we discuss about communications is Dennis Gabor. Although,
he is famous for hologram, his work as has been given there particularly lays the
foundation for the time frequency resolution analysis which again found its importance
during the contention of waveforms on 5G.

So, he was one of the founders of the waveform analysis space where the Gabor
waveform was developed and the generalized frequency division multiplexing which
was one of the contenders for 5G is based on the structure and time frequency analysis as
presented by Gabor. And we hope probably in future generation of wireless
communication system this advanced methodology finds its place and its mature enough
to be used as a technology solution.

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(Refer Slide Time: 22:23)

Shannon requires no further explanation; he is the founder of information theory. Again

a lot of things that we see in 5G are because of the foundations that have been laid in
information theory; whatever we see in MIMO and massive MIMO are again having
foundations back in information theory. Whatever we talk about non orthogonal multiple
access has again been proved in information theory to provide the highest spectral
efficiency for multi user communication as is possible.

(Refer Slide Time: 22:51)

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Some side note on the Nyquist contribution because the entire domain of
communications depends upon sampling which was due to Nyquist. So, we just need to
remember some of the major contributions because as we move beyond and look into the
advanced technologies. We sometimes miss out the minute nitty-gritties which run into
the system so often that we tend to neglect them.

So, I take this opportunity to remind ourselves of the great contributions. And probably
there could be greater contributions by the future generation researchers motivated by
some of the fundamental works done at an early stage.

(Refer Slide Time: 23:31)

So, thereafter was the age where instead of individual contributions they were more of a
holistic or system level of group level contributions. Because, it was more of system
development when we look at 5G the development is because of hundreds and thousands
of engineers and scientists all over the world who has gone together to produce the
technologies which will be of use. So, it is no longer one single persons; it is more of a
team effort and we briefly take a look at some of the developments which have happened
over the past so that we are in sync with some of the aspects.

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(Refer Slide Time: 24:11)

In the 1860s it was mostly the developments that we had seen before, thereafter it was
the period where the cellular telephony became important around 1948, 1950s it was the
region where fully automated mobile telephony came into play. And then around 1970s
to 1980s the mobile telephony became very commercial; lots of people were using it.

(Refer Slide Time: 24:37)

From 1980s onwards, it was the cellular concepts which came into being and today we
are still using those concepts of cellular, we have cells, we have frequency reuse. And
this is one of the most important methods by which the area spectral efficiency has been

19
increased over the different generations from 1G to 2G to 3G to 4G and 5G. And over
the years, the cells have become smaller and smaller and smaller, because the spectrum
is limited, and this is one way by which you could simply keep on increasing spectral
efficiency.

(Refer Slide Time: 25:15)

This particular picture is capturing some of the technologies of the yester-years that is up
to 4G we deliberately did not bring 5G into account because that is yet to come which
will see in some future slides. However, in this particular slide, we try to bring about the
locations of the different technologies with respect to user mobility and transmission
rates.

So, what we see is that some of the technologies were very good at providing high
mobility support, while other technologies were very good in providing the high data
rate, but at low mobility, and 4G had a target of providing very high data rate while
providing very high mobility. Now, when we look at 5G; 5G also aims to provide very
high data rate also supports very high mobility, but that’s not the only aspect as will be
clear in the future lectures.

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(Refer Slide Time: 26:13)

In this particular figure, we try to see some of the different applications that have been
pushing the development of the earlier generation mobile communication systems. And
we will slowly look at some of the applications which are the drivers for the 5th
generation mobile communication systems.

(Refer Slide Time: 26:33)

Till recent past, there have been lot of effort where different types of communications
have been brought into convergence. Although, this particular picture shows that there
has been lot of effort in trying to bring them into one board, but unfortunately that has

21
not happened much, but that is one of the agenda that 5G wants to achieve that they want
to bring around different communication methods and applications under one platform.

(Refer Slide Time: 27:03)

So, this particular slide summarizes the different technologies along with some of the
timelines. So, as we go from 1G to 4G we see that analog modulation slowly moved
towards digital modulations. The access technique moved from time division multiple
access to code division multiple access; then there was wideband code division multiple
access and when things move towards 5G there was orthogonal frequency division
multiple access.

One of the major changes that happened over the periods was the frequency reuse factor,
which was initially a large number. Then finally, it came down to frequency reuse of 1.
And although OFDMA systems are of frequency division multiple access nature, but still
they use they are capable of using frequency reuse factor of 1, in order to provide very
high spectral efficiency, because additional higher level higher layer methodologies
bring into account interference management techniques which help it survive.

We stop this particular lecture here. And, in the next lecture onwards we will look at the
different aspects of 5G, and how it stands with respect to the previous generation mobile
communication standards.

Thank you.

22
 Evolution of Air Interface Towards 5G
Prof. Suvra Sekhar Das
G. S. Sanyal School of Telecommunications
Indian Institute of Technology, Kharagpur

Lecture – 02
Evolution of Wireless Communication Standards From 2G to 5G (Part – I)

Welcome to the course on Evolution of Air Interface Towards 5G. This is the 2nd lecture
and in the previous lecture we have discussed about the Evolution of Wireless
Communication, a bit of historical perspective, but sometimes it is important to get back
to history for reasons which we have discussed earlier. In today’s lecture, we will take a
brief overview of how the communication standards have evolved.

(Refer Slide Time: 00:47)

So, towards this we will have a structure as presented in this particular slide, where we
will initially talk about the standards and the development cycle. Then we look into the
ITU-R recommendations, followed by a summary of GSM and IMT-2000, and then we
will take a look at the requirements of IMT Advanced. So, with this let us proceed.

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(Refer Slide Time: 01:10)

So, we were discussing about the evolution and in this particular picture, which we are
seeing in the previous discussion, that we have summarized the different technologies
which have evolved from the first generation to the fourth generation. And, there were
different kinds of modulation techniques, different data rates, and different kinds of
access methodologies, that have been summarized. And, what we recall is that a very
famous statement that was put that it is dangerous to put limits on wireless data rates, is
true and it will even remain true when we will discuss the fifth generation of mobile
communication systems.

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(Refer Slide Time: 01:49)

So, in this particular picture what we see is that the first generation communication
systems were mainly analog, and they were primarily designed to cater for voice
communications. The way the channel were multiplexed amongst the different users is
essentially frequency division multiple access. And this particular set of technologies
existed before the 1980’s which was mainly analog domain communications.

We moved on further and we looked at or we came to the generation of second

generation communication system, where the primary change was digital voice
compared to what was there in the first generation. Primary methods that were used were
time division multiple access and code division multiple access; we will get an
opportunity to briefly see them sometime in the lectures. This set of technologies existed
from 1980’s onwards and even today we have a huge percentage of mobile subscribers
who are still connected to the second generation of mobile communication systems. It is
one of the most successful mobile communication systems which are in use today, and it
is expected that 2G will continue for at least a few more years before it becomes
obsolete.

Beyond this from 90’s, the work on third generation system started and the main access
technique was WCDMA, that is Wideband Code Division Multiple Access and the
primary difference from the previous generation communication systems was not only
digital voice, but there was data also which was pre-designed into the system. If we look

25
at the transition from 2G to 3G, data was slowly brought into the system, but it was
essentially into the circuit switched network whereas, as we will see, the data was part of
the design where packets switched data services were brought into the systems.

This started around 1990’s and around 2000, we had the third generation systems
deployed and then the work on fourth generation system started. And, around 2010, we
had the 4G system in place and it was a wireless broadband system. It was one of the
first wireless broadband systems as such although 3D 3G was itself a broadband system,
but 4G was effectively one of the most efficient broadband systems compared to the
previous generations. And, the access technique that was used was Orthogonal
Frequency Division Multiple Access and in short it is usually called as OFDMA.

Moving beyond that somewhere after 2010, the work on 5G started and we have one of
the preliminary versions of 5G which has been accepted by lot of organizations. It is
expected that around 2020, 5G will start to get rolling out into the different parts of the
world. There have been a lot of changes in the access techniques from fourth generation
to fifth generation which we will see in this particular course. What we also see in this
particular picture is that from the different generations, first generation was mainly
analog voice.

But, leaving that apart from 2G onwards, as we move towards the fifth generation, one of
the common things that have remained is increase in data rate. Whereas, it was only a
few kilobits per second most of the users or most of the viewers can easily accept that the
in the fourth generation technology few megabits per second per user is a reality. In fifth
generation system amongst many other requirements one of the requirements would be
to support even higher data rates compared to the previous generation systems. But, as
said and we will see the data rate is only one of the few parameters that have remained in
5G compared to the earlier systems.

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(Refer Slide Time: 06:02)

So, what we see from the previous slides is that generally there is a 10 year cycle when
one standard evolves into a newer standard. So, this entire process starts with the setting
up of goals as depicted in this particular slide. So, initial set of goals are the kind of
objectives where, the new set of technology are supposed to meet. And, then this gets
translated to a set of requirements which are more of specific requirements in terms of
numbers for example, data rates and delays and all other constraints.

Spectrum allocation also happens, which is usually discussed in the world radio
communication conferences and this plays a vital role in selection of the methods that
come into the standards. So, by this time, most of the methods or the techniques or new
inventions have been discussed thoroughly. And, addition to the spectrum allocation
information, whichever technology requirements or whichever technology solutions fit
into the system are discussed in the standards organizations. And, then around a 10 year
cycle from the setting up of the goals, the standards gets finalized and implementation
and deployment starts.

Thereafter, the standard continues to live and there are further enhancements to the
standards while, a new standard starts getting designed from the phase after the 10 years.
So, what we essentially have is that while a previous generation standard continues to
evolve a new generation standards activity already get started. What you see is that the
GSM technology, although it was pretty old it evolved into newer versions where it

27
would support higher and higher data rates. While, the newer generation that is the third
generation communication systems started to getting designed.

Even when the 4G system was getting designed 3G system was still evolving and to a
certain point it had almost the specifications meeting, that of the 4th generation systems
in terms of at least the data rate. Although, the methods the way they are implemented
were quite different from each other.

(Refer Slide Time: 08:30)

So, this has been summarized and if we look at the dates, GSM was around the 1990’s,
IMT-2000 came into being around 2000, IMT-2000 is also called 3G, and 4G which is
also called the IMT-Advanced came into being in around 2010, and IMT-2020 which is
5G will come into being around 2020. So, what we see is that there is roughly a 10 year
gap between the deployment of the standards. However, there are contentions that this is
not a one step jump from one standard to another. So, there has been continuous
evolutions and you may have come across names such as 2.5G, 3G, 3.5G, 3.9G, 4G, and
so on and so forth.

So, there is a gradual change of technological evolution which keeps on happening and it
is not a sudden phase change that the industry experiences. Even a sudden phase change
is not possible to accept because of several such interconnected devices a huge amount
of investment, a huge amount of effort that gets involved. So, it is a natural process that

28
things evolve slowly from one phase to another, but finally, what we see is when there is
of 10 year gap there is a significant amount of difference from one technology to another
technology.

And, one of the other aspects is that people to look forward to a feasible set of
framework, a platform which is remain valid for a next period of 10 years which can
evolve within the framework yet provide sufficient time for the new generation things to
be deployed, as well as adopted, and which gets backward compatible with the earlier
generation systems so that they can co-exist simultaneously.

(Refer Slide Time: 10:33)

In this picture which we have taken from the 3GPP information which shows the
timeline of development of IMT 2020 which is the fifth generation standards; what we
see is while the activity of fifth generation standard carries on there is still evolution of
HSPA and LTE that is 3.5G and 3.9G that goes on along with the development of 5G
activity. So, these activities continue to a certain point until and unless these are no
longer supported by the global community.

29
(Refer Slide Time: 11:13)

Next we take a look at a series of recommendations. One reason for bringing in this list
is so that those who are interested in finding out the specifications, the requirement as
given by ITU can easily look into these references and find out the detailed inputs or the
material that is present over there. For example, M.687 is the name of a particular
document which describes IMT-2000. Then a series of other numerologies are present
like M.817 discusses the network architecture of IMT-2000, M.1035 is a framework for
the radio interfaces, and radio subsystem functionality for IMT-2000 which is the 3G
standard.

M.1034 discusses the requirements for radio interfaces for IMT-2000, 1079 discusses the
performance, and quality of service requirements of IMT-2000. And finally, 1225
represents the guidelines for evaluation of radio transmission technologies for IMT-2000.
So, what we see in these few set of documents is the sequence of things as we have seen
earlier like there is a set of requirements that get set up, then there is a specification, then
there is a performance and quality measure as well as a set of recommendations on
evaluating the performance of such systems.

Then we proceed on to the next number 1308 which explains the evolution of land
mobile systems towards IMT-2000; that means, as they move towards 3G. And 1457
presents the detailed specification of terrestrial radio interfaces of the IMT-2000
standards.

30
(Refer Slide Time: 13:19)

As we move ahead in the 1645 I mean it is not necessary to remember this, but this
particular set of slides can act as a reference for you to look into and get details of the
information that you may require. So, the first document talks about the framework and
overall objectives of future development of IMT-2000; that means, whatever happens
beyond IMT-2000. I mean advancement of IMT-2000 as well as beyond IMT-2000; that
means, for evolution of 3G as well as things beyond 3G. 1034 are the requirements of
radio interfaces, 2012 are the detailed specification of the radio interfaces of IMT-
Advanced. So, we have now moved to the set of documents which start discussing about
IMT-Advanced which is the fourth generation communication system.

2134 describes the requirements related to the technical performance of IMT-Advanced

radio interfaces which we will see in some of the lectures. In 2370 this is also a very
interesting document which talks about the IMT traffic estimates for the years 2020 to
2030. Now, these documents are very interesting and important because, they predict the
traffic that is going to be coming into the system and based on the description of the
traffic the detailed solution of systems need to be developed.

So, such analysis and predictions are the ground or basis on which new technological
solutions come into being. Then the 2410 describes the minimum requirements related to
the technical performance of IMT-2020. So; that means, the fifth generation and 2083 it

31
is the IMT vision or framework for overall objectives of future developments of IMT
2020 and beyond.

So, this talks about 5G and beyond systems and so on and so forth. And along with this
the ITU-R FAQ that is the Frequently Asked Questions on IMT is also a very interesting
document which answers many of the queries which are usually present in our mind.
And, I would recommend to the users of this particular course to find some time and get
into these documents. These are very well described documents which can provide you
with a good background of how things have evolved from earlier generations to the next
generations.

This will lay the foundation of how things keep on evolving and at least for the next
generation how things have moved on. And, probably the process is going to continue
for at least one more generation.

(Refer Slide Time: 16:08)

So, if we check back on GSM which is the second generation communication system a
bit of historical aspect, it was the European Conference on Post and Telecommunication
Administration or CEPT which was which founded the Group Speciale Mobile which
talks about the objectives of better and efficient wireless communication than analog.

So, this was one of the objectives and it was established in the GSM standards. And, a
very important aspect it is a single standard for all Europe that was the initial objective.

32
But, what you can see is that it is it was made available across a huge part of the world.
India is one such country where GSM is hugely popular and very effectively it helped
connect to the remote areas through telecommunication network which was difficult with
wireline systems. TDMA was one of the access techniques which was agreed upon by all
the groups of members which were part of this community and it is still in use.

(Refer Slide Time: 17:17)

In GSM we may all know, but it is interesting for us to take a look that it uses the
Gaussian Minimum Shift Keying as the modulation. And it is a kind of continuous phase
Frequency Shift Keying which is very effective in the sense it is smooth transition
between symbol to symbol.

So, when the symbol changes which we will discuss at some point that depending upon
the pulse shape the spectrum of the signal is formed. So, if we want a signal to be well
contained within a certain pulse shape, within a certain bandwidth, we require to design a
modulating technique by which the bandwidth is well contained. GMSK is one such
modulation technique in which the bandwidth is well contained as well as the peak to
average power ratio is also limited.

So, if the peak to average power ratio is limited, it helps us in enhancing the battery life
because the power amplifier which is in use is operating at its higher efficiency. And,
this helps in providing higher battery life to the handheld devices which is very very

33
essential for most of the handheld devices that we require and it is still a big challenge as
you increase the bandwidth.

For GSM we all know the bandwidth of occupancy is around 200 kilohertz whereas, as
we moved beyond to higher systems we have seen earlier and we will see later also the
bandwidth has become larger and larger. So, these problems still remain as important
problems in next generation systems. And, there have been newer methods which have
been there to help contain the signal bandwidth within a certain amount of spectrum as
well as reduce PAPR amongst other technological enhancements.

(Refer Slide Time: 19:13)

IMT-2000 which is the 3G, it had a set of objectives we will just pick up few of them
just to highlight what are the contents of the documents as were listed earlier. So, one of
the objective was to make voice and non-voice telecommunication service available to
users were mobile and roaming. So, if you see the earlier requirement; early requirement
was to make analog communication system to digital, and to provide a single
communication standard for all Europe. Whereas, here the objective is to make voice as
well as non-voice telecommunication services which comes into being as a requirement.
So, hence your entire system design starts to be looked at from a different perspective
altogether.

34
This is the starting point of the development of a new technology. It is also expected at
that time they discussed that it is expected to accommodate a variety of mobile terminals.
So, they had already foreseen a variation or multitude of devices; that means a variety of
devices from small devices which could be carried on person as well as devices which
could be mounted on vehicles. A small command on this would be if we look at 5G
systems which we will see shortly is that this requirement has carried on and in fact, only
the variety has become much more than was perceived in those times.

So, as a general objective it still remains to accommodate a heterogeneity of devices into

the communication system. It was also foreseen to account for road traffic management
and control system. If you look at some of the use case scenarios of 5G, this still remains
as one of the requirements. But, it is not surprising because at some point of time there is
a vision, and there is a requirement, people find technical solutions, but with time the
challenges also evolve. When challenges evolve, the overall objective remains the same,
but new solution needs to be found for the increase in magnitude of the problems.

So, as we see that overall objectives have continued from 3G to 5G, but newer solutions
are required given the magnitude of the problem. Interestingly, out of the many many
requirements, I could pick out one of them which says to ensure minimize the theft of
IMT-2000 mobile stations. So, that got built into the standard. So, this kind of
requirements are very essential in order to maintain safety; further as you may also see
that support for emergency services was also discussed to be brought into this to the
standard.

So, as to support emergency situations like in case of emergency, the emergency call
information for example, the user identity, the location information which are required
by authorities are automatically provided to the network. Because in emergency it is not
possible to provide a whole set of information whereas, a simple call to the center of
rescue is sufficient to provide huge amount of extra information which can be used
immediately for the mission. So, these kind of requirements create a huge impact on the
design of the solutions that are looked into by these systems.

35
(Refer Slide Time: 22:49)

So, if we look at the objectives and carry on with them; one of the objectives was to
allow extension of cell site in rural or remote areas. Now, this has even continued to 4G
and probably it will continue into 5G as well because, there is still a vast majority of
areas where there is scanty population and which is mainly agrarian based. So, in those
areas you would like to have cell sizes which are large whereas, if you look at the
evolution from 2G to fifth generation systems, the primary cell size have become smaller
and smaller.

One of the reasons is to increase the term called area spectral efficiency or bits per
second per hertz per meter squared. So, if we have to increase the area spectral efficiency
amongst several things, the frequency reuse factor or the cell size needs to be adjusted.
The smaller the cell size, the better it is it provides higher efficiency. But, what it states
is that the larger cell size should be supported without much modification into the
baseline standards because, we would like the same devices to operate in a highly dense
scenario as well as in a rural area.

So, the radio interfaces have been defined in several ways and the R1 and R3 amongst
the many I have just picked up only two of the because, of limitation of space and since
this is not our main objective of discussion. But, since it is still important that these are
the ways in which radio interfaces between the mobile station and the base station have

36
been defined in R1 and the radio interface between the satellite and mobile earth station
is defined in R3.

So, what we see is that the third generation system also had provisions to connect to the
satellite communication system and this is also a very important part of 5G. Now why I
am bringing this up? So, that you are aware that certain things which may appear as a
new requirement which may suddenly appear as a new thing in the fifth generation
system is actually not so they have been existing since the time of data communication
systems. In terms of quality of service, the transmission quality is described in terms of
Signal to Noise Ratio or Signal to Interference Ratio.

As well as it is also described in terms of service area reliability or the percentage of time
over the service area, the services are available. The other parameters of quality of
service were blocking probability especially important for voice calls. And Cut-off
probability such as cut-off probability due to handover blocking; that means, when you
are moving from one physical region to another physical region because of handover of
call from one base station to another base station there could be called drop. So or there
could be the cut-off because it the next cell is unable to accept the new connection
request.

So, for all these reasons a cut-off probability is also taken as one of the important metrics
which should be measured. Initial connection delay is also one of the measurements of
quality of service. So, what we can see is there is a small list of quality of service from
the entire set of list that has been captured over here. And, some of these have continued
as quality of service measure in the new system while, some more things have been
added as we move to 4G and 5G systems.

37
(Refer Slide Time: 26:40)

Some measures from the documents which describe the 3G requirement specifications as
we can clearly see is that there is a variation of traffic requirement estimates from 500
Erlang per kilometer squared to 5000 Erlang per kilometer squared. So, there is a huge
variation of traffic requirement on different scenarios. So, again what I am trying to point
out in through these set of numbers is that with 3G onwards, there has been a variation in
the requirement or a range of variations that starts to get defined. Instead of just a single
requirement that voice needs to be communicated which was the first generation and
second generation communication system.

As we move beyond this into the fourth and fifth generation system we will see even a
wider variety of description which tells about the requirements. So, there has been more
detailed description of requirement and hence we are able to come up with better design
to meet better quality of services for the fourth and fifth generation system. We conclude
our lecture on the evolution of communication systems, till this point over here in this
particular lecture. We will continue in the next lecture to talk more about 3G and 4G
communication systems.

Thank you.

38
 Evolution of Air Interface Towards 5G
Prof. Suvra Sekhar Das
G. S. Sanyal School of Telecommunications
Indian Institute of Technology, Kharagpur

Lecture – 03
Evolution of Wireless Communication Standards from 2G to 5G (Part – 2)

Welcome to the course on Evolution of Air Interface Towards 5G. So, in the previous
two lectures, we have been seeing the development of wireless communication a little bit
of historic perspective. And then we started to look at the GSM communication, which is
the 2nd generation system, and which translated from analog to digital. So, we carry on
with our journey and start taking look at the 3rd generation systems also known as IMT-
2000s. And then we will move forward slowly towards the development of IMT as
things have followed.

(Refer Slide Time: 00:58)

So, in this particular lecture, we are going to cover the topics IMT-2000, requirements of
IMT-Advanced, LTE, and LTE-Advanced, and how they fare against each other and
where do they stand. And then we will move forward to the IMT-2020 or which is the
five 5th generation of wireless communication systems.

39
(Refer Slide Time: 01:16)

So, what we see in this particular picture of the IMT-2000 is that on the radio interface
side, there has been multiple technologies, which could meet the specifications of IMT-
2000 whereas, on the core network side, they were again multiple methodologies or
techniques or technologies, which could support them. And as has been clearly
mentioned that each of these radio technologies must be operable on two major 3G core
networks that is the DS-mode is the so called W-CDMA mode.

So that means, there are multitude of technologies, so although there had been some
agreement that there should be a common technology, but interoperability and things
have been tried to be maintained. But, end of the day there were multiple technologies,
which satisfied the requirements and they were labeled as IMT-2000, and that you can
clearly see as has been described in this particular picture.

40
(Refer Slide Time: 02:18)

Moving ahead what we take a look at is that the W-CDMA proposal, which was from
Japan had a bandwidth of 1.25 megahertz, 5 megahertz and so on and so forth. In
Europe, it was ETSI, which presented the UMTS or Universal Mobile
Telecommunications System. And it was known as the UMTS terrestrial radio access
also usually referred to as the UTRA or U T R A, and it had W-CDMA which is FDD
paired, and it had TD-Time Division CDMA.

China had proposed the Time-Division synchronous CDMA, which is similar to the
UTRA TDD. While from Korea, there was multi-carrier IMT-2000. So, if you look back
at some of the publications, there have been a huge amount of comparison of the
different technologies, their benefits, and their disadvantages. And then, you could see
that how different technologies pair against each other, how do they perform against
each other, and there are different reasons for selecting different technologies in different
regions.

End of the day, what we take a message from this is that there could be multiple different
technologies, which could meet the specifications of a particular generation of
communication standard, and a brief summary of its genesis has been given in this
particular slide.

41
(Refer Slide Time: 03:52)

As we move ahead. So, beyond 3G that means, 3G plus plus as I have mentioned over
here though there is nothing called 3G plus plus, but there are like 3.5G and 3.9G, some
of the important things that came into play were variable data rates, which were
supported by means of multiple code word assignments or a variable spreading factor
that means, since CDMA technology, which uses spreading mechanism.

So, one could allocate multiple code words to a user or one could use a variable
spreading factor. So, as you are spreading factor changes, the data rate supported would
also change, so thereby a variable data rate was supported. Modulation and code rate
were also made flexible. Flexible in the sense multiple options were available. So,
different modulations like BPSK and QPSK and 16-QAM, were also brought into
picture, different code rates not only a fixed rate half, but other code rates were also
available.

And the mechanism of error correction codes such as turbo codes and other techniques
were brought into play, which improved the error probability and hence the coverage.
The method of hybrid ARQ; ARQ is the Automatic Repeat Request, which enhances the
performance of a communication system was also brought into this particular series of
standards. The hybrid ARQ, which if time permits, we will discuss at some point, not
only does automatic repeat transmission, but it also has a mechanism to adapt every
repeated transmission based on the previous link that means, it could change the data rate

42
in the next transmission or it could save the previous samples of the data, and could
combine together in order to improve the performance or reduce the number of ARQ
transmissions.

Link adaptations are also great mechanisms, which were brought into the system, which
could be used in order to cancel or take care of the fluctuations of the wireless channel
links. We will discuss about the fluctuations of the wireless channel links at some point
of time. Now, while these were going on, the second generation system also evolved, and
there the link adaptation methods were also brought into play. So, it is not as we have
discussed earlier, that is not necessary that when a new standard and new methods come
in the previous generation standard stands still, and does no improvement. So, what we
see is that as new technology improves, the previous version also keeps on becoming
better and better and better.

The capacity improvement was brought into by use of multiple antennas. So, again at a
later time, we will discuss about the multiple antennas. So, what happens essentially in
multiple antennas primarily two important gains come in, though there are many more
gains that come in at this level, we just say that by means of having multiple antennas,
we, in turn increase the effective aperture of the system in a virtual sense. What does this
do? Essentially, it captures a larger amount of energy, and when you have a larger
amount of energy, your signal to noise ratio becomes better, and hence it improves the
capacity of the system.

The other way multiple antenna performs more than a single antenna system is that when
there are multiple links available, then usually by virtue of the propagation mechanism
the link conditions on the two different spatial antennas are not necessarily same. So,
there is a lot of de-correlation, which is present. And this is exploited in order to make
better performing systems in terms of error probability. So, when we use the multiple
antennas as a diversity mechanism, the error probability improves.

Then, there were mechanisms of multi-user scheduling, which were also brought into
play. So, by means of multi-user scheduling, we will again a get an opportunity to see
this what is meant is that, in earlier systems multi-user scheduling was there, but it was
kind of a fixed process. For example, in time division multiple access, you would assign
users in a round-robin fashion that means, the 1st user, then the 2nd user, then the 3rd

43
user and so on, and again it repeats the entire cycle from 1st user, 2nd user, 3rd user, and
so on and so forth.

In case of frequency division multiple access, you allocate different frequencies to

different users and so on and so forth. But, here what happens is the data was one of the
important traffic. And the basic nature of data is that it is bursty that means, that there is
a sudden requirement of data, and the requirement time is not known a priori. So, there is
a randomness in demand of a link.

Whereas, on the other hand, there is randomness in the fluctuation of the link conditions;
so, what this multi-user scheduling does, is it takes inputs from multiple users
simultaneously, compares the link conditions as well as takes a look at the data rate
requirements and does a mapping, so that the sum rate is maximized. We will again get
an opportunity later on to look into the details of such mechanisms, which are again
extended further in the new generation communication systems.

(Refer Slide Time: 09:47)

In 3G, as we have said earlier, there are multi-carrier modes as well as there is the direct
spectrum mode, and there is the TDD mode. So, there are multiple modes and we will
not discuss the details of this, but again there are different forms, which existed
simultaneously. And in these modes, they were the chip rates, which is essentially

44
needed to describe the system so around 3.8 mega chips per second is one of the
important parameters, which define the 3rd generation systems.

(Refer Slide Time: 10:20)

The 3rd generation systems were drastically different than the previous generation
system; in the form that the channel bandwidth was much larger than the previous
generation system. In the GSM, it was 200 kilohertz allocated to one user, whereas in 3G
5 megahertz channel bandwidth was available. Duplexing mode as said earlier, supports
FDD and TDD. Direct sequence spread spectrum was possible. Chip rate as just
mentioned is 3.84 megahertz. Frame length is 10 milliseconds. And slot lengths are 15
slots per frame. Modulation QPSK and BPSK later on things were improved to 16-QAM.

45
(Refer Slide Time: 11:08)

So, the channel coding, it supported convolutional code, turbo code as well as no coding
depending upon the link condition. Spreading factors were variable from 4 to 256, and
five 4 to 512. So, as you increase the spreading factor, your effective data rate decreases
and as you decrease the spreading factor, your data rate increases right. So, when the link
conditions are good, or when there is interference is less, then one can think of using a
smaller spreading factor, thereby increasing the data rate.

Whereas, in adverse situation, when there is heavy amount of interference, or when the
link conditions are really bad, then larger spreading factors could be used, and as can be
clearly seen from the specification the uplink and downlink spreading factors were
different because of several technical reasons. So, there were different sequences that
were available for use while spreading these symbols, and the different symbol rates
were also possible to implement.

46
(Refer Slide Time: 12:12)

So, if we compare between WCDMA and IS-95, which is also a CDMA technique, and it
was an earlier generation system what we find is that, the bandwidth increased from 1.25
megahertz to 5 megahertz, accordingly chip rate has also increased, and power control
has also changed between both the systems. And then if we look at the radio resource
management method, so in the IS-95 it was since only for speech networks that was not
much necessary, whereas WCDMA which was also going to support data, it was
important to have radio resource management methods. So, it was introduced in such
systems.

Packet data scheduling as has been mentioned before, scheduling is an important part,
whenever you have packet data. So, packet data scheduling came into play where
whereby you could schedule the packets and different times, whereas in the previous
system it was circuits-switched calls, and the time slots available you could use them for
transmitting data. Transmit diversity was supported in the new system, whereas it was
not supported in the previous generation system.

47
(Refer Slide Time: 13:22)

Then we get into the other important technology that is this WCDMA and GSM, which
is more popular at least in this part of the world. The bandwidth comparison we have
said before is directly available. The other important change, which happened from GSM
to WCDMA is that the frequency reuse factor. So, in GSM systems, which use the TDM,
FDM kind of an approach. There, two neighboring base stations were allocated different
center frequencies or different bands of operation. This was simply because in order to
reduce the interference. So, the concept of frequency reuse came in, because without
frequency reuse, you cannot support a huge number of users.

So, what is done in such systems is, with the distance of a certain factor n counted in
terms of number of consecutive cells or consecutive base stations. The frequency of one
base station is used in another base station, which is at a certain distance from one of the
base stations, whereas neighboring base stations would use different carrier frequencies.
So, as given over there that the reuse factor was varying between 1 to 18, it is possible in
GSM.

So, as you increase the reuse factor, the interference term decreases. This gives rise to
better signal to noise ratio or better link quality, whereas since you are using the
frequency less often, so the overall capacity supported by such networks was limited.
Whereas, when you moved to WCDMA system, the frequency reuse factor was one. So,

48
it could be a natural question that how come it performs well, even if there is frequency
use factor of one.

The main idea is, the use of codes, which were designed in such a manner that they could
cancel the co-channel interference, so that one could get back to use the same frequency
amongst the neighboring base stations. By allocating proper codes to users, and by using
mechanisms of canceling interference a frequency reuse factor of one was feasible,
thereby allowing a larger capacity to be deployed in the system by the 3rd generation or
WCDMA systems.

The quality control was possible in WCDMA, by means of dynamic radio resource
management. Whereas in GSM, primarily it had to be a prior frequency reuse plan, a
location wise deployment of base stations, so there is to be a lot of planning beforehand,
whereas in WCDMA systems it could do a dynamic resource management, thereby
reducing amount of effort that required in the network planning.

However, in GSM systems or in the advanced version, there was possibility to do

dynamic channel allocation also. So, the dynamic channel allocation would help in
accepting the change in capacity. For example, if there are a lot of cells next to each
other, whereas you have allocated a predefined set of bands and frequencies to each of
these cells. But, the user distribution has changed from the time you have planned the
network.

So, then suppose most of the users have gathered in one of the cell for a situation let us
say a particular sporting event or there could be some particular situation happening, let
us say a political meeting or some kind of a situation. So, there a huge crowd would
gather in one cell, whereas there would be lesser number of crowds in the other cells.

So, whereas in the neighboring cells, you need to support lesser number of calls, but in
the desired cell that is a denser cell, you need to support more number of calls, or support
more traffic. So, there was a concept of frequency borrowing by means of which you
could borrow frequencies from the neighboring cells, and allocate for a certain duration
of time. And, once the traffic has dispersed, and it has changed over you could again give
back the borrowed frequencies to their original base station. So, there were some

49
improvements that were brought into the system whereas, in WCDMA it was already
implicit inherent into the system from the basic design itself.

In terms of frequency diversity, GSM, there is frequency hopping technique that means,
during a call the slot that is allocated to a user, jumps over different frequencies. Now,
you may know or we will discuss at some point that the wireless channel is such that the
signals keep on fluctuating, and there is a certain rate of fluctuation. So, if the user is
moving slowly or there is less Doppler, then once a signal is in fading condition, it would
remain in that condition. Whereas, if the channel allocated to the user would hop from
one frequency to another frequency, then on an average the user may experience a better
channel condition. So, this is one mechanism of frequency hopping, which is used in
GSM in order to provide a better link condition, which averages out the fading effect.

Whereas, in WCDMA, the multipath diversity, so whenever you have multipath in other
words you have a frequency selective channel generally that is the case. So, one can use
rake receivers, through which the rake fingers can collect the signal power from the
different multi-paths, combine them together, thereby achieving multipath diversity,
which can also be viewed in another way of collecting energies from the different
frequency bands and combining them together, so thereby it combines the frequency
diversity and enhances the signal strength, whereas in the other one it averages out the
signal strength. So, they could be different algorithms, which would run, while you
combine the signals over the different bands.

In case of packet data, packet scheduling as has been mentioned is already part of
WCDMA, whereas in the previous system, it was slot based GPRS, so GPRS came in
when data was supported. So, within slots which was allocated for voice, you could give
data. And when GPRS and edge came in, you could accumulate a larger number of slots
dynamically, and you could allocate to users thereby providing a variable data rate.

50
(Refer Slide Time: 20:08)

So, roughly one way of comparing GSM and CDMA is that this is a typical frame
structure of GSM.

(Refer Slide Time: 20:19)

And what why one would see is that in large cells the GSM symbol duration would span
around 1.1 kilometers taking into account the speed of electromagnetic wave
propagation. And a path difference of 5 kilometers would account for 5 symbol inter
symbol interference, ISI. So, MLSE equalizer is required, and MLSE equalizer the
complexity grows exponentially. Whereas, in WCDMA systems, although there is larger

51
ISI coming into play, but by virtue of using rake receivers, you can handle things to a
certain rate. So, the complexity would go grow linearly in such systems.

(Refer Slide Time: 21:02)

So, then after reviewing the 2nd and 3rd generation system, we move towards the next
generation or the 4G systems, and as per ITU this is termed as IMT advanced. So, IMT
we have described before, it stands for International Mobile Telephony
Telecommunications. So, in that the ITU-R, which is a recommendation from ITU. And
the report number M dot 1645 describes the framework and overall objectives of future
developments of IMT-2000, that is 3G, and systems beyond 3G. So, if you have to look
at IMT-Advanced, you have to start from the ITU-R M 1645 document, which provides
a lot of information about such systems.

52
(Refer Slide Time: 21:54)

So, in this particular document that means, ITU-R M 1645, there is an illustration of the
capabilities of IMT-2000 and systems beyond IMT-2000. So, this diagram has been well
labeled, it has been taken directly from that particular document. So, what we see on the
X-axis or the horizontal axis, there is the peak useful data rate given in Mbps, whereas
on the Y-axis we see the mobility. So, we see mobility becoming an important factor.
And it has been described, when we are discussing earlier in terms of requirements. So,
what we see is that IMT-2000 is designed to support high mobility situations, and
whereas the data rate is not really that high, few Mbps.

And the enhancement as we can see over here, in this particular arrow, as we can see
here; so this particular enhancement is indicating the development of IMT-2000 or 3G
towards advanced systems. So, amongst the various things it requires the data rate
support to be increased while the mobility support remains intact. However, as you can
see described by this particular dashed line is that at very high mobility, the maximum
data rate supported is require the requirement is lesser compared to the maximum data
rate supported at lower mobility conditions or pedestrian speeds.

Now, this comes because of the effects that mobility brings into play. So, depending
upon how we go we will plan a short session on the effect of Doppler, on the error
performance. So, usually what happens is as your Doppler increases or as your mobility
increases, the Doppler frequency increases. So, as your Doppler frequency increases,

53
usually there are many effects amongst which the frame error rate increases. So, you
would like to have specific numbers defining certain systems, and which is possible if a
good model and understanding of the propagation effects are available.

Beyond those systems, there was also expectation of newer schemes, which would have
even higher mobility even at high mobility, it would support higher data rates. And this
particular diagram as you can see is very commonly and popularly referred to as the
VAN diagram, it looks like a VAN. And this has been clearly explained over here the
dashed line indicates that the exact data rates associated with the systems beyond IMT-
2000 not yet determined, so when this particular document was made that was around
2003 right. So, these numbers were yet to be determined, but yes the numbers were
something around these and clearly at different mobility conditions different data rates
were designed to be supported.

(Refer Slide Time: 24:57)

So, IMT-Advanced as we are discussing the recommendation document M dot 2134,

talks about the requirements related to the technical performance of IMT-Advanced radio
interface. So, the International Mobile Telecommunication-Advanced or IMT-Advanced
systems are the ones, which is basically the 4th generation communication system and
which we are experiencing right now.

54
So, what it says is that mobile systems that include new capabilities of IMT that go
beyond IMT-2000. So, there is an development in terms of IMT genealogy that means,
IMT systems, IMT-2000, IMT-Advanced and then you have IMT-2020, so whatever is
there before, there is usually a specification, which goes beyond that and there is a
reference to the previous systems.

So, as has been mentioned that IMT-Advanced system, it supports all mobility
conditions, a wide range of data rates, high-quality multimedia applications, worldwide
roaming. So, you may recall that at some point when GSM systems were discussed, it
was talking about roaming in Europe, but now things have moved beyond to worldwide
roaming. Peak data rates of 100 Mbps for high-mobility, and 1 Gbps for low-mobility.
So, this is the top level requirements for IMT-Advanced or 4G. And then we will see that
how does 4G has performed, when things finally got designed and deployed.

(Refer Slide Time: 26:33)

So, there are minimum set of requirements. So, the intent of these requirements have
taken in verbatim from the document is to ensure that IMT-Advanced technologies are
able to fulfill the objectives of IMT-Advanced, so IMT-Advanced is the particular
standard.

And these are the different technologies as we had seen in when 3G was discussed there
is proposal of technologies, so which should meet the requirements. And minimum

55
requirements essentially mean, the minimum set of performance, but this does not
restrict the new technologies to go beyond the minimum performance. And generally that
has been the case, and as we shall see that the numbers which these technologies meet
are quite and much more than the numbers, which are usually prescribed by the
requirements of the IMT-Advanced systems.

(Refer Slide Time: 27:22)

And then when we compare such systems, we need to look at a few definitions amongst
the few definitions one of them is the cell spectral efficiency. So, this is a very important
term, which comes into play when we discuss such system.


i 1
i

T ..M

So, I think it is important that we see it. If x i x sub i denote the number of correctly
received bits by user i in downlink or from user i in uplink direction in a system
comprising of N users.

So, there is a cell, cell is a base station and there are N users within that base station. And
x i denotes the number of correctly received bits ok. And there are M cells and the
channel bandwidth is w w hertz, and the T is the time over which the data bits have been

56
received. So, cell spectral efficiency is defined as the sum of the bits divided by the time.
So, bits per second by the bandwidth, so bits per second per hertz, and the number of
cells. So, it is basically bits per second per hertz per cell.

So, for every cell, so you added over the N number of users in the system. So, they
usually specify in the test conditions that how many users to be taken during the test, and
how many users supported by the system. So, the system might support a certain number
less say 100 or 1000, so that has to be taken into account over here. So, the unit is bits
per second per hertz per cell, which is a very important metric, when comparing the
performance of such systems.

(Refer Slide Time: 29:00)

So, if we look at this the cell spectral efficiency, as has been defined for different test
environments, test environments like indoor test environments. And these test
environments has specified over here are described again in the ITU report M 2135. So,
if you take a look at M 2135, detailed description about simulating these conditions have
been well explained in that particular document.

So, what it says is that bits per second that is the time per hertz that is the w, and cell is
M is given over here, so for indoor it is 3 and for high speed condition it is 1.1 and all
numbers in between. In uplink, there is again a different set of numbers, and these have
been defined for different antenna configurations. So, with the definition of cell spectral

57
efficiency and the numbers, what we now have to see whether the IMT-Advanced
systems meet the specifications. So, with this base and background, we should be able to
discuss the IMT-2020 or IMT or five 5th generation wireless communication systems in
the upcoming lectures.

Thank you.

58
 Evolution of Air Interface Towards 5G
Prof. Suvra Sekhar Das
G. S. Sanyal School of Telecommunications
Indian Institute of Technology, Kharagpur

Lecture – 04
Evolution of Wireless Communication Standards from 2G to 5G (Part – 3)

Welcome to the lectures on Evolution of Wireless Communication Towards 5G or

Evolution of Air Interface Towards 5G. So, far we have been seeing the technical
requirements for 2G, 3G, some of their solutions. And in the previous lecture, we have
also started looking at IMT-Advanced that is 4G.

And we have reached the point, where we described the cell spectral efficiency, and have
also described the met parametric values, which are the requirements. And then we said
that now onwards, we will move forward and discuss about the performance of such
systems. So, we will continue with the IMT-Advanced in this particular lecture, and then
we will move forward to IMT-2020.

(Refer Slide Time: 01:07)

So, in this particular slide that we have we have talked about the cell spectral efficiency,
and these numbers that are pointed out over here are basically the downlink cell spectral
efficiency as described in bits per second per hertz of bandwidth per unit of cell. And this
is the same thing, however the requirement is given for the uplink. As you can clearly

59
see, there is distinction between the downlink and uplink for several system
configuration related issues.

On the left hand side as we had said, there are different propagation environments which
have been classified from indoor to micro cellular to the base coverage urban area, this is
rather the urban area, which is more important, and high mobility scenarios. And as said
earlier these were defined for different configurations of antennas, we will see the
description of these at a later time.

(Refer Slide Time: 02:19)

So, the next important metric that we are supposed to see is the peak spectral efficiency.
In the peak spectral efficiency, it is defined as the highest theoretical data rate
normalized by the bandwidth that means, bits per second per hertz, which is the received
bits assuming error-free condition assignable to a single mobile station. When all
available resources for the corresponding link direction are utilized, that is excluding
radio resources that are used for physical layer synchronization and all those things.

So, effectively what it means, what this description means is that if there is only one user
equipment present in the system, as has been described over here, single mobile station
and all resources diverted to this. However, you are leaving out the headers or additional
pilots other things, so that is the reference signal or pilots and guard bands, which are
used or necessary in order to make the communication feasible or realizable.

60
So, in this sense this is the maximum that can be achieved, so this is another important
parameter. Usually, you will find that when they say the data rate, usually if nothing is
mentioned people talk about the peak data rate, because that is usually an attractive term
whereas, what is more important are some other terms, which will come and see like
average spectral efficiency. And also the other term, which we had seen in the previous
slide that is the per cell that means, overall in an in a cell what is the spectral efficiency.

So, when we look at the downlink peak spectral efficiency that is 15 bits per second per
hertz, so this is very very high number. In order to find out that if there was only one user
in the system, then and you are mentioned about the bandwidth say there is 20 megahertz
of bandwidth. So, if I multiply 15 by 20 megahertz, then we are going to get the
maximum bits per second that is possible, then 15 multiplied by 20 into 10 to the power
of 6 hertz, hertz as cancels out, rest of it is the maximum downlink spectral efficiency.
Spectral efficiency is the data rate per unit hertz of bandwidth. Similarly, in the uplink,
the number is given over here, which is 6.75 as the required peak spectral efficiency, and
again antenna configurations have been mentioned.

(Refer Slide Time: 04:55)

The bandwidth is again obviously a very important parameter. So, scalable bandwidth is
available or is the availability or the ability of the candidate radio interface technology to
operate with different bandwidth allocation. So, what it means is that the scalable
bandwidth is supported by the system, which in other words means that the system

61
should be able to access lower bandwidth as well as larger bandwidth as per necessity or
as per allocation. So, systems or the equipment should be capable of accessing different
bandwidths as per allocation or as per the situation or controlled by the access point or
the base station or the entire network.

Another important term is the cell edge user spectral efficiency, now this is a very very
important metric so, although the peak spectral efficiency is very very attractive. But, as
we see through the description that the normalized user throughput is defined as the
average user throughput, ok, the number of correctly received bits by user, over a certain
period of time, as was discussed earlier, divided by the channel bandwidth and is
measured in bits per second per hertz. So, this part of the definition is as per the
definition of spectral efficiency.

However, the cell edge user spectral efficiency is defined as the 5 percent of the
cumulative distribution of the normalized user throughput. So, 5 percent means, the 5
percentile point. So, if we collect the spectral efficiency over the entire cell that means,
that each point in the cell, so for example I mean if we take a cell, ok, so let us say this is
an area of a cell as per classical hexagonal layout although things are different nowadays.

So, in this particular setup, if we are taking users in different locations, all right, and if
suppose the base station is located in the center, so then the user which is close to the
base station is going to experience a better SINR compared to the user at the cell edge
right. So, if we collect the spectral efficiencies of all the points, and we plot the
cumulative distribution function, then the 5 percentile points performance is basically the
cell edge spectral efficiency. So, this point is the 5 percent point. So, this is how we
define the cell edge spectral efficiency, again we will see these in more details when we
see the performance evaluation criteria and other things, there we will try to look at how
these things are actually done, ok.

62
(Refer Slide Time: 07:59)

i
i 
Ti .

So, moving forward, so in this again if we define x sub i, as the number of correctly
received bits of user i. And T i the active session time, because we had divided by time
for user i, and w the bandwidth of the channel, then the normalized user throughput is x i
that is number of bits received correctly divided by the time and the bandwidth.

So, earlier when we define the cell spectral efficiency, there we had a summation over
here. So, in that case we had a summation over here, over the number of users right. So,
this is not required over here. You have to only take for a user and i-th user so you have
to take over all possible users in the entire thing and in entire area plot the CDF, and then
take the 5 percentile point right. So, this is how you usually get it. And again if you look
at the requirements that have been defined, so what you see is that in indoor condition in
downlink it is 0.1 bits per second per hertz, where is an uplink, it is 0.07. As usual the
downlink is higher than the uplink. And this entire range covers the different propagation
environments that have been described in M 2135.

Now, what this essentially says in some other situations, this is also described as the
outage spectral efficiency. 5 percentile outage spectral efficiency that means 95 percent
of the time, the spectral efficiency in the downlink direction in indoor condition would

63
be above this particular number. So, this is kind of the bottom line performance of the
system. We had seen the peak; we had also seen the cell spectral efficiency, so these are
different metrics, which together describe the performance of such a system. And again
these are the requirements that are necessary to be satisfied in order to be called a IMT-
Advanced or a 4G system.

(Refer Slide Time: 10:09)

So, then there are some more terms that are again, which come up when we discuss such
technologies, the control plane latency. I considered it important that we go through
these at least once, because whenever you will be going through such documents, you
will be coming across control plane latency, user plane latency. And it is important that
we read at least for one situation, so that we do not have to get into confusion ever again.

So, here control plane also referred to as the C-plane latency is typically measured as
transmission time from different connection modes that is from idle to active state ok. A
transition time excluding downlink paging delay and wire-line network signaling delay
of less than 100 millisecond shall be achievable from idle state to active state in such a
way that user plane is established. So, this clearly defines what is known as the control
plane latency. Whenever requirements of control plane latency comes up, you can refer
to these particular definitions, which are there in the ITU documents.

64
The other one is the user plane latency. The user plane latency also known as the
transport delay is defined as the one-way transmit time between the SDU packet being
available at the IP layer in the user terminal or the base station. So, in whatever direction
we are discussing.

So, if it is the uplink, then it is the user terminal; if it is the downlink, it is the base
station. And the availability of this packet that is the protocol data unit, PDU, at the IP
layer in the base station. So, when it is the terminal, it is the base station. When is the
base station, it is the terminal that means, in the uplink direction, the packet from the IP
layer of the user to the IP layer of the base station. And in the reverse direction from the
IP layer to the base station to the IP layer of the user terminal. So, this is defined as the
user plane latency.

So, in IMT-Advanced systems the user plane latency of less than 10 milliseconds in
unloaded conditions that is the target. So, unloaded condition means a single user with a
single data stream for small IP packets like 0 byte payload and so on and so forth. So,
these are idealistic conditions, so these set the limit for performance. So, when one
specifies or one evaluates the performance, one has to meet the numbers. And the test
has to be done as per the description as given over here, and detailed in the ITU
documents, which have been referred in this lecture as well as in the earlier lectures. So,
it is very important to be aware of this, because whenever performance evaluation has to
be done for such things one has to know exactly where to start the measurement, and
where to end the measurement.

65
(Refer Slide Time: 13:05)

Now, comes the mobility we had seen the van diagram so called not the venn diagram.
So, here there is definition of mobility, so stationary conditions are of course no mobility
that is 0. Pedestrian conditions are when people are walking kind of situation where it is
up to 10 kilometers per hour, so like 3, 5, 7. I mean all kinds of values are good enough.
And vehicular traffic is like 10 to 120 kilometers per hour again details are described in
the document M 2135. And high-speed vehicular is from 120 to 350.

So, I mean high speed vehicular usually is associated as per these documents in the rural
environment, but that is specific to one particular evaluation scenario, whereas there
could be other rural scenarios, where it is actually reverse. So, I mean rather than
classifying as rural and urban, which is mainly to do with the multipath environment.
Separately specifying mobility as defined over here is makes things clearer.

So, for example one can have urban while a high mobility, so that could be possible I
mean and it may not be high mobility, but it could be like vehicular speeds, where you
nowadays have long flyovers running across for maybe 5 to 10 kilometers. So, were
probably speeds within this range is highly possible, so I mean it is important that you
specify the mobility as well as you specify the multipath propagation environment. And
you can club them together to make the description of one complete specific
environment.

66
(Refer Slide Time: 14:49)

So, in this particular slide, what we see is the traffic channel link rates ok. So, what we
see over here is the mobility class is supported if the traffic channel link data rate,
normalized by the bandwidth, on uplink is as shown in particular table-4 is in the specific
document that is with which we are referring to. So, what it says is that in indoor
conditions, it is a stationary or mobility, so the test condition says 10 kilometers per
hour. So, there this spectral efficiency of 1 bits per second per hertz should be supported.

Now, if this is supported, then we know that this particular mobility class is supported. In
high speed, when speed of 350 kilometers per hour is used for developing the test
scenario, there the link spectral efficiency should be 0.25. So, if this is achievable, then
we know that the high speed mobility case is satisfied, so that is all that is described in
this particular text.

67
(Refer Slide Time: 15:56)

Again handover is a very important thing, when it comes to mobility, handover is again
naturally comes into play. So, there the intra-frequency handover is defined as around
27.5 milliseconds, and the inter-frequency handover is defined within the spectrum and
is 40 and between spectrum bands is 60. So, again these are like numbers, which have to
be met and these specific situations have to be tested for.

So, if the protocol, and the framework, and RAN architecture supports these numbers
which are ITU specified numbers, then you know that case it is an IMT system. So, the
importance of discussing these things are again that when you move on to IMT-2020.
Similar, such specifications would come in, the numbers are going to change, along with
it additional requirements would also come into play.

68
(Refer Slide Time: 16:51)

So, now comes the next important thing. So, when we discussed about these 4G systems
in our earlier discussion, we had said that this is one such system, which does not
provision for circuit switched voice, which is which was still available in the earlier
generation. Like the 3G had a circuit switch voice as well as a packet switched data
possibility, but here the entire thing is packet switched data.

So, all real time traffic are also available as packet data, including voice. Now, although
it might appear pretty normal today, but when we look at the transition earlier it was
voice, which was circuit switched. And, there was fixed slots at which things were
getting transmitted whereas, here there is randomness or a stochastic nature of
scheduling which comes into play, which make things very very different.

Further the mobility is also a big factor, which comes into play over here. So, when you
combine the mobility which brings in a huge amount of uncertainty because, of the
Doppler effects along with the stochastic nature of packet scheduling, then supporting
real time traffic such as voice or VoIP is a critical challenge. IMT-Advanced has
provisions or if the technology satisfies the certain numbers as displayed over here, then
it can support the specific VoIP activity.

So, there as described over here, VoIP capacity was derived assuming 12.2 kilobit codec
with 50 percent activity factor. So, there is a detailed model, which describes how you

69
generate VoIP traffic in order to be tested for a particular operating environment ok, such
that the percentage of users in outage is less than 2 percent ok, so that means, 98 percent
of users would be satisfied right. So, how would you define whether a user is satisfied or
not? So, there comes a user is defined to have experienced a voice outage if less than 98
percent of the VoIP packets have been delivered successfully or in other words if 98
percent of the packets are delivered successfully, then you would say that user is
satisfied, and that to within a delay bound of 50 milliseconds right.

So, these are again defined for certain set of antenna configurations. So, what it says is
that under indoor configuration, 50 VoIP users per sector, per megahertz to be satisfied
right, where is in high speed again the same thing comes up 30 there is a huge drastic
difference, again because of the high mobility condition. 30 VoIP users, active VoIP
users, per sector, per megahertz required to be satisfied. So, it clearly brings out the
association of mobility with data rate, mobility with number of VoIP users that can be
supported in a sector. Now, if this is possible, then you are then the technology under test
would be classified as IMT-Advanced or 4G. And fortunately most of the technology
submitted satisfied these things quite easily. Especially, if we look at LTE and LTE-
Advanced, they also satisfy these numbers quite comfortably.

(Refer Slide Time: 20:32)

So, with all these requirements in the next particular slide as we have over here, it is a
summary of the methods that essentially help achieve these different massive

70
requirements. So, one of the primary changeover is basically the OFDM system, which
will find opportunity to discuss, because as we go to 5G there is a variation of OFDM,
which comes in this remains as the base layer. Higher order modulation. So, OFDM
essentially is an overlapping waveform, whereby you get a huge amount of spectral
efficiency.

As we go to higher order modulation, your spectral efficiency increases. Then there is

MAC optimization in terms of packet scheduling, radio resource allocation, which
further improves the spectral efficiency. Turbo encoder and decoder improves the
reliability. MIMO facilities increase the spectral efficiency N times, so it clearly says N
times that oversee so link. So, all these help in increasing the spectral efficiency along
with of course link adaptation and HARQ that is hybrid ARQ. Whereas, carrier
aggregation provides a huge improvement in the aggregate data rate that is possible. So,
when we move on to 5G, quite a few of these things move forward, so MIMO carries on,
but there are more enhancements, then these carry on the higher order modulations
variation of OFDM carry on.

So, the carrier aggregation carries on, and radio resource allocation again newer methods
come into play. So, it is important that we understand the baseline structures that are
available in 4G, so that it is easier to move on to the translation or the transition that
happens, when one moves from 4G to 5G. So, we will set the background or set up the
foundation based on which, we will discuss the enhancements that are present in the 5th
generation air interface.

71
(Refer Slide Time: 22:33)

So, as we see the 3GPP is the 3rd generation partnership project, where LTE or Release
8, which is kind of near to 4G system. And in this particular slide, we have some of the
important parameters. And what we will see very soon is that even LTE, which is not
LTE-Advanced meets quite a few of the IMT-Advanced requirements ok. And what we
will see later is the LTE-Advanced and meets it meets them comfortably.

So, in LTE, we find that there are various scalable bandwidths, which are supportable.
And if you remember, when we discussed earlier that flexible or scalable bandwidth is
one of the important things that is required to be supported. The minimum transmit time
interval is 1 millisecond, this is an important number, which we will see when we move
to the 5th generation system.

Sub-carrier spacing for OFDM is 15 kilohertz, again we will see a variation when we
move to the 5th generation system. The cyclic prefix length when we discuss OFDM in
details, these things will become clearer two possible values are available, the short and
the long. And we will see why these are used, so 4.7 microsecond and 16.7
microseconds. So, two options are available, in order to take care of different
propagation conditions. Modulation as indicated in the previous slide QPSK, 16-QAM
and 64-QAM are allowed.

72
Spatial multiplexing or MIMO as we see a single layer MIMO for uplink per user is
supported in LTE, and up to 4 layers for downlink per UE, UE is the User Equipment
and may MU-MIMO that is multi-user MIMO is supported for both uplink and
downlink. So, these are some of the important technical parameters you can say, which
can be used to describe the LTE air interface.

(Refer Slide Time: 24:43)

So, in LTE itself, the user equipment have several categories as has been in the title of
this particular slide. So, there are category 1, 2, 3, 4, and 5, and what differentiates them
is the peak data rate. So, what you can see is that as you increase the number, which
indexes the category. It basically indicates that the device can support higher and higher
data rate ok. In uplink, the similar is the picture, but the data rate in uplink is obviously
different compared to that in the downlink, which has been consistent with all our
previous descriptions.

The RF bandwidth 20 megahertz is supported. Now, in downlink what we see the

modulation that is supported in downlink for category 1 to 4, you have all these schemes
which are supported, where is an uplink only two modulation formats are supported ok.
Whereas, if you go to category five, what you find is all the schemes are supported in
both uplink and downlink. So, what it essentially means is that when we take up a higher
indexed category phone or a smart-phone or a device, it can simply support higher data
rate by virtue of providing higher modulation order.

73
And as we can see the 4 cross 4 MIMO is not supported up to four categories, but in the
5th category it is supported alright. So, what essentially we have is the 5th category
equipment is much more complex in terms of signal processing, but at the same time it
provides a higher data rate. So, if you are looking for very high data rate, we should go
for higher category user equipment. And if you are satisfied with the low data rate, then
one can go for a lower category, it depends upon the specific operating requirements of
the particular device.

(Refer Slide Time: 26:44)

So, LTE Release 10, which is beyond LTE, it is basically LTE Release 10 and beyond,
which is the LTE-Advanced, which is rather categorized as IMT-Advanced. So, what we
see is that these specifications are described in the 36 series of documents of the 3GPP
organization. So, if you go to the internet and look up the 3GPP website, then there are
technical specifications, which describe the different technology that they have released.

So, if we are looking for LTE series of documents, we need to take up the 36 dot
something something which will be describing different set of requirements, which we
will probably see in one of the slides. So, basically if you look up the 36 series of
documents you are going to get the technological description of LTE and beyond, and if
you evaluate the performance, what we will find is that LTE-Advanced.

74
The peak data rate is 1 Gbps in downlink and 500 Mbps in uplink ok, IMT-Advanced
also points out the similar thing. And of course, here what you can see is that 10 Mbps
for high mobility and 1 Gbps for so this has sorry this is 100 Mbps, which was described
earlier. So, peak spectral efficiency what you can see is that in downlink there is 15 bits
per second per hertz in case of LTE, which satisfies the requirements of IMT-Advanced.
So, yeah, but LTE-Advanced gives you 30 bits per second per hertz, so which is much
more than the minimum requirements are specified by ITU.

Even for uplink what we clearly see is that IMT-Advanced requires a 6.75 bits per
second per hertz, which we had seen earlier whereas, LTE-Advanced supports 15 bits per
second per hertz. So, what we clearly see is that LTE-Advanced quite easily satisfies the
different requirements of IMT-Advanced. And hence it is the actual 4G system, whereas
the previous one that is the release 8 and onwards releases 9, they were kind of pre 4G or
3.9G as people have been describing. So, we stop this particular discussion here, we will
move forward with more description about IMT-Advanced as well as IMT-2020 in the
next lecture.

Thank you.

75
 Evolution of Air Interface Towards 5G
Prof. Suvra Sekhar Das
G. S. Sanyal School of Telecommunications
Indian Institute of Technology, Kharagpur

Lecture – 05
Evolution of Wireless Communication Standards from 2G to 5G (Part – 4)

(Refer Slide Time: 00:18)

Welcome to the next lecture on evolution of air interface towards 5G. In the previous
lecture we have seen the different requirements for 4G and have also seen some of the
capabilities by which it could achieve the target. And what we have summarized in this
particular slide is the requirement from ITU which is given under the heading of IMT-
Advanced and on the left the LTE-Advanced which is the 4G radio interface technology.
And it is as can be seen and was discussed in the previous lecture that it meets the
requirements of IMT-Advanced and hence it is a 4G technology.

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(Refer Slide Time: 01:01)

So, in this particular slide now what we have is the cell capacity that is bits per second
per hertz per cell which we have described earlier and I have compared them for IMT-
Advanced and LTE-Advanced.

So, what we clearly see is that the requirements are quite nicely met and are actually
exceeded in this case and how these have been evaluated are actually described in these
series of documents where we have said earlier that M-2135 describes the scenario. And
in this the urban scenario has been taken for these set of results and the 36 series of
documents have been used to describe the LTE-Advanced systems and the case 1 for 25
series document has been used in this particular one. What we see over here is that factor
of 1.4 to 1.6 is the increase in the bits per second per hertz per cell as we go from LTE to
LTE-Advanced and they are able to meet the IMT-Advanced requirements.

The cell edge throughput which again we have described in the previous lecture which
presents or which describes the bits per second per hertz per cell per user or which could
also be taken as the 5 percentile point of the area spectral efficiency. So, there we see
again the numbers which are exceeding the requirement, hence this particular technology
is an IMT-Advanced compliant technology.

So, there are many such results which are available through which it can be seen that
LTE-Advanced meets the IMT-Advanced requirements.

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(Refer Slide Time: 02:56)

So, now we look forward to the technical outline to achieve the LTE-Advanced
requirements. So, for that what we see is that in terms of bandwidth up to 100 megahertz
which comprises of multiple basic frequency blocks or component carriers can be used.

So, this is an enhancement. So, as you increase the bandwidth you can clearly enhance
the data rate. So, this directly contributes to the data rate enhancement. In downlink
OFDMA with component carrier based structure is used and in uplink the DFT spread
OFDM which is used. So, these are again well described in the IMT-Advanced
technology, will also see through them when we are discussing the details of the
waveforms as things move towards 5G.

In MIMO up to 8 layers in downlink for 30 bits per second per hertz is doable. So, 8
layer means 8 spatial streams so that means, simultaneously 8 data streams which
operate on the same time and frequency are accessible in downlink. So, they multiply the
SISO data rate by a factor of N or here it is 8. Further there a UE specific demodulation
reference signal. So, when you have such reference signal then it is possible to use non
codebook based precoding.

Now, codebook based precoding are the ones where you have predefined code books and
you choose the best match of the codebook with respect to the channel conditions.
Whereas, if you use non codebook based; that means, you can derive the code book or

78
the antenna weight vectors which are complex in nature, so, as to match the output signal
from the transmit antenna to the channel in the best possible manner and you can use
them in a multiple ways like whether you go for beam forming or you can go for spatial
multiplexing. So, it is there is provision to do such things.

In a single user, 4 layer MIMO in the uplink is feasible. So, in the downlink it is 8 layer,
in the uplink it is 4 layer allowing it to achieve 15 bits per second per hertz. So, as a
increase of factor of two happens over here from 4 to 8 you can see that the same
increase is applicable in the from the uplink to the downlink. So, these are some of the
specifications or technical parameters by which LTE-Advanced is able to meet the IMT
requirements.

(Refer Slide Time: 05:38)

Another important technical solution which is supported known as the coordinated multi
point transmission and reception. So, in this there is joint processing mode which is
allowed so that means joint transmission, that is the downlink physical shared channel
which carries the data is transmitted from multiple cells with precoding using the
demodulation reference signal among the coordinated cells.

So, here there are different base stations which coordinate amongst themselves and they
can send signals so as to provide the best spectral efficiency to the user. Then there is
dynamic cell selection, also there is coordinated scheduling and beam forming. So, here

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the PDSCH which has been described here is transmitted only from one cell side and
scheduling or beam forming is coordinated from the other cell side.

So, basically from one cell you transmit the data and from the other cells they manage
the interference by knowing or having information about the scheduling information
from the other cell.

(Refer Slide Time: 06:44)

So, pictorially what we can see is that one base station with multiple antennas enabled
and beams formed in different directions. So, they will communicate with the different
users via several such prior procedures which enable the communication and along with
it there could be other base stations nearby and they would be connected. So, there is this
central processing unit, so, that they can send signals to the user equipment especially
those who are towards the edge region which are supposed to get interference from
nearing base stations. So, instead of getting interfered they rather send signals in such a
manner that they exploit the channel properties as well as the architecture of the network
and instead of having a worse condition they rather enhance the users capability and the
experienced quality of service by this mechanism.

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(Refer Slide Time: 07:48)

In the coordinated precoding or beamforming one of the base stations communicates

with the user and the other base stations the coordinate amongst themselves so that they
can choose the precoding weight matrix in such a manner, so that the users experience
minimum interference from co channel transmitting base stations and the weight
matrixes are chosen in such a manner that after post processing at the receiver there is
maximization of SINR or as well as the capacity.

(Refer Slide Time: 08:18)

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So, in coordinated scheduling, these are the time frequency resource grids. So, when they
communicate with each other the base stations they also dynamically choose the resource
block along with the weight vectors that are to be used so that the optimized or
maximized spectral efficiency can be achieved in this manner. So, there is heavy amount
of signaling that undergoes between the base stations, but usually one of them
communicates with one of the units, there are many such details which are there in the in
the IMT-Advanced system rather the LTE-Advanced system and as we progress we will
see the different mechanisms.

(Refer Slide Time: 09:02)

So, let us take a look at the VoIP results we had at an earlier point discussed about the
ITU requirements. So, if you evaluate the performance in one specific case these are the
VoIP capacity of number of users per megahertz per cell that are supported by LTE-
Advanced. So, what we see there is a clear cut exceeding of the requirements of ITU-R
so that means, ITU-R as it was said was the minimum set of requirements and these
numbers clearly show that in different environments in all cases this technology is able
to meet the ITU requirement.

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(Refer Slide Time: 09:46)

So, in this particular picture we try to depict the overall process of how things happen.
So, in this particular image on the top corner what we have is the frequency and time
grid along this axis and this axis represents the channel gain. So, typically in a wireless
channel you have the channel strength fluctuating across the time frequency grid as can
be seen over here. So, this is the channel strength in decibels it is an indicative figure and
this keeps on changing with time.

So, it is the snapshot of the random realization of the channel and you have the
hexagonal cell layout, now this is for evaluation purpose and you have nineteen cell
layout with 57 sectors. So, and you take your desired cell as the one in the center while
you have interference from all other neighboring.

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(Refer Slide Time: 10:43)

And then you have the resource block while each of the resource block sees different
channel conditions.

Now, each user will see such different channel conditions in the desired cell and there
will be heavy interference from all the neighboring cells. The base station communicates
with the user equipments with reference signal. They demand different services
simultaneously, and they send back the channel quality indicator which is a
representation of the kind of links that the users experience. Based on the input that the
base station receives one of the primary activities which is does is link adaptation, and
packet scheduler, we have briefly talked about these things earlier.

So, when this packet scheduling happens, transport block size or dividing the packets
into smaller segments code block segments, CRC all these things are done at the base
station then followed by time domain scheduling, then frequency domain scheduling. By
time domain scheduling what is meant is the packets are differentiated in time domain so
that different requirements can be met for different users and by frequency domain it
takes advantage of the fluctuations along the frequency axis so as to allocate the
appropriate resource block to the appropriate user.

Along with that there is a selection of MIMO mode whether it is beamforming, whether
it is spatial multiplexing, and that to codebook based, or all kinds of decisions are being

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made based on the feedback of channel conditions and accordingly communication
begins.

(Refer Slide Time: 12:33)

So, all this is to ensure that the users’ QoS is satisfied. Then there is HARQ mechanism
we have earlier talked about it that is hybrid automatic repeat request and all these
features are used along with the admission control and QoS management.

So, what it means is that the high level mechanisms of admission control and QoS
management do consider all these events that are happening at the lower layer. So, huge
juggernaut exercise goes on in order to provide the huge data rate or the capabilities that
are provided by LTE-Advanced. So, what we can also see is that when things move
beyond 4G to 5G, such situations are not only going to remain, but going to escalate and
things are going to become more and more complicated in order to meet the newer and
more challenging requirements.

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(Refer Slide Time: 13:34)

So, in this discussion we start our requirements and operating scenario analysis of IMT-
2020 or 5G. So, far we have discussed about the previous generations that is the second
generation, the third generation, the fourth generation, that is IMT-Advanced and now
we are at the doorsteps of talking about the fifth generation given our basic
understanding of what prevails and so that we can compare and see what new things are
going to come up.

So, in this discussion we will look at the requirements of IMT-2020, also traffic
prediction, and the operating scenarios. Now this is a very crucial because when we talk
about the traffic prediction because this is one of the early activities that usually happens.
So, when we have a traffic requirement being projected that will give us an indication of
what is the change that is required to be done. For example, if there is a huge growth in
traffic and we know that there is a certain limited bandwidth that is available. So, given
all the new technologies that get developed, we can more or less predict, given the
bandwidth, what is the maximum spectral efficiency that can be achieved. Now given the
bandwidth and the spectral efficiency you can naturally compute the maximum data rate
that can be achieved.

Now, if this data rate that can be achieved or which is technically feasible is less than the
traffic predicted, the next important thing that you need to look at is higher spectrum or
more bandwidth in order to meet the requirements otherwise the requirements cannot be

86
met. So, the first step is requirement analysis which talks about the requirement, then
also traffic prediction, as well as operating scenario. So, when we discuss operating
scenarios things will be clear. So, together we will find that they describe or put in the
problem or the question that needs to be solved.

So, when this kind of question is well described then we can look at the different
technological solutions which can help us meet the different objectives that have been set
up.

(Refer Slide Time: 16:03)

So, in this we will cover ITU definitions, because as we have done earlier we will also
have a few definitions, and abbreviations, and requirements. So, mainly it will be the
abbreviations which we will be looking at in this particular discussion.

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(Refer Slide Time: 16:21)

And let us begin with the requirements of 5G as has been the topic. So, ITU started off
with a focus group on IMT-2020 in around 2015, and the task was to analyze how
emerging 5G technologies will interact with future network. The study group 13 was
there in the period 2013 to 2016, which prepared a report on the standards gap analysis;
that means, there is a certain amount of requirement, there is a certain thing that the
standard provides. So, how much extra that needs to be done and it provided results in
the 5 areas of the study that is high level networking architecture, what should be there,
end to end QoS framework, emerging network technologies, mobile fronthaul and
backhaul, as well as network softwarization.

So, these this particular document is available in ITU website and just as a side note for
all these parts that we have been discussing, I would urge that you look up the ITU
documents which we have mentioned earlier and they give you pretty precise description
and in fact, we have taken things exactly from those documents because they are uniform
set of documents which we can refer to and which is referred globally.

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(Refer Slide Time: 17:47)

So, the IMT-2020, which is described in the document M-2083, it is the systems and
system components, and related aspects that support to provide far more enhanced
capabilities than those described in IMT recommendation, M-1645. Now what we see is
that M-1645 is framework and overall objectives of future development of IMT-2000
and systems beyond IMT-2000 right. So, beyond IMT-2000 is basically IMT-Advanced.

(Refer Slide Time: 18:27)

So, here we have the ITU M-2083, which is the IMT vision- the framework and overall
objectives of the future developments of IMT-2020 and beyond systems ok.

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(Refer Slide Time: 18:46)

So, we are going to follow primarily this particular document and here as we have been
using the term there is a very clear cut statement that the term IMT-2020 is commonly
referred to as the fifth generation mobile networking or simply 5G. So, this is a very
clear cut statement. So, whenever we use the term 5G we are inherently referring to
IMT-2020 and vice versa. So, basically they are all synonymous terms.

(Refer Slide Time: 19:10)

A brief list of abbreviations. So, more or less because we might encounter them so it is
better to have them very very clear. ICT is pretty well described over here, IMT we have

90
been referring to. IoT is again a very common term so it is internet of things. M2M
indicates Machine to Machine. So, whenever we encounter M2M, what we will mean is
that it is machine to machine communication.

MIMO which we have referred already is well known Multiple-Input Multiple-Output.

QoE is essentially Quality of Experience, QoS is the well known Quality of Service,
RAT is Radio Access Technology, and RLAN is the Radio Local Area Network. There
are many more, but I found them to be pertinent so I have just put them over here.

(Refer Slide Time: 20:02)

So, the document begins with a command and which we would all agree, is that mobile
communications is now intricately tied to the socio-economic fabric of the modern
generation human beings.

So in fact, it is not uncommon to find a lot of emergence of notes. In fact, videos which
describe about the menace this particular system has created, but we are here to discuss
about the technologies which can provide them and we would always desire that this
technology is used in the right sense. But what is true that our everyday life is now
enabled through such communication systems only a piece of warning that we should not
get addicted to such system beyond our needs.

So, the tight coupling between mobile communication systems and socio-economic
trends are expected to continue beyond 2020. 2020 is going to come in near short terms,

91
but probably we are going to get matured and things might work differently, but at least
this trend which has started is going to be present. In fact, it is one of the technologies on
which our modern day life is almost dependent on and it is also foreseen, it also states
that it is also foreseen that there will be more traffic volume. This is one of the
interesting things which we will explore, and more devices, diverse requirements, we
will see all of these things, better quality of user experience so that is to be supported.
Better affordability because with more affordability there is more proliferation and if
there is more proliferation then there is more enabling of different kind of services as
well as administration and many more things and will require an increase in number of
innovative solutions. So, this is a very important for technologists, and researchers
especially students, that as your requirements come up and as they evolve with time, you
have a lot of opportunity to be creative and produce many new solutions.

(Refer Slide Time: 22:15)

Further observations are that the wireless communication applications are expected to
facilitate digital economy which we are already seeing. Further, smart grid, e-health,
intelligent transport systems and traffic control. So, we will see more of the descriptions
and some of them we have already started to see, where is in 5G, we expect a huge
enhancement of these services delivered through 5G networks, so which says that which
would bring requirement beyond what can be addressed in today’s IMT application area.

92
So, that will be clear as we further go into the details that it will be almost obvious that
today’s IMT systems are not capable of providing the new requirements, that is pretty
natural because the design of IMT-Advanced was based upon certain requirements which
were at an earlier time whereas, after using IMT-Advanced we are coming up with new
requirements. So, it is pretty natural that we need a newer solution and earlier solutions
would be limited in meeting these new requirements.

Further, there is a rapid adoption of smart phone and mobile applications. So, it is very
very well known with the huge number of mobile phones that are getting sold every day
and things are becoming cheaper and cheaper and advanced features are coming even in
low cost devices. And the number of devices accessing the network are expected to
increase amongst many other things due to the proliferation of Internet of Things.

So, we will see certain numbers which are really mind boggling when you see the
number of connections and devices that IoT is going to bring in.

(Refer Slide Time: 24:01)

And it also predicts technologies such as beamforming, massive MIMO are aligned with
higher frequencies. So, we will see these things in due course of the course. As we go
down wide contiguous bandwidth as have been discussed is going to enhance delivery of
data. Because if the user can access a huge band then that band can be supported by
various forms which again we will come and see.

93
Reduce cell size, so we will again see at a certain point that amongst the various methods
which have been able to increase or provide an increase in capacity the reduction of cell
size is one of the very important such factors although it is very classical, its one of the
very important factors which can enhance the capacity by a significant factor.

So, from the classical few kilometers of cell radius, today we have situations where cell
radius are down to few meters, and people are talking about cell less coverage
ubiquitous. So, I mean you really don’t form a cell, but you form almost a gel like or a
superfluous kind of a network where they are operating autonomously almost.

(Refer Slide Time: 25:21)

And the objectives of this particular document 2083, is to establish the vision for IMT-
2020 and beyond. So, this is very much pertinent for what we are going to discuss and
the potential user and application trends because these will be the drivers. It will also
discuss the growth in traffic technology trends, and spectrum implications, and it is
expected to provide guidelines on the framework and capabilities for IMT-2020 and
beyond systems.

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(Refer Slide Time: 25:57)

Future IMT systems should support emerging new use cases, requiring very high data
rate. So, we were talking about the scenarios. So, will later on see the details of this and
it is also required to support a large number of connected devices. Now as we have gone
through in the previous few lectures we are seeing how the requirements are evolving. If
we just take a few seconds and get back when things were in the second generation, the
primary requirement was to provide digital voice across entire Europe with roaming.

Now, see the changes that have come in. The voice is not featuring at all in the set of
requirements this is assumed that it will be amongst the multimedia services. Things
have gone much beyond voice and very high data rate numbers are not specified over
here, numbers are going to come up at the end of it. Large number of connected devices
this was never a requirement earlier. Ultra low latency, such things were not much
feasible at an early stage. But however, when 3G and 4G came into play the
requirements such as lower latency came into picture because we had seen definitions of
control plane latency, user plane data latency. So, latency definitions were coming into
play, and now we are talking about ultra low not simply low latency we will see the
numbers.

High reliability applications will be present for example, remote surgery, where you
require a very high reliability; autonomous vehicles and things like that.

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(Refer Slide Time: 27:36)

So, for example, in the very low latency and high reliability human centric
communications, users expect instantaneous connectivity so that means, flash behavior
within a split second you are connected right.

Further, if this is feasible, then cloud services would be possible because when services
are in the cloud and you have to access them there is a natural delay because there is a
huge mechanism through which you have to go and get your service. So, if it is possible
to provide very low latency network then cloud services would be feasible which will
enable a huge number of applications, low cost applications and would further help
enhance the kind of experiences that people get as well as support a huge number of
applications which would benefit the society at large.

Further virtual reality applications, augmented reality applications are of course, going to
going to be supported by low latency and high reliability scenarios. Further, for low
latency and high reliability communication the enablers are E-health of course, we talk
about remote surgery and many other things. Safety naturally comes into play, office
environment, entertainment and other sectors for example, games and controls and many
other things. For example, control of drones or any other vehicles is naturally going to be
supported by this particular scenario.

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So, given the time constraint of this particular lecture module we stop at this particular
section. In the next lecture, we will continue into the details of the requirement
specification of fifth generation communication system, thereafter we will slowly get
into the different solutions which are expected to provide the methods by which these
different requirements can be met.

Thank you.

97
 Evolution of Air Interface Towards 5G
Prof. Suvra Sekhar Das
G. S. Sanyal School of Telecommunications
Indian Institute of Technology, Kharagpur

Lecture – 06
Requirements and Scenarios of 5G

Welcome to the lectures on Evolution of wireless communication Towards 5G. So, in

this particular lecture we will see the Scenarios and Requirements of 5G, but before we
go into that let us briefly look at some of the things that we have seen in the previous
lecture.

(Refer Slide Time: 00:37)

So, what we see is the generalized system model which we have briefly described I
would like to revisit that before we proceed. So, what we described there was time
frequency diagram where there was a time axis, frequency axis and on the z-axis there
was the channel gain, relative channel gain in decibels. So, the fluctuation as shown over
there on your screen is basically the fluctuation of signal strength over time and
frequency. And this is exactly what is exploited in the 3rd generation, 4th generation and
rather expected to be exploited further in the 5th generation.

So, view of this is sometimes important and often one needs to recall in order to identify
or understand the different mechanisms especially when we go towards MIMO and other
techniques. So, as said that these particular things capture multipath, it captures velocity

98
or Doppler and several things; so, that some of those things we will again see in details at
a later part. And again when you do such simulations one has to take a cellular or a grid
layout usually that is the model till now this particular picture shows around 57 sectors,
19 cells and each of them should be having such a thing as shown on the top corner.

(Refer Slide Time: 01:59)

But usually we focus on the central cell and once we focus on the central cell the other
cell acts as interference because, we have seen that we are moving into the full frequency
reuse; that means, the situation where we have the entire area using the same center
frequency. So, and just a quick iteration of what has what goes on is usually the
reference signal is sent from the base station to the subscriber stations or the mobile
stations. Then there is this CQI estimation that is channel quality estimation at the
receiver followed by which it feeds back the CQI information. Then the base station does
link adaptation; that means, selects the kind of a data rate that it is going to do over a
particular link.

It also does like scheduling; that means, dividing the time amongst the different users so
that the link the entire area spectral efficiency can be maximized. So, you can inherently
see that we are using the terms of definition that we have given before in terms of
performance metrics of the system. So, when you do the packet scheduling there is a
breaking down of the incoming bit stream into transport blocks of different sizes which
are essentially sent into this time domain and frequency domain scheduler. So, they

99
essentially utilize these radio resources as per the fluctuation of the channel as well as
taking into account, the various delays and traffic requirements of the different users.

So, there is a big scale optimization that goes on in the base station based on which these
resource grids which we will describe further in later lectures are allocated to users. And
this allocation is dependent on the QoS of the users as said because there is delay and
data rate requirement and along with it we have also said that there are several MIMO
schemes which goes on. So, again the base station has to identify the kind of MIMO it
has to give to different users and accordingly a signaling of the different MIMO schemes
have to come in. So, there is a whole lot of processing that goes on in order to ensure that
the communication link is a pretty reliable.

(Refer Slide Time: 04:07)

And so, I mean there is additional HARQ that is the Hybrid Automatic Repeat Request
followed by all of these there are call admission and there are several process which goes
on.

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(Refer Slide Time: 04:23)

So, essentially what you see is that to get a reliable link there has to be several such
process that already runs in the system. And, essentially providing some of the new
requirements of 5G where we will see one of which is to reduce the delay is not a
straightforward enhancement of things as it seems to be. So, after discussing all of these
we went on further and we will continue on this where we look into the requirements and
scenarios. So, we had seen the definitions of some of the terms which are pretty
common.

(Refer Slide Time: 05:03)

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We have also talked about the documents which mention about the requirements of 5G
and how the evaluation has to be done. So, again as we have discussed the previous
standards we will also start looking into these with respect to the ITU documents. So,
especially as we have mentioned the IMT-2020 is referred to in the particular document
2083 which describes the requirements and the capabilities.

And, what it says is that should be far more enhanced capabilities than those described in
recommendation M 1645. If you look at what is M 1645, its basically the framework and
objectives of future development of IMT-2000 and systems beyond. So, this one is going
towards IMT-Advanced.

(Refer Slide Time: 05:53)

So, it says its much beyond that and here we have 2083 which is basically the similar
kind of statements as you can see over here IMT Vision – framework and overall
objectives of the future development of IMT; that means, this is the whole family of
things for 2020; that means, the IMT-Advanced and beyond. So, that is why we are
looking into these set of documents.

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(Refer Slide Time: 06:15)

(Refer Slide Time: 06:21)

These things we have already discussed that IMT-2020 essentially 5G. So, we are going
to use the term synonymously, we have seen some of the acronyms or the abbreviations.

103
(Refer Slide Time: 06:29)

And we have also seen some of the basic statements that have been put forward like it is
expected to be more traffic volume, and diverse devices, variety of quality of experience,
and better affordability. So, let us look at a deeper look because until and unless we
understand the details of it, it is difficult to predict or think of or understand the solutions
that have been proposed.

(Refer Slide Time: 06:55)

So, I mean the typical applications which have been pointed out we have discussed these
things like wireless communication applications which are expected to be facilitated by

104
the new technologies are essentially digital economy which we are almost doing. But
probably the scale of which things are going to happen would be far exceeding what we
are doing today and probably one may expect things to go beyond human
authentications.

So, could be self authenticated things where things could be much much faster and it
could go beyond just a simple economy, it could be more towards physical security
things. For example, your smart home potentially which is a probably bigger than your
economy in the sense that it there is precious life which is kind of guarded. So, you
would like things to be done in a way that it is not shunting out the basic requirement in
order to maintain security while, it does not allow mal or intuitive actions to be to be
allowed and that to happen in a seamless manner. So, it looks a very very big process,
but we have to break down to the requirement into smaller requirements.

And come in to specific technical requirements, but that is: what is the objective of this
particular lecture at least in the initial part. So, of course, there is rapid adoption of smart
phones and mobile phones which are driving these things. And, the number of devices
which are accessing the networks are expected to increase because of a Internet of
Things. We will see numbers which are kind of predicted to tell you the difference in the
numbers when people talk about Internet of Things and when they talk about smart
phones. So, that will give us an indication that how this might be one of the major drivers
for a 5G.

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(Refer Slide Time: 08:45)

And some of the techniques which we have also mentioned last time was like
beamforming, MIMO, and wide contiguous bandwidth, reduced cell size, are our
objectives which we' will look at in details in a future slides. So, this basically captures
in a broad scale some of the major things which are expected to be there and again these
are not very new to 5G, but there are enhancements which are going to come beyond the
4G. So, we will look at the basis of the primary setup and we will see what exactly are
expected in the 5th generation compared to previous generations.

(Refer Slide Time: 09:23)

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So, we have also read out this particular thing where we said that this particular
document aims to establish the vision, the potential user application trends, growth in
traffic technology trends, as well as spectrum implications, it also expected to provide
guidelines on the framework and capabilities for 2020 and beyond. So, this is kind of
naturally the document should provide us as per the title of the document and we are
supposed to get into the details of it.

(Refer Slide Time: 09:49)

And, the future IMT systems should support emerging new cases. So, so these are slowly
we are getting into a slightly refined description of the requirements. So, one thing we
can see is that very high data rate communications has been is still there I mean at some
point we said that high data rate I mean as you go from 2G to 3G to 4G to 5G, data rate
is kind of growing that is pretty natural because, of certain things which we said in the
past that the number of connected devices, IoT, and all kinds of things are simply
growing. So, I mean the effective bandwidth and also the kind of the traffic; that means,
let us say today we are more interested in video and other such multimedia traffic
because more is given.

And people are getting more used to them and there is more demand, more number of
users, hence high data rate requirement is an natural consequence, but we also said that
this is not just the only one, there will be large number of connected devices. And we
will see certain more descriptions where you will see the massiveness of this. Ultra low

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latency again for real time you can talk about cyber physical system relies I mean
implementations. So, ultra low latency applications are very very necessary for example,
control applications and high reliability applications are also essential I mean if you are
talking of medical operations being done through such network connectivity in from a
remote location, then of course, high reliability is absolutely essential. As well as if you
are doing certain mechanical large scale experiments or some work industrial work for
all those things I mean both these things almost go hand in hand and their extreme
requirements which are not so easy to bring out.

(Refer Slide Time: 11:37)

So, I mean the users are expected to be connected instantaneously, this also we have
discussed and the flash behavior; that means, they do not want to wait and I mean this
low latency, high reliability as we just said these are the typical working situations which
require such kind of protocol requirements. So, basically the communication system
must provide these things and we would encounter activation of such use cases or
protocols under this situation under these situations.

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(Refer Slide Time: 12:09)

So, furthermore what we see is that in the present day communication systems mostly it
is designed with human user in mind I mean that is I do not need to explain it further
because either it is the entertainment or there is a control. So, most of the time there is an
end user who is having a control on the knobs and play button or let us say I mean
fetching a new source of information or doing a search or maybe making the or pressing
the submit button towards payment or kind of doing a maneuvering of the control
through some joystick or even from the smartphone.

So, mostly it is the user and when it is the user is the human being there is more or less a
limit in terms of response time because of the typical latency of human beings, but what
is expected is that the next generation things there would be a lot of non-human
communication. And beyond human probably you can say or subhuman up to up to you,
but I mean the requirements are probably different than what human interface are
required to be there.

So, there is a design is to consider machine to machine communication with real time
constraints. So, this is very very important and if we take a look at driverless cars so, I
mean, it is pure machines, machines talking to machines, and machines controlling
machines. So, human interface is almost not there I mean you can you can argue with
this that no there would be some human around to take care of emergencies and other
things, true, but most of the immediate controls are through I mean machine to machine.

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And beyond this even if we look at drones and UAVs, the pilot would be at a far far
remote location whereas, this fleet of drones or this fleet of UAVs are supposed to
interact with each other and they are supposed to sense the environment and make a
decision and execute the decision on a local level. So, there will be lot of things that will
be going on at the machine level with the intelligence which is not human which is kind
of beyond human intelligence and control. So, there things have to be done in the
corresponding perspective.

And furthermore it is also said that it would be like enhanced cloud services would are
also expected to be facilitated by virtue of this because, probably a lot of cloud services
can be accessed and they can be becoming more beneficial or more usable in these
conditions. And of course, there is a list of operating scenarios and I think some of the
important ones are traffic control, optimization, I mean real flow of real traffic, let us say
cars and all other stuff and emergency and disaster response, I think this is a very very
critical e-health is also adding one of the most critical applications. Efficient industrial
communications are also very important because, if let us say and you cannot afford to
have a failure in the systems because industrial application big levers moving and lot of I
mean big machineries moving around.

So, you cannot happen to give a wrong command because you might have the system
might have chosen the right command, but as it goes through the link if one of the bits
flip the command becomes a different execution already. So, instead of probably
transferring a huge sort of material from one point to another the whole bucket might be
emptied over there immediately. So, it is very important to have a very reliable links in
that cases and of course, we have discussed UAV situations.

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(Refer Slide Time: 15:45)

High user density is also another very very critical thing which we will see further like
shopping malls stadiums open air festivals and there will be a lot of other users who will
be using them in traffic jams probably or in public transit. So, these are a lot of a lot of
scenarios which are expected. So, we will see a little bit more graphic descriptions of
these where we will appreciate them.

(Refer Slide Time: 16:07)

And of course, during mobility we would like to have higher quality while you are
located inside a moving platform let us say a car or a train and as its its natural that the

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mobility speeds are kind of increasing and we will see that the mobility definitions have
changed from IMT-Advanced to IMT-2020. So, enhanced multimedia services further
so, not only mobility, but along with that there are enhancement in the multimedia
services for example, like ultra high definition displays, multi-view high definition
displays, mobile 3D projections, augmented reality.

So, what we are seeing is that there is a much more enrichment of the media and content
that are getting generated and hence being also consumed by the user. So, this particular
content which was not so rich earlier is now packing much more amount of data into it.
Further the user conditions under which they are accessing such information is also
changing from static indoor to high mobile.

So, we have lot of challenge to be addressed and we will see probably a better
description of this, and if we understand the details of it then only we can come up with a
solutions which are appropriate in meeting such things. So, clearly I mean if you think of
this in a very in a very short note, there is a huge amount of information that is generated
and there is a lot more users moving in a lot more random environment. So, I mean to
meet to provide huge amount of information to a large number of highly mobile users is
a big challenge which is being seen.

(Refer Slide Time: 17:55)

Of course Internet of Things we have already said. So, the number of connected things
are going to exceed the human user devices which we will see in numbers and further the

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things that we are talking about can be smartphone, sensors, actuators, cameras and
vehicles. So, what it means is that there is a whole variety of different things which get
connected it’s not only one type of thing and hence the energy requirement and energy
consumption will be different for the different kind of devices. The transmission power,
the latency requirement because, depending upon the applications. For example, if it is a
camera if it will be just one way communication. If there are like sensors and actuators
there will be like two way communications. In vehicles of course, it is two way
communications.

So, the different kinds of things are going to come up, different latency requirements,
cost and other indices, are for suitable operations are also going to be different. So, all
we are seeing is that one size fits all kind of a solution is not so easy to come up with. So,
we are just kind of a motivating in this particular part, the complexity of the problem, the
variety of the problem, and the kind of quote unquote flexible solution that is expected to
be delivered in the future generation systems. So; that means, what we can see is that we
cannot have multitude of solutions rather, we should have solution which easily gels and
be flexible which can transform itself from one form to another, and which can serve the
different requirements in a in a seamless manner. So, of course, there are different
application areas for this.

(Refer Slide Time: 19:37)

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And ultra accurate positioning applications; so, I mean precise ground based navigation
services are necessary. I mean if you look at present day navigation services when it was
initially available probably we were very excited that yes we have a lot of navigation aid
these days. But beyond that what things have happened is the complexity of this problem
has also increased, our expectation have also increased, if you go to cities I mean there
are a lot of flyovers, and multi tier road architectures, there are tunnels, but we expect the
service to be available in all situations whereas, we also require the accuracy. We would
almost like our cars location in the lane to be provided as accurately as possible with
today’s technology, I mean there is a huge amount of error we given the kind of
expectations because at one point of time we were not having this service. So, when we
got the service we were pretty happy that yes I know more or less I am in a particular
lane, in a particular street, and I use additional information to maneuver to the left or to
the right.

But now we expect that we to be told in which particular lane we are and when to take a
right turn, when to take a left turn, or if there is a change in the dynamic change in the
traffic. So, I mean there is a huge amount of there is a huge amount of change that has
happened further if we look at a drone based delivery of things, automated delivery of
things, then of course, this is going to be a huge. So, with unmanned vehicles, I mean its
a huge thing.

So, in case of relief operations of course, you would like precise information. You would
be going around and probably picking up a living thing maybe a human being who is
probably I mean somehow saved himself or herself and you would like to go to the exact
location with the UAVs and probably help the person out of the situations. So, there you
need even precise locations. So, what we are seeing is that then this new requirement has
provided a lot more challenge, and an opportunity to provide new solutions as well.

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(Refer Slide Time: 21:49)

Amongst the many drivers which influence the traffic demand are adoption of devices
with enhanced capabilities of course, I mean if you go back 10 years and see the kind of
devices we had and see the kind of devices we have these days are kind of significantly
different the kind of processing power, the displays and all are pretty different. So, that is
one of the driving factors. Use of video, device proliferation and also we should not
forget the evolution of new applications with time. So, we should always anticipate that
something new is going to come up.

And it is good if you can, if your solution can support certain new changes without much
change in the architecture. So, this is another very very challenging area because you do
not know what is going to come, but you would expect to be solving it in some manner at
least and this particular document 2370 tells us that it anticipates that IMT traffic will
grow 10 to 100 times from 2020 to 2030. So, while the traffic grows you cannot have a
system a priori which is as per the finely predicted traffic, but you would like to invest
slowly and you would like the system to be modular which can scale.

And so, that it could finally, take the new traffic requirements with added portions of
newer portions of the traffic or the system deployment. So, that it can grow with the
traffic demand which appears to be very simple, but it’s not so, straightforward when
you go and implement things.

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(Refer Slide Time: 23:33)

So, if we if we look at the different scenarios or the different drivers for traffic the
increase beyond 2020 as described in the particular document as we have been referring
to what we see is that there are a whole set of different requirements or different drivers
which have been pointed out. So, one of them is the accelerated deployment of new IMT
technologies.

So, kind of beyond two thousand seventeen is expected to be in more than one point four
billion smartphones we will see some statistics of course. Then enhance screen
resolutions, so, kind of 4K ultra high definition displays are some of the driving factors.
Cloud computing users are increasingly adopting more services that are required to be
ubiquitously accessible.

Now, when we say ubiquitously accessible we will see the definition it does not mean
that you access it over all places on the globe right it rather means that over a service
area there is a ubiquitous accessibility. But of course, I mean what it means is that cloud
computing should be one of the facilities that to be provided. Growth in audio visual
media streaming, and what is expected that almost two third of the entire mobile traffic
would be multimedia audio and visual. Proliferation of ambient screens, so, there will be
lot of lot of large screens and surfaces there are already displays which are like see
through displays and depending upon situation you can wake up it can provide this
displays and then can act as a window as well, and it is kind of a 4 K ultra high definition

116
info bearing surfaces. Then shifting demography is also another interesting figure or a
fact that which we can look at is the urban migration. So, what it’s expected is that
around 600 cities produce around 60 percent of the GDP global GDP. So, it is kind of
pretty skewed I mean if you look at the distribution of traffic.

So, over entire large area this is of course, over a large area, but if you concentrate on
smaller areas I think similar features happen that you need to provide a network which
can handle huge amount of traffic emanating from a small tiny place whereas, a large
area is not having that much demand. So, it is not a uniform distribution traffic over a
geographical area so, this makes the problem even more challenging. So, evolution in the
usage or traffic characteristics so, which basically means the emerging services will be
different pattern with traffic asymmetry. So, from one the downlink would be from 1 7th
to 1 10th so; that means, uplink downlink ratio is going to be very very different. So, that
is what it is saying.

So, if we are aware of these things, if the uplink and downlink ratio are different then we
would redesign the system in a manner which can handle such changes right and like
subscriber behavior or the place or the replacement of fixed broadband with mobile
broadband. So, basically what we are seeing is that it is kind of expected in many regions
of the world that you provide an alternative to the wired broadband through such
wireless services. Now to provide a wireless broadband which is almost equivalent to
wired broadband or a fixed broadband service is not an easy problem to handle given all
kinds of variations. So, what we see is that there are various factors which drive the
traffic increase.

So, not only it’s just the volume, but also certain changes in behavior, asymmetricity,
which are going to change the traffic characteristics beyond 2020. So, it is also predicted
that the annual global downloading of applications or apps is kind of 270 billion in 2017
and interesting facts are that the most applications are not used more than once after
being downloaded. So, probably if we can ask ourselves we will probably find that in our
mobile phones we have downloaded many applications or some of them are pre-loaded.
So, that is ok that is better off, but if you are not using that application and if there is a
huge number of such things happening then there is usage of bandwidth.

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Now, you might question the usage pattern, but it is probably important also to accept the
fact that it is a behavioral trait or it is happening, and if you would deny that service
probably it becomes a big question mark whether it is kind of the right approach, or its
kind of helping anyone because we are not sure about what is going to happen with the
app once downloaded. So, additionally the amount of regular updates and upgrades, I
mean if you if you look at the number of apps that are in your phone, and you would also
be aware that these there is a regular up gradation of the apps like every week months is
probably pretty good. But sometimes everyday is that it waits for an update because
without update it does not work any further now every device large number of such apps
are happening in this manner. So, although we discount for it, but if we aggregate the
total thing it’s a huge number it’s a small number sometimes we carry multiple such
phones and although we do not use them, they are still I mean participating in the overall
growth of traffic. So, these are some facts, some factors, which if we are aware we can
probably design to provide service to such requirements in a manner which is going to
help manage the entire thing in a nice manner.

For a very simple thing is that if it is not a very critical app we can probably delay the
download of information or the up gradation of the app to a time. When the traffic
demand is low overall we can distribute it for different users at different times and many
other optimizations can be done of course, with the consent of the of the user.

(Refer Slide Time: 30:01)

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So I mean one more factor that is that is coming into play is that the technologies will
increase the bit rates that is what is expected and the quality of experience, of course, so,
that is that is one additional factor which is going to come in. Furthermore, the energy
aspects are also very important.

(Refer Slide Time: 30:15)

So, what we see is that the energy consumption may become one of the limiting factors.
Because, if there is unsustainable level of cost of operation then things might take a
different turn; so, we should be very very much careful about the energy consumption
also. And, this has been one of the important considerations for design of systems and
according to how we layout we will see that we will actually try. And see one of the
particular views in this particular direction, and how things can be improved there of
course, many ways, but at least we will see one of the reason.

So, energy consumption of wireless networks in 2011 was a 17 kilowatt hour per year
per user. So, I mean if you add up all the users it was almost 100 terawatt hours for users.
So, which is a big number which has already happened in 2011; now if you go to 2020
and down to 2030 when traffic is expected to grow 10 to 100 times of the previous of the
previous generation of systems. Then you can easily imagine the amount of energy
consumption that is going to happen.

So, I mean this is a very important factor. So, what it essentially tells us is that most of
the designs and solutions should consider the energy that is used overall in the system so

119
that we can come up with a better design, and ours our system is already pre-designed to
reduce energy or energy comes as a constraint in the optimization problem which you are
usually solving. So, that it is already taken into account at the design time and not at a
later stage as a post connection.

(Refer Slide Time: 32:07)

In this particular figure, there is a kind of prediction of the global mobile subscription
from 2020 to 2030. So, what we see is that there were its expected around 10 billion
mobile subscriptions in the year 2020 and it was around 6.7 billion in 2013 and it is
expected to grow to 17 billion in 2030. So, I mean that is the kind of a numbers in terms
of mobile subscription that are expected over the next 10 years of the 5th generation of
communication system that we are trying to see.

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(Refer Slide Time: 32:53)

And in this particular picture we are kind of seeing again this particular image is from M
2370 which is an ITU-R document. On the x-axis it is the years from 2020 to 2030 and
on the y-axis it is the number of a different categories of devices. So, what we see in one
particular column is that it is around 10 point something nearly around 11.

So, it is basically the number what we have here 10.7 billion devices that is broken down
into different types of devices. So, there is a feature phone which is kind of 30 percent
roughly speaking and around 13 percent of tablets or other smart devices, and
smartphones are around a big 63 percent or 60 percent plus kind of. So, so that is the
change that has happened over years where actually earlier this was the major portion of
devices and this was only a smaller portion of devices.

And it is expected by 2025, the feature phones would almost vanish in comparison to the
entire network. Now if you have a very tiny fraction of such devices then what comes
into play is that the traffic demand by these devices are significantly different compared
to the traffic demand by these devices right. So, another hidden information which is
kind of coming out from this picture is probably the traffic that is generated by feature
phones are going to vanish, and it will be generated it will be dominated only mainly by
smart-phones and tablets from this year onwards from around 2026. And, thereafter you
are going to have devices which are much more multimedia capable and capable of and
having multiple sensors. So, it will be every user will be generating a huge complicated

121
set of traffic which we need to address. So, we stop this particular lecture here and we
will continue on this further in the upcoming lectures.

Thank you.

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 Evolution of Air Interface Towards 5G
Prof. Suvra Sekhar Das
G. S. Sanyal School of Telecommunications
Indian Institute of Technology Kharagpur

Lecture – 07
Requirements and Scenarios of 5G (contd.)

Welcome to the lectures on Evolution of Air Interface Towards 5G.

(Refer Slide Time: 00:23)

So, we have been seeing the drivers for traffic growth and we will just summarily look at
that. So, this is the particular slide that we were looking at and various factors, which are
driving the increase of traffic 2020 and beyond are basically captured in this particular
slide. And, we have more or less discussed some of the aspects and reasons why and we
have also said that it is important to look at these kind of parameters. Because, when you
get trained in designing new systems, you must start looking at it from this perspective.

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(Refer Slide Time: 01:01)

So, the other thing that we also mentioned is energy is also a very crucial parameter in
the whole thing and it must be taken into account in the design. And we will obviously,
see at certain point that how energy saving mechanisms have been built and at least one
energy saving mechanism.

(Refer Slide Time: 01:17)

And in this particular slide, we have also discussed this, where it projects the growth of
traffic up to 2030, on y axis is a billions of global mobile subscription.

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So, what we have is around 2020 it is expected that around 10.7 billion connections
would be there and it will grow to 17.1 billion, this is what we discussed in the previous
lecture.

(Refer Slide Time: 01:42)

And also this particular one image, which is again from M 2370 discusses the breakup of
the kind of devices which accesses the connectivity. And so what we see is around 2020,
there would be quite a few feature phones, while the larger numbers would be
smartphones. And mid way up to 2030 the feature phones are almost going to be
negligible and finally, they are going to go out that is what is predicted and mostly it will
be tablets and smartphones in part of global mobile subscription.

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(Refer Slide Time: 02:24)

What we have also seen is that the M2M that is machine-to-machine, it is expected that
around 2020 2030, there will be 97 billion devices, which will be connected and this is as
per M 2370 which is an ITU-R report.

So, what we see is the massive growth in devices is one of the huge things that are going
to come up and accordingly we will see a scenario, which talks about large number of
connectivity as well. So, these predictions help us set targets for the next generation
systems and also design solutions, which would meet such large volume of connectivity.

(Refer Slide Time: 03:13)

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So moving beyond what we have here is a summary of definitions in terms of network
capacity units. Because, when you have a huge number of things connected and data is
flowing through the network, we have to measure in bytes and bytes is a basic unit rather
bits is a basic unit. But, the number of 0s that get added when you have so many devices
and such large number of such large connectivity it is not easy to use the simple bits per
second.

So, I mean as you know that at some point of time kilobits or kilobytes was a good
number to capture the data rate and whereas, now we have moved through megabyte and
through gigabyte in terms of connectivity and then terabytes, we are used to in terms of
personal data storage. So whereas, at some point personal data storage of few kilobyte
was a huge number whereas now, we are used to a few terabytes TB in short form like
we buy hard drives 1 TB 2 TB. At certain point 1 GB was a big number; so now, it is like
our phones come with gigabytes of memory storage.

So, as you look at the network traffic capacity, these numbers are not enough to take care
of the description of the traffic which flows. So, there are other units which have been;
which have been developed like the petabytes, which is 10 to the power of 15 bytes,
exabytes 10 to the power of 18, and zeta bytes it is 10 to the power of 21. So, it is
growing in the same rate like 1000 terabytes make 1 petabyte, 1000 petabyte makes 1
exabyte, 1000 exabyte makes 1 zetabyte.

So, these are the units which are usually used in terms of describing the traffic flow. So,
we are kind of getting ourselves accustomed to these numbers and this would also serve
handy, whenever you want to refer to a particular specification, I mean these this table
would always help you. So, just a quick reminder terabyte is what we are in, the next
level is petabyte, then exabyte, then zetabyte, and each grows by a factor of 10 to the
power of 3.

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(Refer Slide Time: 05:35)

So, in this particular figure, now again we have estimation of global mobile traffic in the
period 2020 to 2030 and this is M2M traffic is included in this particular picture. So, it is
expected from 2020 to 2030, the traffic would grow from 62 exabytes. So, what you see
is exabyte is 10 to the power of 18 bytes that is kind of 1000 petabytes, that is kind of 1
million terabytes right. So, that you can clearly see and 1 billion gigabytes; so, that is
what is the number over here and it would grow significantly.

So, by in 2 years it is expected to double and a rather more than double in 2 more years is
it is more than double and it is growing in more or less the same phase, it is kind of more
than double of this and again in 2 years it is more than double of that and then again it is
significantly grow. So, there is kind of exponential growth that is expected. So, around
here it is around 5000 exabytes. So, that is kind of 5 zetabytes of data that is are expected
around 2030. So, which are huge numbers.

So, the network has also to be designed in a manner that it can handle this amount of
traffic, which is like significant growth, I mean huge growth from where it is and in this
period it is expected that the network is capable of absorbing this traffic. And as said
earlier, it is not, it is required that you do not lay out the entire network. Because, you
would like to invest slowly as and when the demand comes in, but we are just getting
ourselves aware that such kind of requirement have to be supported by the same network
in future.

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(Refer Slide Time: 07:26)

In this particular slide, it is shown the estimation of mobile traffic by different service
types globally. So, again these are exabytes of data again, this is the year as we have
been showing. So, what we see is that video is going to be a major portion of the traffic.
A major chunk is expected to be video. So, this again there gives us some information
about the kind of traffic and hence the kind of resource allocation the kind of
mechanisms, which are feasible, which are non-feasible, the way you should divide the
bandwidth, the way you should divide your resources and things like that.

So, this prediction helps us in taking lot of technological decisions towards deployment
and accepting solutions as accepted part of the technology solution. M2M is going to be
a major part as well as non video will be there. So, these are the broad classifications of
which video is expected to be the major chunk of traffic.

129
(Refer Slide Time: 08:29)

In this one again, it is the estimation of global mobile traffic subscription per month from
2020 to 2030 in terms of gigabytes. So, what we see again 5.3 to 257. So, that is again a
factor of like 20 plus, I mean it is a huge number, it is around kind of 50; it is kind of a
huge number. So, more than 20, it is more than 40 50 nearly a factor of 50 growth from
2020 to 2030. So, that is that is again like exponentially everything is growing between
2020 and 2030.

(Refer Slide Time: 09:09)

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So, in this is an interesting a figure, which is slightly different compared to the traffic
growths that were shown in the previous slides. So, these were all traffic growths in
different forms, what we see over here is the daily traffic profile of I mean this is for
North America region again as given in 2370 of major applications as they are predicting
in 2020.

So, there is a streaming application, there is storage, there is communication, there is

gaming, and there is computing, and this is the hours of the day on the x axis midnight
starts over here 12 midnight. These are the hours, when people are travelling towards
their office and this is the usual office hours and these are the hours, when people start
returning back home and this is where they are at their home. So, what we see is that one
particular profile, which is for the gaming is kind of given over here this there is not
much nothing much to say, except that this is more or less something to be expected.

So whereas, what we can make an observation over here is that the streaming traffic is
kind of here, this is the curve for the streaming traffic as you can see and communication
is here. Computing is following the mark that I am trying to follow through over here
and storage is kind of this. So, these are the hours, which it is expects the daily traffic
profile to be and what you can see is that there are some traffics, which are similar in
certain part of the day, when they are actually low, which is in percentage and in some
portions it is pretty contrast with other traffic.

So, these differences are and these similarities are actually the ones, which can help us
make designs, which are more meaningful, we will see especially one particular
application, which is related to energy savings, where we will show that how this traffic
profile fluctuation has been used to provide mechanisms to save energy. And many
others solutions could also be taken care of by being aware of the distribution of traffic
in a 24 hour period.

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(Refer Slide Time: 11:38)

So in this particular figure, what has been captured again in the same report M 2370 is
that there are different dimensions of the performance metric, which are important and of
which we have identified like connection density as one of the important measures, user
experienced data rate as well as capacity density. So, these 3, which have been encircled
in this particular figure are the ones which directly influence traffic and this is basically
the capabilities envisaged in there in the particular study that is 2370 for the current and
emerging voice and data applications.

So, these are mostly the when it is voice and data, it is kind of human connected
situations, where they will be using and this red particular curve is kind of indicating the
core capabilities. While, these individual markers as has been shown over here are the
individual situations which make them different. So, as we can see as given in this
particular figure that these 3 primarily, they are the ones which directly influence the
traffic right. So, for example, the connection density, the higher the connection density,
the higher is the traffic, higher the user data rate higher is the traffic, higher is the
capacity density higher is the traffic.

So, I mean that is the kind of direct influence whereas, there are some other parameters
also which also influence the traffic, but not directly indirectly rather. Like latency, as we
have over here in milliseconds. So, latency is kind of a QoS metric that you would
require to traffic to be delivered within certain duration that is not pushing the traffic

132
much higher, but it is more of a demand on the radio resource utilization algorithms,
which would have to deliver the service. So, although the traffic is not huge, but you
might have to reserve a lot of resources in order to guarantee the delivery of service
within a certain deadline or a certain latency. A spectrum efficiency, yeah I mean of
course, if you have higher spectrum efficiency then you can provide high quality
services. Mobility is also an influencing factor because, higher your mobility generally
your spectral efficiency goes down and the capability to push more data within a narrow
bandwidth becomes less.

So, you have to provide more and more bandwidth and if you have to provide the same
data rate at high mobility then obviously, you require more bandwidth and so basically
there is a complicated relationship with all other factors. Terminal battery life is also one
which influences traffic in a way that, if you would like longer terminal battery life then
you would have to schedule the traffic in a manner that it utilizes the most of the awake
time to transmit the data and has a has a periodic sleep hours so that, it could conserve
most of the energies and the terminal devices could last for a long duration.

Similarly, coverage probability is also very very important and as these markers are
indicating like let us say this public safety. Obviously, I mean for public safety
applications, you would like to have a coverage reliability, which is very high and when
if we take the indoor situations, there again the connection density is expected to be very
high. And similarly, I mean all other different things like when you are in moving
platforms for example, in vehicles or in trains, so, there the mobility factor is one of the
critical factors. So and let us say this particular marker, which is the web page element.

So, when you are loading some web page and it has certain objects which need to be
updated or uploaded or which needs to be rendered. So there again, the latency factors
come in to play and similarly, this star with the yellowing inside, which you see his voice
is also another critical application, where latency is very very crucial. So, I mean this in
through this particular picture, you can capture the different the different capabilities,
which are required of the services that are expected of 5G and as well as which kind of
situations demand, which kind of capabilities in more importance compared to others.

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(Refer Slide Time: 16:25)

In this particular picture again, from the same report it talks about the capabilities
envisaged for current and emerging multimedia applications right. So, I mean this
particular one is for assuming with ultra high definition and again what we see is that,
there are different metrics as has been highlighted for the different situations, that means,
let us say spectrum efficiency is expected to be very high.

So, if spectrum efficiency is very high then you can provide very high bit rate. On the
other hand, if the mobility is pretty high then providing very high quality is kind of pretty
weak. So, basically at relatively lower mobility you are expected to provide this kind of
services. So, more or less this again captures for another set of situation.

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(Refer Slide Time: 17:21)

In this particular one again, the capabilities for emerging Internet of Things, sensors, and
actuator applications are kind of demonstrated. So, what we see over here is connection
density will be high because, Internet of Things. So, there will be large number of such
devices, which will be deployed and coverage reliability has to be high because, if these
are sensors and actuators, so, if you have an automated system, then you would like that
the system gets input from all the sensors and it serves the purpose.

So, in that manner your coverage reliability has to be high and again since these are
sensor networks it is typically required that the terminal battery life is also high because,
you would not like to go and replace the battery very often. Whereas, mobility
requirement is not that high, spectrum efficiency need not be high, because generally
speaking for such things, it is usually the case that there is intermittent data, which is
usually small amount of data which is sent and the devices need to last long.

So basically, you need to save the battery life, it needs to be lasting longer, spectral
efficiency requirement is not extremely high, but high is; obviously, good but relatively
lower compared to the higher end demands. The capacity density can be low, and the
device experience data rate can be low relatively low compared to the other values. So
on and off they would be sending data, large number of devices need not have a stringent
latency requirement, but should have high coverage reliability, and high terminal battery
life. That is how this emerging Internet of Things and actuator applications are the

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scenario is described through the different requirements of the different parameters in
this particular figure.

(Refer Slide Time: 19:25)

And then we look into some more applications like mission critical and low latency
applications and as the name suggests a low latency. So, your latency requirements
would be very very stringent, what you see the latency requirement here the number is
decreasing as we go away from the center. So here, we have around 1 millisecond as the
latency requirement and of course, reliability factor is high.

So, if we go back along with it the terminal battery life was required to be high, but here
the terminal battery life may not be required to be high, it is much lower. So here, what
you see is in order of years. So, generally it is kind of 10 years that is required for
Internet of Things that is kind of expected a few years at least whereas here, that is not a
stringent requirement because, it is mission critical requirement. So, probably there is
some availability of power in this particular case.

Well, in this situation mobility has not been kept very high. However, it might be like as
you are seeing driverless cars situation, there could be high mobility where it could be
100s of kilometers per hour. So, I mean there are aberrations which have been captured
by these extra markers and spectrum efficiency yeah on the lower side compared to this,
overall the spectrum is a requirement is high, but this particular application, because it is
mission critical it is more important that, these two are satisfied heavily maybe at the

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cost of this because that is we can see when we will go into deeper discussions will kind
of find out why this may be kept low right.

Whereas, if you are talking of gaming applications then the spectrum efficiency
requirement needs to be high for a large amount of multimedia service, multimedia or
rich content to be delivered. And here again, as you are seeing for mission critical
applications generally speaking the user data rate is not very high, you would send
critical information. For example, location or some update or help needed and maybe the
health status and things like that whereas, if it is a gaming application you can clearly see
that the user data rate requirement is high.

So, these pictures basically captured the different scenarios in terms of description of
parameters of the future generation system that we are discussing.

(Refer Slide Time: 21:53).

So, this particular figure captures the capabilities that are expected to be required for
future IMT-2020 and beyond applications; so, for the new capabilities that that would be
expected. So again, there is variety of different parameters, you can read them quite
easily from the points that have been marked over here and as have been given over here
that different markers possible at very high frequencies. So, high spectrum efficiency and
high reliability and may be needed for some applications.

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So basically, they have described the different scenarios and different marks, different
lines and different numbers, which have been clearly indicated over here which are
expected.

(Refer Slide Time: 22:44)

So, some of the technologies, which are required to enhance the radio interface are
basically the spectrum, which is required that large blocks like carrier aggregation things,
which have been going on. In the physical layer again, it is expected that lot of these
MIMO and massive MIMO and lot of other things would come in which is, which we are
going to discuss. Network densification, as we have said is again another important
technical aspect which is, there is a hope that it would provide us a lot of this capacity
demand that is being placed will be satisfied when it is network densification and yeah.

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(Refer Slide Time: 23:28)

So, I mean if you look at how all these things have been have been developed, we have
already given a picture earlier that it has been through years of such development, we are
coming to a close of this particular discussion.

(Refer Slide Time: 23:37)

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(Refer Slide Time: 23:39)

So again, it is available from ITU that which describes the development of different I
IMT standards. So, initially it was a 15 year cycle then it was a 9 year cycle when it was
IMT-2000 IMT-Advanced and then again from IMT-Advanced to IMT-2020, it is kind
of decreasing time period. But, I mean only time will tell us that, whether this
changeover is going to be becoming smaller and smaller it is going to remain roughly at
an average of 10 years from deployment of one technology to another technology.

(Refer Slide Time: 24:16)

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So, the usage scenarios as we have been describing are broadly categorized into the
enhanced mobile broadband, ultra reliable and low latency communications, massive
machine type communications. So, these are significantly different situations, which are
expected to be present in 5G or it is kind of broadly categorized in those ways.

(Refer Slide Time: 24:42)

So, amongst the different scenarios, there is this tactile internet is also one of the
important things, where the response time is expected to be pretty fast. I mean much
faster than human response time, I mean which is typically applicable for remote surgery
and where 100 microsecond physical layer budget kind of things are expected. And, then
there would be gigabyte wireless application scenarios, where a very high spectral
efficiency per user is kind of required and some of the technology, like massive MIMO
and millimeter wave are expected to deliver the solution.

Then massive machine type is another scenario, which is expected to be there and which
is primarily going to be driven by Internet of Things. And there would be requirement of
relaxed synchronization, there would be requirement of low complexity, and low peak-
to-average power ratio at the device end. Then there could be super real time scenarios
requirement like automated driving and there could be great crowd great service in
crowd.

So, these are broadly some of the scenarios, which are expected to appear in 5G. And we
will see we have already seen some of the characteristics will see a little bit more of them

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in the upcoming lectures. And, then we will proceed towards meeting the solutions,
which are expected to provide methods to address these different scenarios.

Thank you.

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 Evolution of Air Interface Towards 5G
Prof. Suvra Sekhar Das
G. S. Sanyal School of Telecommunications
Indian Institute of Technology, Kharagpur

Lecture – 08
Requirements and Scenarios of 5G ( Contd. )

Welcome to the lectures on Evolution of Air Interface Towards 5G, we are discussing
the Requirements and Scenarios of IMT-2020 that is 5G.

(Refer Slide Time: 00:33)

And in the previous lecture the last thing we were discussing is basically the scenarios,
where we have summarized that tactical internet could be one potential situation, which
needs to be addressed where remote surgery is one of the strong potential applications,
which is the need of the day. And, then there could be machine type communications,
there could be super real time and reliable requirements as well as, there would be a
gigabit wireless scenarios, and great service in crowd situations. So, let us take a look at
some of these cases.

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(Refer Slide Time: 01:07)

So, overall if we have a huge picture, which captures more or less all the scenarios that
come into play and we categorize the different situations, we have on one end amazingly
fast as the description of the scenario and which we could map down to a requirement on
bit rate and delay. For example, if we have a situation which requires amazingly fast
connectivity, the data rate would be very high as well as the delay requirement would be
pretty stringent; that means, that very small delay with very high data rate, you have to
provide connectivity.

A great service in crowd situation would effectively mean accessibility; that means, all
devices are connected in large crowds. Then there was also at some point of time
description about the best service follows you which is again a key word or acronym or a
particular description from the industry, which would translate to accessibility, coverage
and mobility. That means, while you are moving around and you have access from all
situations in different mobility conditions.

Then there is like super real time and reliable connections, which would translate to
delay, reliability and which would apply to industrial applications, where there is control
of production, machinery, and all the kinds of things. There would be a requirement of
ubiquitous things communicating; that means different kinds of things communicating,
which would translate to many simple devices connected as well as this coverage is an
important issue and redundancy in connectivity is also important.

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So, there could be same kind of data going through while on one hand, while on the other
hand, you need to provide communication while not flooding the entire network. So,
then there are different scenarios and which each scenario would translate to different
requirements, we have seen a different pictorial representation earlier and this is another
way of looking at a similar thing.

(Refer Slide Time: 03:13)

So, like the gigabit wireless situation could be addressing work and infotainment, where
there would be like a great user experience provided by data rate. One could imagine
virtual office scenario and many other situations. If we look at this particular picture as
shown here it is kind of picture representing a dense urban information society.

So essentially, if we look at the density of connections in this particular environment and

try to imagine the amount of data rate that could be required to be provided to the large
number of users, it is a huge-huge challenge that needs to be addressed. So, situations
like this are coming up it is a reality and everybody in this particular situation in this
environment would like to have a same kind of service and a huge great experience at the
same time. So, finding solutions to meet them is one of the focus of the fifth generation
communication system.

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(Refer Slide Time: 04:21)

Great service in crowd; so, again these pictures highlight the situation of a shopping mall
as over here, and a stadium, and an open air festival, and an event. So, what we see is the
crowd is huge that is very large number of people and almost everyone over here would
like to be connected, while they are participating in a particular activity. So, here there
could be infotainment as well as shopping and advertisement and many things going on.
So, the user devices would have to be connected offers of different products and different
launches would have to be given to users based on their location and their interest.

So this is one scenario, where you have a huge crowd while at the same time you have a
heavy quality of service requirement. In stadium situations again, you see in a small area
as well as in this there is a huge density of people around. And, although they are
participating in a live event many of them would like to convey the information of the
field off the field, while some of them would like to see a replay or a closer view of what
is happening in the field. There could be more immersive experience like there could be
multiple cameras around and taking different views and one would be switching from
one view to another, could be seeing a particular operation or a particular event
happening in one location of the field and so on and so forth.

So, if you look at this situation probably, this is more challenging than the other two and
while these situations have advantage that there is some kind of an infrastructure
available through which you can provide service. But, on the other hand these

146
environments as you can clearly see are not going to be crowded throughout the day over
here. There are certain cycles over which the crowd appears then over a period of 7 days
the crowd changes, while over a period of months the crowd changes. For example,
before big festivals like in India, we have this Durga Puja and other of occasions before
that there is a heavy presence of crowd in the shopping malls, in sporting events, this
happens intermittently this situation would happen once in a year and then once in a few
years the crowd would be unimaginable.

So, providing great service in this kind of situations is not a easy task. Whereas on the
other hand the demand of users are increasing with time; that means, they are getting a
better service in the previous year and they expect that at least that quality is maintained,
while every year the crowd is becoming more and more and more. While for example,
this situation you do not get to have this situation throughout the year, it is once in a year
and probably one day and maybe only a few hours in a day. But, you require to provide
the same service as if there were maybe 1 100 th 1 1000 th or maybe 1 10000 of the
population around over here in other times of the year.

So, designing a network which is flexible, which is scalable, which is able to handle
these kind of situations, which is dynamic, which is reconfigurable, and which is readily
deployable to address these situations is a challenge, which is required to be addressed
by 5G.

(Refer Slide Time: 08:01)

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Other situation are like super real time and reliable communications like typical situation
of traffic getting stuck or bottleneck in crossings although this is a much better situation,
I mean typically things are much worse. So, had there been communication between the
vehicles and the nodes around these crossings, this entire traffic could be managed in a
much more efficient manner. And, obviously, among several things which get saved is
fuel. And of course, we all know the heavy demand and price of fuel, which is affecting
the entire economy all over the world, further the time that the users spend while
traveling would be significantly reduced, if a real time communication between the
moving platforms and the infrastructure is enabled which is finally able to drive the
traffic in the path by which the entire system is optimized like there are certainly certain
stretches, which people like to use whereas, there could be another option at that point of
time which is more beneficial for a particular user.

So, if there is a communication with the infrastructure and the traffic is controlled
through a global connected network then such efficient or such advanced or better
quality of a experience or quality of life can be delivered to the users and such situations
could be easily avoided and you would end up in a situation, which is much simpler and
more efficient.

(Refer Slide Time: 09:35)

And in a massive machine type communication example situations; we have

representative images taken from the internet, which shows that there are different kinds

148
of requirements on one hand, which could be collecting information related to the
weather, to the environment, to the biodiversity, which are not so often which is one way
flow of information. There could be other situations would which would require
actuators and control may be the farming operations as represented over here, sensors
while these are being controlled from a remote locations.

Whereas, these situations which are capturing CCTV images of a huge event that is
going on maybe there is a huge amount of data flow from one direction and on the same
time, you may require to process this information and take control action on the other
side. So, in these 3 situations, what we see is that, there is a significant difference in the
kind of traffic that is flowing while here there is intermittent low data signal going in.
Here it is bidirectional, whether it is control information has to come in here it is kind of
single direction.

But huge amount of information which may require to flow, but the common thing is
there could be a large number of devices, which are connected. Here, it could be
situation, where there is redundant data and you would not like to replace, I mean take
care of these devices very often, you would like to deploy and let them run. Here the
energy may not be an issue and here you would you can probably provide energy on a
daily basis. So, there is again different requirements or scenarios in terms of energy, in
terms of data rate, in terms of traffic flow, which need to be addressed under the category
of machine type communication, again 5G is expected to be flexible enough to provide
support for these devices.

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(Refer Slide Time: 11:37)

When we look at the tactile internet situation, so, here a response time of less than 1
millisecond is required, while very high availability is required. If we look at the typical
flow of information from the core network to the user terminal, we will find that the
overall delay is significantly large it turns out to be in orders of a few milliseconds up to
10 milliseconds in present day network. So, I mean there could be a processing delay in
just propagation, processing delay at the base station, then there is a basic frame structure
and there is again processing at the user terminal, and then the entire process has to
repeat in the reverse direction, then only some activation can happen.

So, if we want fast control this entire loop, if it is required to be processed within 1
millisecond, you need to change the different parts altogether, you need to reduce the
propagation time, you need to reduce the processing time. And, hence in turn, you need
to reduce the TTIs or in terms in other words, the frame duration, which would rather
result in changing of the symbol duration and if the symbol duration changes that could
result in a significant growth of the bandwidth so that means, if you have to make
symbol duration smaller the bandwidth would become larger, if the bandwidth occupied
by the signal becomes larger, then the effects of the multipath fading would come in that
would mean that which was previously experiencing flat fading condition and the
receivers were designed to operate in a very simple manner would now have to be
completely changed.

150
So, what we are trying to point out is that such requirements although, appears very
simple is not so easy and straightforward, if we look into the breakdown of the details
and if we try to crunch the entire time, there is significant impact on the overall physical
layer signals, which needs to be completely changed and thereby affecting the entire
technology in a significant manner.

(Refer Slide Time: 13:51)

So overall, what we see is that in the next category that is a enhanced mobile broadband,
which is again another scenario as has been has been described earlier. It is expected to
provide fiber like speed; that means, almost like wire line speed, which is 10 at least 10
times of what is experienced today. Uniform experience, so that means, when we are
connected to wire-line usually there is less fluctuation in the quality of service compared
to wireless scenario, we will see of course, and many of you already are aware that in
wireless scenario the signal strength fluctuates with time and space. So, we would like to
have a same quality of service at different situations, unlike wire-line in wireless, as we
have seen the connection density can also be different and the different new applications
that are coming up. So, you would like to have uniform experience under all these
conditions in the category of enhanced mobile broadband, the latency is a lower latency
is expected, higher spectral efficiency is required to be supported, and huge enhancement
in the traffic capacity is supposed to be supported, again because of the multimedia
services that are going to come in are expected to be more rich in content.

151
So, overall there is a huge scaling up of all the demands or the all these parameters that
are existing today under this category. While at the same time whereas, your bits per
service are increasing one would not like to increase the cost. So, in other words, if you
have to maintain even the same pricing then the cost per bit has to be lowered
significantly and that can be done, if the efficiency of the system is increased by a huge
factor.

So again, under this category there are lot of demands that are to be met and hence lot of
challenges that have to be catered by the fifth generation system.

(Refer Slide Time: 15:55)

Again as we take a look at this picture, which is in 2083 M 2083 ITU document, which
captures the 3 environment, which you have been talking about, there is massive
machine type communication on one end of the spectrum, there is ultra reliable and low
latency communication on the other end of the spectrum, and enhanced mobile
broadband on the other end of the spectrum.

So, these 3 are the prime scenarios, where you have variety of applications coming up as
has been given in the particular description. So, what we see in the enhanced mobile
broadband, in the hotspots case, that is the area with high user density, very high traffic
capacity is required and low mobility with high user data rate. So, I mean that is a
classification or description of one of the scenarios whereas, if you look at ultra reliable
low latency situation, applications would be control industrial control in terms in case of

152
manufacturing let us say, an automated factory, production process, remote medical
surgery, distribution of automation in a grid, and transportation, safety, etc.

So, there is a significant difference in the kind of requirements and services in these
different operating scenarios. In case of machine type, we have been saying there would
be large number of users connected and they would be transmitting low volume, non
delay sensitive data and devices are required to be low cost and having a long battery
life. So, this is the overall picture, which captures the different scenarios that required to
be supported by 5G.

(Refer Slide Time: 17:41)

So, in this picture, we have summarized all the things that have been that we have been
discussing and again this particular picture is present in M 2083. So here, what you see is
that the outer radius and the different points describe the IMT-2020 requirements will
again go through them further and this inner one is the IMT-Advanced requirements.

So, as we have said the spectrum efficiency requires to be 3 times that of the previous
generation system, we can clearly see that indicated in this figure and the network
efficiency is required to be 100 times that of the previous generation system, the area
traffic capacity has to be 10 compared to 0.1 that is a factor of 100 again over here, peak
data rate has to be significantly large and so on and so forth. So, what we see is that there
are different requirements and these parameters, which have been existing before
required to be simply bloated up that is what this particular diagram brings out.

153
So, for example, if we look at over here the achievable data rate that is available
ubiquitous is what is the user experience data rate, and throughout our discussion
whenever this ubiquitous term comes in it is actually meant and to describe that the
target coverage area and not intend to relate an entire region or a country.

So, whenever we think of ubiquitous, it is wherever there is coverage the entire coverage
area has to have ubiquitous coverage. Now simply in wireless just because of path-loss
the user, who is closer to the transmitting station gets a better signal to noise ratio and
hence can access a higher data rate whereas, users who are far away from the
transmitting point experience a lower data rate. Now it is desired that this discrepancy is
as low as possible and enhanced by virtue of different mechanisms, which can be
introduced.

So, I mean here again when we talk about mobility, it defines about it talks about the
maximum speed at which a defined quality of service and seamless transfer between
radio nodes, or radio access, and multi layer radio access technology, that can be
supported ok. So similarly, different things are described and can be referred to you as
these slides would be given back as coarse material.

(Refer Slide Time: 20:17)

So, in this particular figure again from M 2083 the importance of capabilities of eMBB
and URLLC and MMTC are described. So, what you see is this particular sector, which
describes the ultra reliable low latency communication situations. So, here what is

154
required that latency demands are very stringent, in the massive machine type
communication what we see is that the connection density is required to be stringent.
Whereas, when we look at the enhanced mobile broadband service, we see that network
efficiency, traffic capacity, all these parameters are required to be important.

So, broadly speaking the enhanced mobile broadband act uses a few set of parameters
which are more important for it whereas, massive machine type has a different parameter
or capability which is important for it, and URLLC is another has another important
parameter, which is very very critical for it. So, that is how these different scenarios have
come up and when you talk about a particular scenario with this picture, you can clearly
identify what are the important metrics that are relevant for the particular connection
then a particular scenario.

(Refer Slide Time: 21:45)

So, the other capabilities are of course, flexibility, reliability, resilience, security and
privacy and operational lifetime.

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(Refer Slide Time: 21:55)

So, these are also added requirements as described in it and in this particular figure, it
basically shows the timeline of how the IMT-2020 has been developing over the years.

(Refer Slide Time: 22:07)

So, this also suggests that the focus area for providing the solutions are in the radio
interfaces, and the interoperability access network related issues, spectrum related issues,
and traffic characteristics. So, what we can see is that the solutions that are supposed to
be looked at are primarily driven by the traffic, while most of the solutions lie in the air
interface or the radio access technology, which is the main focus of this particular

156
course. And, this is this statements as have been put down over here are essentially
statements put down by ITU suggesting the different areas, which one has to investigate
in order to find solution towards IMT-2020.

(Refer Slide Time: 22:59)

So, the technology trends as has been identified by 2320 are advanced modulation and
coding schemes, which we intend to also discuss and they will be influenced by the
different deployment conditions like machine type communications, small cell indoor
systems, etc. It also talks about non orthogonal multiple access, which we again aim to
discuss in this particular course, because non orthogonal multiple access has the potential
to achieve the sum capacity, which the orthogonal multiple access cannot achieve.

So, all the orthogonal multiple access is a much easier to implement and can be easily
deployed, the NOMA system has a potential to improve the capacity requirements over
non orthogonal multiple access and we have seen through over the previous few lectures
that the connection density is very becoming a critical requirement, the data rate is
becoming critical requirement. So, we have to find mechanisms by which these can be
enhanced and at least two methods have been identified and we aim to discuss this in the
upcoming lectures.

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(Refer Slide Time: 24:11)

Advanced antenna systems and multi-site technologies are also expected like 3D
beamforming. So, this was as described in M 2320, and we also aim to discuss them
active antenna systems. So overall, this comes under the category of multi-antenna, while
on one side there is a specific enhancements of MIMO schemes, while on the other side
it talks about the RF components such as power amplifier transceivers are integrated with
an array of antenna elements. So, thereby providing improved performance and reduce
energy consumption. So, this is more of a realization of a particular mechanism whereas,
here what we see is, there is a lot of signal processing advancements that have to come in
order to provide these.

Now, with the 3D beam-forming what it says is that as there will be high-rise buildings
then if one can provide a 3 dimensional sectors, then there is even more aggressive reuse
of the spatial reuse of the frequency, which earlier had been restricted to the two
dimensional plane. Whereas, now it will be in the 3D and with more precise beam-
forming, one could provide better coverage to indoor situations in a dense urban situation
in a scenario.

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(Refer Slide Time: 25:29)

Massive MIMO is again one of the technologies, which are expected to provide support
towards meeting the different requirements. Because, with massive MIMO one can get
high beam gain. Massive MIMO, essentially talks about providing very large number of
antennas and interestingly the newer spectral bands, which are expected to be used are
the ones where the wavelength will be much much smaller, thereby the spacing between
the antenna elements are expected to go down even further.

So, if that is going to happen then within a small area, one can plug in a large number of
antenna elements. So, if we go to the millimeter band, that means, 30 gigahertz, 60
gigahertz then a large number of antennas can be packed into a small space and if that
can be done then we have very large number of antennas, which at one point was called
large MIMO systems. And, now the common terminology is massive MIMO systems,
which can provide very high gains in terms of beam-forming as well as spectral
efficiency, which we also plan to investigate in this particular course.

So, technology is to improve network energy efficiency, at some earlier stage, we said
that energy is a very important point it should be taken into account. So, bit per joule is a
suitable performance metric and the cost of energy to operate network is part of the
operational expenses and methods to reduce base station energy consumption can open
up new energy efficient network deployment and the traffic this is primarily, because the
traffic will be both diverse in temporal and spatial domain. So, if that can be exploited

159
then probably a huge amount of energy can be saved, which will again see towards the
end of the course.

(Refer Slide Time: 27:15)

Network densification is of course, we have mentioned that it is one of the ways to

increase the spectral efficiency. So, a cell miniaturization is a one way and that is what is
happening. So, you have more and more closely packed base stations and when you have
them then managing the manually is almost not a feasible task. So, the self optimizing
network methods are expected to be operating. So, that these can coordinate amongst
themselves and choose operating parameters, and maybe handover act as relays and
probably coordinate and do many many things, while at the at the same time the ultra
dense network are also expected to come in.

So, they all are expected to operate in a hand in hand manner and they also go hand in
hand if it is a dense ultra dense network making SON that is self optimizing network is a
natural way of doing things. So, they are expected to operate together and provide a
better spectral efficiency support more connection density and a larger traffic.

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(Refer Slide Time: 28:23)

So, with this we stop this particular lecture over here, in the upcoming lectures we will
specify the minimum requirements of IMT-2020 and thereby setting the ground for
looking into the technological solutions, which we expect to meet those basic minimum
performance requirements.

Thank you.

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 Evolution of Air Interface towards 5G
Prof. Suvra Sekhar Das
G.S. Sanyal School of Telecommunications
Indian Institute of Technology, Kharagpur

Lecture – 09
Requirements and Scenarios of 5G (Contd.)

Welcome to the lectures on Evolution of Air Interface Towards 5G. Till the previous
lectures we have been looking at the different requirements of the earlier generation
communication system as well as we were also looking at the differences.

(Refer Slide Time: 00:33)

That are expected to come in the next generation and we have also seen how the 5th
generation system is getting defined through the description of different scenarios, and in
the previous lecture we have been talking about the different situations that one would
like one would encounter summarily the ultra reliable low latency communication as one
of the scenarios. Enhanced mobile broadband as one of the scenarios and machine
massive machine type as another scenario. And in this particular slide we had
highlighted what are the important performance evaluation metrics that are important for
each of the different scenarios.

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(Refer Slide Time: 01:15)

We had also talked about the other capabilities which are also significant for such
systems such as flexibility in bandwidth and spectrum so that large data rates can be
delivered. Reliability of course, is one of the important things that required to be
improved, so is resilience security and operational lifetime.

(Refer Slide Time: 01:35)

And we were also discussing the timeline of the development of IMT standards. So,
again as per the report what we have is a brief summary of how things have been

163
happening from 2000 to the 2020. So, initially there was issues with spectrum then IMT-
2000 finally, came the IMT-Advanced and then we were talking about IMT-2020.

And the activities started certain somewhere around 2012 2013-14 and we are currently
in this phase where the standards development activity is going on. Release 15 is already
done and work is going on towards the next release in terms of 3GPP. So, it is expected
that around 2020, the deployments would slowly start to come in. Although there are
claims that there are already existing deployments which are kind of somewhat before
5G that is release 15 and hence we are almost going to experience 5G in phases. So, by
2020, it is expected the full fledged deployment of 5G is going to come in.

(Refer Slide Time: 02:45)

And we have also said some of the focus areas are like radio interface, access network,
spectrum and traffic characteristics and we have actually started off with the traffic
characteristics. And in the next phase of the discussion or the lectures in this particular
course we will be interested and we will be discussing more about the air interface which
this course is particularly designed for and we will also talk about the access network and
spectrum related issues which are important for 5G.

164
(Refer Slide Time: 03:21)

So, we have also briefly talked about the different methods or different principles which
would be vital in the previous lectures namely the advanced modulation coding, non
orthogonal multiple access, we will talk about them. Then the advanced multi-antenna
techniques, we have also discussed this particular issue in the previous class and we will
talk in more details about them in subsequent lectures.

(Refer Slide Time: 03:33)

(Refer Slide Time: 03:45)

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Massive MIMO, simultaneous transmission reception, and methods for increasing the
spectrum efficiency or the energy efficiency, is also some of the things as we have said
we are going to take up in the future lectures.

(Refer Slide Time: 03:55)

A network densification, when we had a brief discussion about ultra dense networks and
SON and again we will get an opportunity to see them in more details in the upcoming
lectures.

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(Refer Slide Time: 04:05)

So, now we discuss the minimum requirements for IMT-2020 and these requirements are
specified in the document M 2410 as is being highlighted here. So, this is the particular
document. So, one particular thing I would like to point out here is I have been referring
to several 3GPP documents and numbers. So, with the prime intention that while going
through these slides or going through these video lectures, you would get an opportunity
to download these freely available reports and go through them for more clarity over and
over again.

So, that you are assured and you are yourself sure about what is present in them and
could read them in your own convenience. So, let us look at the minimum requirements
specified for IMT-2020. So, one of the characteristics is the peak data rate which is a
minimum requirement. So, it is the maximum achievable data rate under ideal
conditions. So, this is very very important and it is measured in bits per second that is
pretty normal and it is defined as the received data bits assuming error free condition. So,
this is a pretty important.

So, you can almost do this calculations theoretically because, whatever is transmitted
assumed to be received without error in this particular case. So, this is the error free data
bits assignable to a single mobile station so that means, this is talking about the
maximum number of bits that could be given to one user that is a single mobile station

167
there could be restrictions in the amount of bandwidth that is accessible to one user and
different other constraints.

So, we must take this word very very in a in a significant manner to find out what is the
maximum assignable error free bits to the single user and this will be specified by the
details of the radio access technology which will form part of IMT-2020. So, when all
the assignable radio resources for the corresponding link direction are utilized. So, this is
very very important. So, if I am talking about downlink in that case if all the radio
resources are given to a single mobile station then all the bits that could be transmitted
and received without error would be the peak data rate.

R p  W  SE p

So, for example, if we have let us say 10 resource elements just for the sake of an
example and if we give all these resource elements to this user then the maximum data
rate would be attained when the highest modulation is used highest order modulation. So,
if it is 256 QAM then we are talking about 8 bits per symbol which have to be given to a
user and then you multiply that with the number of symbols that can be carried by all the
resources that can be assigned to a user. And hence you get the total number of bits. So,
if W is the channel bandwidth, SE sub p is the peak spectral efficiency.

So, in that band so, this peak spectral efficiency you will get by calculating the maximum
number of bits that can be sent per unit of hertz and this is influenced by MIMO and all
other mechanisms that come into play. You would also have to take in the error
correction coding so, if you are using rate half encoding, so, 50 percent of the bits are
redundant if you are using rate three fourth, then one fourth of the bits are redundant. So,
if you take that into account in order to calculate the spectral efficiency, then the peak
user data rate R sub p is given by the bandwidth multiplied by the spectral efficiency.

Q
R   W  SE pi
i 1

And if bandwidth is aggregated across Q bands; that means, Q number of bands are put
together through carrier aggregation. Then the total peak data rate is the sum over all
such bands where Wi and SE sub p i over all the bands are the component bandwidths

168
and spectral efficiencies respectively. Now, if this is kind of generic in the sense that the
Wi's are flexible in the manner that it need not be the same value. If they were the same
value would have simply multiplied by Q over here. Further this spectral efficiency in
the different bands may be different by virtue of restriction of the different modes of
operation for certain bandwidth because of many other system level constraint.

So, for each band you will calculate the data rate that is as given by this, you are doing it
for each band and adding it up over the different bands. So, if I have a 20 megahertz and
a 10 megahertz and a 5 megahertz, I may have different spectral efficiency supported.
And if I am aggregating them I have to calculate data rate separately for each of the
bands and put them together. So, when you do it the minimum required requirement for
peak data rate is for downlink direction it is given as 20 gigabits per second. So, 20 Gbps
and in uplink it is a 10 Gbps.

So, these are the minimum numbers which are required to be satisfied. So, if the user if
the system or the radio access technology is such that you can support these numbers
then it will qualify as IMT-2020.

(Refer Slide Time: 09:59)

Next we look at the definition of peak spectral efficiency that was one of the terms in the
previous definition. So, peak spectral efficiency is the maximum data rate under ideal
condition normalized by the channel bandwidth, and here it is the enhanced mobile
broadband usage scenario for which it is getting defined. So now, it is kind of an iterative

169
definition that is data rate is in terms of spectral efficiency, spectral efficiency in terms of
data rate.

So, one could effectively actually calculate the spectral efficiency from which one can
calculate the data rate. And spectral efficiency calculations will be based on the
modulation, the coding rate, the MIMO schemes, the overhead, and everything put
together. So, the minimum requirement for peak spectral efficiency that is the best. So,
here you are going to use the maximum possible loading of bits on a resource block and
this would entitle one to use the maximum spatial multiplexing mode, as well as the
highest order modulation, and the least error protection mechanisms.

So, when you put all these things together you can get the highest spectral efficiency. In
downlink it is 30 bits per second per hertz. Now, if you have a bandwidth of 10
megahertz, you have 300 bits per second. So, if you have a peak data rate of 20 Gbps you
divide by 30 bits second per hertz, you can calculate the maximum aggregate bandwidth
that is supported in each of the directions. Here also we are seeing that the uplink and
downlink spectral efficiency requirements are different, its basically half and that is
scaling to these numbers; that means, the data rate requirements are accordingly scaling
in a ratio of 1 is to 2.

Now, antenna configurations for these things up to eight spatial streams in the downlink
directions and four spatial streams in the uplink direction. Now this way also you can
categorize that when you have eight spatial stream it is theoretically you can support
twice the data rate or twice the spectral efficiency of the uplink which is a hint towards
the numbers which are being reflected over here.

So, essentially its being driven by these parameters which are the pinpoints of control.
So, through these parameters we can get these numbers and from these numbers we can
get back to these numbers with the appropriate multiplication of the bandwidth factor.
And again these are defined for different operating scenarios so that we must be very
very careful and all details are specified in M 2410.

170
(Refer Slide Time: 12:43)

The next important parameter which we are supposed to look at is the user experienced
data rate. So, if we look at the definition it is the 5 percentile point of the cumulative
distribution function of the user throughput, when user throughput during active time is
defined as the number of correctly received bits which is equal to the number of bits
contained in the service data units, which is usually referred to as the SDU delivered to
layer 3, over a certain period of time ok.

So, what it effectively means is that again we are talking about the number of correctly
received bits. So, essentially we can say that the number of bits that can be sent and one
can assume that these bits are received error free and so, you can calculate the users
throughput and then you would find the 5 percentile point on the cumulative distribution
function of the user throughput during the active time.

So, if you would collect all possible data rates that is achievable by the user and then plot
the cumulative distribution function and then take the 5 percentile point. So, roughly
speaking, if let us say this is the user data rates in bits per second and in this side if you
have probability that the data rate is less than the abscissa.

171
(Refer Slide Time: 14:03)

So, generally we have curves which appear to look in this manner and here this particular
line it extends to 1 or 100 percent that is the maximum. And here you have different
values of user throughput, and at a certain point you have the peak value of user
throughput which is here.

So, if we look at the 5 percentile point and read this number you get the 5 percentile user
throughput ok. So, that is how one calculates the user throughput and you get all these
different points by a large number of simulations over the service area. So, once you
collect all those data you can go back so that is how you calculate the user throughput.

Now in case of one frequency band and one layer transmission, one layer means like
SISO reception points, that means, transmits interception point the user experience data
rate could derived from the fifth percentile of user spectral efficiency through this
naturally this is again the same kind of definition we are seeing before. So, you have the
user spectral efficiency multiplied by the bandwidth and you get the user.

Ruser  W  SEuser

So, if there are multiple layers you again multiply this by the number of layers and each
layer would provide a certain data rate and then it is the aggregate data rate in that case.
Now in case of bandwidth is aggregated across multiple bands, that means, one or more
and one or more transmit layers, the user experience data rate will be summed over all

172
the bands, so, that is as defined in the previous case. And the target value in the dense
urban eMBB environment, eMBB is enhanced mobile broadband environment.

The downlink user experienced data rate is supposed to be 100 Mbps and in uplink
which is 50 Mbps; now these are pretty large numbers compared to what were available
in the previous generation systems. And clearly if you compare these spectral
efficiencies in IMT-Advanced you would remember that peak download spectral
efficiency was 15 and uplink was 6.75. Whereas here, if both the numbers have become
almost double and also at the same time we would we may recall that LTE-Advanced
was supporting these figures.

So, in some manner its kind of LTE-Advanced is pretty much equipped to provide these
kind of a spectral efficiency values. So, the newer generation 3GPP technologies and
other technologies may be expected to far exceed these numbers which are provided by
ITU. So, these numbers are kind of already achievable within the technologies that are
available in present day.

(Refer Slide Time: 17:19)

So, moving on and further so, in the previous this definition we had referred to the 5th
percentile user spectral efficiency. So, as was given over here, in case of one frequency
band and dot dot, the user experienced data rate could be derived from the 5th percentile
user spectral efficiency.

173
So, let us look at that particular definition. So, rather this is more fundamental definition
the 5th percentile point of the CDF of the normalized user throughput. So, let us look at
that. The normalized user throughput the number of is basically the number of correctly
received bits, that is the number of bits contained in the SDU that is service data units
which have been defined before, deliver to layer 3, over a certain period of time.

Ri (Ti )
ri 
Ti  W

So, you are taking time into account divided by the channel bandwidth and is measured
in bits per second per hertz. So, the channel bandwidth for this purpose is defined as the
effective bandwidth times the frequency reuse factor, where the effective bandwidth is
the operating bandwidth normalized appropriately considering uplink downlink ratio. So,
if we take everything into account, so, if there is a certain bandwidth and you are sharing
it for a certain fraction of uplink and certain fraction for downlink then that must be
taken into account. With R sub i T sub i denoting the number of correctly bits for user i
and T i is the active session times; that means, that is the duration over which it transmits
for user i and W is the channel bandwidth, then the normalized user throughput of the
user i that is R sub i is defined according to R sub i is equal to this capital R i over T i
divided by T i that is bits per second this is the bits per second per hertz.

So, if we collect all these numbers over the entire coverage region and plot the
cumulative distribution function and then take the 5th percentile point we are going to
get the 5th percentile spectral efficiency.

174
(Refer Slide Time: 19:25)

So, moving further the minimum requirement towards IMT-2020 and the 5th percentile
user spectral efficiency are given in this particular chart and that is again in M 2410. So,
what we see is that in the indoor hotspot enhanced mobile broadband, the downlink 5th
percentile spectral efficiency is given as 0.3 and uplink it is 0.21 I mean these are not
very small numbers because this is the 5th percentile spectral efficiency number. Dense
Urban eMBB is a 0.225 and rural it is 0.12 and these numbers also scale down
accordingly.

So, what we see is that in the rural scenario the number is the lowest, where is an indoor
it is the highest, and urban dense urban is somewhere in between. Now there could be
several reasons for these things which will become clearer. So, in indoor situation you
are very strong desired link and the interference is relatively less when you go to dense
urban you have a strong interfering link, but there are a lot of interference. Whereas, in
rural, the signal power is less because the distance between the transmitter and receiver is
pretty large the cells are expected to be larger in size.

So, its not possible to provide very high signal strength in such situations because
smaller number of cells are expected to cover a larger area and hence the outage or the 5
percentile spectral efficiency is having a smaller value. And these requirements as given
in this particular note will be evaluated under the macro transmits transmit received point
layers of the dense urban eMBB test environment defined in 2412.

175
So, when we look at M 2412, it describes in details how do you create the environment
over which you test these things and there these definitions will become even more
clearer. And once you set up the environment run your system, get these numbers, then
we should match with these, and if it satisfies these numbers then again you can claim
the technology to be IMT-2020 compliant.

(Refer Slide Time: 21:43)

 R (T )
i 1
i
SEavg 
T W  M

Then the next important term is the average spectral efficiency. So, this average spectral
efficiency corresponds to the definition of spectrum efficiency within quotes as it has
been given over here in M 2083. So, you could refer to M 2083 and see the definition of
spectrum efficiency and which is basically the one which is the average spectral
efficiency in this case. So, if R i R sub i T denotes the number of correctly bits for user i
which is in the sub index from user i in downlink I mean received by user i in downlink
and from user i on uplink in the system comprising of user population of N users.

So, you have a environment where there are N users, i is one of the users and there are M
transmit receive points. Furthermore let W denote the channel bandwidth and T the time
over which the data bits are received, the average spectral efficiency SE sub average is
defined as you sum over the data rates of all the N users and divide by T which is the

176
time of transmission, W the bandwidth, and M TRx P s. So, then you get the average
spectral efficiency. So, effectively what you are seeing is that you are averaging it over
the different users that are present in the system.

So, different test environments are described in 2412. M 2412 is the document which
describes the way to evaluate these things and 2410 basically tells you what is the
minimum numbers, which these should be satisfying. So, in the indoor hotspot what we
are seeing is the average spectral efficiency in downlink should be 9 ok. Whereas, we
had seen the peak spectral efficiency numbers earlier it was 30 bits per second per hertz
right and we have also seen that in indoor hotspot the downlink 5th percentile user
spectral efficiency is 0.3.

So, here what we are saying is the average is 9, in rural the average is 3.3, and in dense
urban it is 7.8 for all reasons which we have discussed earlier, and in uplink it is 6.75.
So, what we are seeing is that on an average 6.75 bits per second per hertz is required to
be supported by IMT-2020 whereas, this was the peak spectral efficiency for the
previous generation system and again everything is described in 2412.

(Refer Slide Time: 24:31)

Then we look at the next important metric according to which things have to be
evaluated and one of them is the area traffic capacity. So, area traffic capacity is
described as the total traffic throughput served per geographic area in megabits per
second per meter squared.

177
Carea    W  SEavg

So, what you are seeing is that the meter squared comes into play. So, over a certain area
whatever throughput is getting served, you divide it by the total area. So, per bits per
second per meter squared; that means, over every unit of area how much is traffic is
flowing through. So, if W denotes the channel bandwidth, and rho the transmit receive
density; that means, so many transmit receive points per meter squared, the area traffic
capacity that is C sub area is related to the average spectral efficiency which you have
defined before as the area as C area that is the traffic for the area is the density of TR xP
multiplied by the bandwidth multiplied by the spectral efficiency.

So, this is the spectral efficiency you multiplied by the bandwidth you get the data rate;
that means, you get bits per second and then you multiply by the density of the transmit
points per meter squared and then you get bits per second per meter squared. The target
value of the area traffic capacity and downlink is 10 megabits per second per meter
squared; that means, roughly speaking if you are taking indoor environment for every
meter squared you can expect 10 megabits per second it roughly translate to that.

So, over an area that is the kind of traffic it should be able to support that is kind of a
another definition which was not much prevalent in earlier generation systems. In terms
of latency the user plane latency we have defined the control plane latency and user
plane latency earlier the minimum requirement for user plane latency are 4 millisecond
in enhanced mobile broadband scenario, and one millisecond in the ultra reliable low
latency communication scenario.

So, what we are saying is that in the low latency communication scenario, the latency
requirement is 1 millisecond which is very very stringent requirement, and in the mobile
broadband requirement it is around 4 milliseconds, which is not that stringent but still
these numbers are much lower than the latency requirements in the previous generation
system. So, with one millisecond latency constraint one should be able to control a lot of
industrial applications to a great extent.

178
(Refer Slide Time: 27:13)

So, control plane latency is again defined over here as the transition time from the state
of idle to the state of active we have discussed this earlier, and the minimum requirement
is 20 milliseconds which is also much reduced from the from the earlier generations. And
it is also saying that the technologies should be able to or may be supporting even lower
number that is always welcome. Connection density is something which we have seen
before in the graphs is the total number of devices fulfilling a specific quality of service.

So, it is not just the number of devices the devices which satisfy the QoS per unit area.
So, whenever we give these numbers, the QoS support is always to be taken into account
and QoS is to support delivery of message of a certain size within a certain time and with
up to a certain success probability again these are defined in 2412. So, this defines the
specific method or the way of calculating QoS and the minimum requirement for
connection density is 1 million devices per kilometer squared.

So, it is kilo meter squared. So, now essentially you are seeing that if we have smaller
and smaller cells with cell radius of a few 10s of meters it probably becomes more
feasible to support such things where these kind of situations are expected to be
encountered in massive machine type communications.

179
(Refer Slide Time: 28:41)

So, there are energy efficiency requirements, reliability requirements are also there, in
terms of mobility requirement, now, what we see is that even higher speeds are required
to be supported.

(Refer Slide Time: 28:49)

So, we will see a few more of these in the next lecture and then begin our discussion on
the waveforms which is one of the first most important thing that we are supposed to see
in the next generation systems. And we will begin with discussion of the earlier
generation system because there lies the foundation of some of the important things

180
which have come up later and which will also come up in the systems which go beyond
the 5th generation communication system.

Thank you.

181
 Evolution of Air Interface Towards 5G
Prof. Suvra Sekhar Das
G.S. Sanyal School of Telecommunications
Indian Institute of Technology, Kharagpur

Lecture – 10
Requirements and Scenarios of 5G (Contd.)

Welcome, to the lectures on Evolution of Air Interface Towards 5G. So, currently we are
reviewing the minimum requirements for IMT 2020 or 5G.

(Refer Slide Time: 00:27)

And in the previous lecture we were seeing some of the requirements. So, here we
continue on that. So, as was briefly mentioned that energy efficiency is an important
metric which we should be taking care of. And in that efficient data transmission in
loaded case is something which we, we should look at. As well as low energy
consumption when there is no data.

So, these are the two different aspects which are to be looked at and we will try to look at
some of these in the later part of the course. Reliability is in the range of 1 minus 10 to
the power of minus 5 success probability, that is very huge success probability for layer
2 PDU of 32 bytes within 1 millisecond in channel quality of coverage edge for the
urban macro URLLC test environment, assuming small application data.

182
So, basically it talks about huge success probability when you talk of reliability, a packet
delivery probability; that means, with a very large number of packets most of it is
successfully delivered within the channel conditions of the test environment as would be
specified. So, this ultra reliable low latency communication test scenario which is of
interest under this condition a very high success probabilities is required during low
latency, a very low latency has to be satisfied.

And there is certain packet size which is to be a specified and probably larger packet size
would be also ok, but one has to check with the latency requirements. So, such
requirements are usually with respect to control and command applications. So, then
large packet size is generally not the situation in that case which has to be delivered
within short delay.

(Refer Slide Time: 02:15)

So, moving beyond this was one of the last things that we were seeing in the previous
lecture. So, here mobility has been specified in multiple classes like stationery,
pedestrian, vehicular, and high speed vehicular. So, there are different range of velocity
stationeries of course, 0 km per hour, a pedestrian is like walking. Vehicular is with the
traffic with cars and others other things moving around in city and urban areas, semi
urban area.

Whereas high speed vehicular is kind of moving on highways and high speed trains so
speed up to 500 km per hour have to be supported. So, what this essentially means is that

183
this influences Doppler and further when we have higher and higher frequency bands,
the cumulative effects become terrific. So, that has to be addressed in some of these
solutions.

(Refer Slide Time: 03:05)

So, the traffic channel link data rates normalized by bandwidth have been specified with
different mobility conditions. So, what is it saying like under indoor conditions, one has
to take the pedestrian and the normalize traffic channel link data it is bits per second by
hertz is 1.5, whereas in rural the mobility is 120 and 500 kilometers per hour two
different cases are have been have been given. And the spectral efficiency of bits per
second per hertz is given by this numbers. So, what we essentially sees that as your
mobility increases, the spectral efficiency decreases, for all reasons of communication
and channel properties that keep on getting worse and worse, when higher and higher
mobility comes into play.

So, what it also says that it should support bandwidth of 1 gigahertz above 6 gigahertz.
So, when you talk about millimeter wave band this becomes 1 gigahertz bandwidth is
required to be supported when we give the specification of bandwidth. And at least 100
megahertz have to be supported in the other bands that means the sub 6 gigahertz. So, if
you go to higher spectrum and we add mobility to that it becomes a terrible situation to
address.

184
(Refer Slide Time: 04:23)

So, what we summarize now all our discussion till date as what we could see is that there
are diverse deployment scenarios. We have seen at least three different deployment
conditions, there is diverse spectrum, we have clearly seen here that one is below the sub
6 gigahertz and the other is above 6 gigahertz which is usually in the millimeter band.
And when you go to the 30 gigahertz or 50 gigahertz or 60 gigahertz band of spectrum
the propagation characteristics of different the device characteristics are different.

So, this spectrum actually makes provides make lot of impact on the system design. As
well as not only is your device get influenced, but the available bandwidth is different.
And since the bandwidth is different therefore, again you have lot of opportunity to play
around with the design of the system.

So, the spectrum is not a single spectrum nor is it uniform it is kind of quite different
which is to be present. And they would be variety of services and variety of devices like
machine type communication, smart-phones and all things would be present. So, what
we are seeing is that by one single technology, one is required to serve different
deployment scenarios, different spectrum, and different devices and services, and this
gives birth to the new radio also referred to as the NR.

So, there on we will start looking at some of the new aspects which have been
introduced. But we will lay our foundation strong by revisiting the things which have
happened earlier because what things are going to come in future have their foundation

185
on what is happened in the past. So, we will kind of go back and forth in building the
foundation as well as looking into the future technologies.

(Refer Slide Time: 06:19)

So, in this particular screen or in this particular slide we have more or less summarized
some of the important aspects or some of the notable contents which come as part of air
interface for the next generation. So, the self organizing networks have been there and
they will still remain very very critical for the fifth generation system. One very
important thing that is come up is scalable OFDM wave numerology which is part of the
new radio which we will discuss. Multiuser Massive MIMO, some sometimes this is an
extrovert put along with massive MIMO.

But this class this clarifies the entire details this is also an important part of the fifth
generation system. LDPC coding has already been there are more error correction codes
which are potentially capable of providing the necessary benefits that are required. Low
latency slot structured design. So, basically the to support the low latency one has to
redesign the frame structure which is otherwise not supporting low latency; that means,
if we look back at the LTE-Advanced or the fourth generation system it is not capable of
supporting a very low latency of 1 millisecond as desired in this.

Adaptive beamforming and beam tracking especially in case of millimeter wave is also a
very very important. So, we will get some time to look into these aspects. Non
orthogonal multiple access, data offloading into heterogeneous networks, so these are

186
some of the important modifications or enhancement or improvement in the radio access
network or overall radio access technology, which drive the future generation or the fifth
generation mobile communication systems.

So, with this we more or less close our discussion on the understanding of how the
requirements come up. And how things have changed from previous generation right
from second generation to fifth generation with one of the important motives is to
understand or to kind of train ourselves and kind of predict the future. That what is
expected or how things are going to grow because, we have seen this industry for quite
many decades now. And the other aspect is also to highlight how the numbers have
changed and what new requirements have come in as well as the deployment scenarios
are becoming different.

So, I mean in overall this entire growth in all possible dimensions. If you look back in
what we have discussed some of the early generation systems had only few parameters
and only countable objectives to meet. Whereas in the newest generation of technologies
the number of parameters to be observed or measured has increased phenomenally as
well as the requirements have also grown many folds. And if you check back with the
amount of data that is expected to be flowing around in these networks it is I mean and is
beyond the normal imagination, it is a huge amount of data. And, what has what is the
outcome of such things is that we have been able to get new technologies new solutions.

So, there was a challenge and the challenge has been met quite successfully and a lot of
development has happened in the technology front which we hope is only going to help
us help us help the society evolve into a better human society and more safer and
probably much superior being in the future. So, with this we continue on this particular
lecture and we will look at some other aspects that are necessary as part of the
curriculum yes. So, we continue with the next lecture.

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(Refer Slide Time: 10:13)

So, in the next part of what we have to cover somehow we were not well synchronized
with the timelines for each of the lectures slot, but that does not matter we will continue.
So, far we have seen the requirements and specifications we also seen the requirements
for the fifth generation. And now we are supposed to look into the solutions for the fifth
generation. But however, I thought it is pertinent that will look back at some of the older
solutions and some of the foundations.

Now the reason is that if we are supposed to begin with the study of waveforms. Now
when we look at the waveforms for the fifth generation we can get a jump start and get
into things. But we also have said that we also want to look at some of the front runners
in the waveform technology that were in the contention towards being a air interface.
Here it is important to note that how things have evolved over time when the second
generation came in; there was the TDMA, FDMA approach or the GMSK which was the
fundamental waveform.

At that time the spread spectrum communication was also well known and it was also
being discussed. But however, with consensus people choose to remain with TDMA
FDMA and they came up with GMSK. They rejected the spread spectrum method of
communication which could provide us the CDMA technology. When the third
generation solutions were been discussed, then the multi carrier or OFDM based

188
technology was already available. Now at that time, spread spectrum or CDMA
technology was a little bit more mature.

And then if you look back into the waveforms for the third generation, it was spread
spectrum communication, it is rather CDMA communication and it is also known as
WCDMA wide band CDMA. Whereas, OFDM although was pretty much available was
rejected as the candidate wave form. When we move forward and go into the fifth
generation what we find is that in the period of 2010 to 2015-16, there have been several
candidate technologies which were in the foray. And they were like generalized
frequency division multiplexing, filter bank multicarrier, UFMC and many other
windowed OFDM and many other proposals which have been there.

However, what has been accepted is large largely of variant of OFDM, which is the
small scalable numerology structure of OFDM. So, what we see is that at every stage
some technologies which are new which can contend with an existing technology or
more mature technology, are proposed, their well compared and usually where this more
consensus, it is taken. So, it is very vital that we also look at the wave forms which were
there and contending for five for the fifth generation candidate technology.

Because there is a high potential that one of them will become air interface for next
generation not simply by virtue of the progression of history. But these were being
developed by a large number of people over a long period of time because they had felt
that OFDM has certain shortcomings which need to be addressed. So, over the next few
years it is further expected that these waveforms and these technologies are even
improved beyond what they are available today more things get added to them, so that
they are more matured and they can probably replace the existing OFDM and overcome
some of the shortcomings which OFDM has. Now incidentally some of the important
waveforms in this category have their roots in the second generation system and some of
them like filter band multi carrier and others I have a special property by which the out
of band radiation, that means, when the signal goes out into the air interface then the
amount of signal that leaks outside its bandwidth is much lesser in the schemes than in
OFDM.

And if we look back at what happened in the second generation that is the GMSK; it is
one of the most bandwidth efficient signaling techniques. And when we will look at

189
some of the base line structures and if you study them it will be easier for us to study the
filter bank multicarrier and other setups because it is built on the same platform. So, in
order to create, setup the platform we decided that let us look into the basics and through
which we will cover the earlier generation. As well as give us it will give us the premise
and foundation for looking into the future generation systems which are yet to come in.

So, with this we set up the basic signal model. The other intention for us to look into this
basic signal model is that they would be many participants who have been working with
lot of advanced protocols and mechanisms. But when we talk about signals we need to
get back to the basic framework, the basic way of writing the expressions so that it so
that we benefit end of the day by revisiting some of the original things so that we get
trained. And finally, we are able to write the newer solutions by ourselves.

So, for that we need to relook at the foundation we will not really going to lot of great
details, but only the important foundation that is necessary to help us carry through the
important parts of this particular course. So, with this let us get into the basic signal
model.

(Refer Slide Time: 16:37)

So, typically when we communicate the channel is usually band limited, I mean that is
kind of understood by all of us. We do not have infinite bandwidth to transfer the given
signal because the channel is split into smaller-smaller chunks and each particular
service is given one particular set of bandwidth that is pretty well known to many people.

190
And those were new in this particular domain just taken example of GSM where each of
the carrier occupies 200 kilohertz overall 1.25 megahertz that is kind of given for
communication. If you look at the fourth or the fifth generation is kind of overall 5
megahertz is given for any one communication band. So, it is always decide the signal
occupies a certain finite bandwidth.

And hence we usually say that the channel is the band limited and of course, it is centred
around the carrier frequency. There is a carrier frequency which is associated with the
band. And when we talk about the sub 6 gigahertz, we also mention the centre frequency,
when we talk about the millimeter wave we also mention the centre frequency. So, the
carrier frequency is kind of the centre of frequency. So, signals and systems and channels
are usually narrowband.

And so we are talking about narrowband systems. In narrowband systems, the bandwidth
of the system should be much much less than the centre frequency. So, rule of thumb
could be 10 percent, but usually it is even smaller than that. So, we are generally going
into the realm of narrowband systems that is something we should remember. The
transmitter generates a band pass signal that is again something many probably young
students would also participating in this particular course and our intention is to set
things proper.

So, just to get things in place, the band pass signal is essentially the signal which has a
certain band centred around a carrier and carrier is not 0 alright. So, that is what is meant
by band pass and when the carrier is 0 and you have your signal which is spanning
around the 0. So, it is usually the base band or the low pass signal that is what is referred
to we will see them in the in the model. So, usually it is convenient to represent in
equivalent low pass forms, this is what you usually study in digital communications; that
is when we are studying systems we can create a signal which we can up-convert to any
frequency of our choice. At the receiver, we have to down convert the frequency and
then do the baseband processing.

So, what is very important is that we will look at the baseband signal processing part or
the baseband signal model part. Because, if it is only the carrier and we can choose any
value of the carrier then we should rather focus on the baseband part and when necessary
we can uplift carrier to a particular centre frequency and down convert it at the receiver.

191
However, we will not put in this particular model, but we will see later on is that since
the signal is band pass, it passes through a band pass channel, to analyze the overall
effect we should also have the equivalent low pass of the channel. And so that we can
study the entire transmitter channel receiver in the equivalent low pass form.

So, one of our objectives here is to start with this setup so that all of us who are on board
are able to handle this setup. I understand that many of you already know this, but I also
believe that the some of us who would who would be benefited with this basic analysis.
So, we consider s(t) as the signal which is real valued and s(t) is narrowband and centred
around the carrier frequency fc. So, the aim is to get the mathematical expression of such
a signal that is that is what we are interested to do. So, we first construct a signal which
contains only the positive frequencies is in s(t).

So, that is the first step towards getting that so that means, your S(f) which is the
spectrum of s(t) is having plus fc and minus fc and signal is around fc ok. So, the fc is
the carrier frequency, the signal is somewhere around fc and it can have particular
structure of the spectrum of occupancy. So, when we say that we want only the positive
set of frequency, that means, we are interested only this frequencies and the other reason
is that from this you can regenerate them. So, it is probably good enough to do with the
positive set of frequencies.

(Refer Slide Time: 21:23)

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S  ( f )  2u ( f ) S ( f )

So, S plus of f which the plus indicate the positive frequencies and S(f) indicates the
spectrum of s of t or is the Fourier transform of s(t); is two u(f) times S(f). So, where S(f)
is the Fourier transform and u(f) is the unit step function in the frequency domain. So,
that means, you take only the right hand portion and you do not consider the left hand
portion. So, that means, as if we do not consider this, but since you considered only half
of them because if taken the unit step function, you multiply by 2 so that the total power
or the total energy is conserved right.

s (t )   S  ( f )e j 2 ft df  F 1  2u ( f )   F 1  S ( f )  , where F 1  S ( f )   s (t )
j
F 1  2u ( f )    (t ) 
t
j
s (t )  s (t )   s (t )
t
1
Define: s ^ (t )  h(t )  s(t ), where h(t )  (Hilbert transformer)
t

So, that is why we have 2 u(f) S(f) in order to describe the signal which is not a to
describe the signal which contains the positive frequencies. The equivalent time domain
expression would be s plus of t which is the inverse Fourier transform of S(f) or S plus of
f. So, which is the inverse Fourier transform of S plus of f, if you look at it; it is basically
these two things these two things. So, it is convolution of the inverse Fourier transform
of 2 u(f) and that of S(f). Now we already know that the inverse Fourier transform of S(f)
it s(t) or S(f) is the Fourier transform s(t) by definition that is what we have over here
that is what have been given over here.

So therefore, it is a convolution of two time domain signals, the inverse Fourier

transform of 2 u of f can be written as delta t which is the delta function plus j upon pi t.
So, what we have is this entire function convolved with s(t) this is s(t). So, delta function
convolved with s(t) is s(t) and this particular is expression is something which we should
look at. So, here we will define s hat of t as h(t) convolved with s(t) where h(t) is defined
as 1 upon pi t. So, see that you have one upon pi t over here, if I define this as h(t) then
h(t) convolved with s(t) is defined as h hat of t. So, this h(t) which is 1 by pi t is usually
known as the Hilbert transformer right which is a 90 degree phase shift.

193
s (t )  s (t )  js ^ (t )
Equivalent Low pass Sl ( f )  S  ( f  f c )  sl (t )  s (t )e  j 2 fct
sl (t )   s (t )  js ^ (t )  e  j 2 fct  s (t )  js ^ (t )  sl (t )e j 2 fct

So, s plus of t can be written as s of t plus j s hat of t going by this expression. If you use
this particular line in the previous you get s plus of t plus j s cap or s hat of t. So, this we
have obtained as the inverse Fourier transform of s plus of f. So, essential in this is the
time domain signal which contains the positive frequencies only; the equivalent low pass
that is Sl of f ok.

So; that means, we want equivalent low pass from this it is very easy that S plus f plus f
c; that means, whatever is if I put S l of 0 we get s plus of fc correct so; that means, this is
down converting your s plus of to Sl right. So, that it is removing the effect of fc right.
So, this is the low pass equivalent form. So, if I put f as the value which is just a little bit
positive that means delta positive this is S l of f is basically s plus of f c plus the little bit.
That means, in other words it is nothing, but this particular point. So, like that we can
keep increasing values of f and we can collect all the values of f over here and all the
values of f over here. So, essentially speaking Sl of f would appear like this centred
around 0.

So, that Sl of f and then we can get the sl(t) that is time domain representation by simply
getting from this, which is S plus of t by Fourier transform properties e to the power of
minus j 2 pi fc t which is also representing a down conversion operation. And which is
equivalent I mean this also is equivalent to the expression of down conversion which is
done at the receiver. So, that frequency domain translation of frequency in time domain
it is simply the down conversion on multiplication by e to the power of j.

So, this is by virtue of Fourier relationship. So, s l of t that is what we have is the low pass
equivalent of the positive set of frequencies of the signal or the signal containing only the
positive frequencies; can now be written as s plus of t. We have obtained s plus of t
which is over here that is s(t) plus j s cap of t. And we have the remaining term e to the
power of minus j 2 pi fc t. So, what we have over here in other words we could also write
that s(t) plus j s cap of t is s l(t) e to the power of j 2 pi fc t. So that means s l(t) is
modulated and here what is see it is demodulated.

194
So, this is like up conversion of the low pass equivalent form of the message and this is
the structure as it should be. And it is kind of a single sideband transmission that what
you have studied earlier in analogue communication systems and other courses. So, this
is the baseline structure which some of you have already done and those who still
remember it is a revision of those concepts. And those who have probably forgot I mean
it is a good way to recapitulate some of the things.

(Refer Slide Time: 28:03)

sl (t )  x (t )  jy (t )
s (t )  x(t ) cos(2 f ct )  y (t ) sin(2 f ct )
s ^ (t )  x (t ) cos(2 f ct )  y (t ) sin(2 f ct )

Also s (t )  Re  x(t )  jy (t )  e j 2 fc t 
 
 Re sl (t )e j 2 fct , Re  real part

So, therefore, what we see is that sl is in general a complex nature. So, what we see over
here sl is having here j and there is e to the power of minus j. So, in general this is a
complex in nature. If this is complex in nature I could write s l of t as generically x(t) plus
j y(t) because this is of complex form what we have seen. So, I could say that let me
write it in this form so then I have to connect what would be the relationship of x(t) with
s(t) and y(t) with s(t). So, we are saying that let this whole thing quickly, let me take this
whole thing let us write it as x(t) plus j y(t) right.

195
This is what we have mentioned yeah and this is exactly what is written over here. So, if
we replace this into the previous equation what we are going to get is s(t) equals to x(t)
cos 2 pi fc t minus y sin 2 pi fc t. So, this is also straight forward because you can clearly
see that you would be writing that x(t) plus j y(t) e to the power of minus j 2 pi fc t and
this would expand as cos 2 pi fc t minus j sin 2 pi fc t.

So, simply x(t) cos 2 pi fc t would come over there and y(t) sin 2 pi fc t would come over
there. So, then you have to go back to the previous page and equate the different terms
that is there. So, we have sl(t) with this and we have said that s(t) is real valued. So, if
you take the real valued part of this then. So, basically we are going to have the other
terms which is the j y(t) cos t and j x(t) sin t. So, the real valued terms are x(t) cos 2 pi fc
t and y(t) sin 2 pi of fc t.

So, this is the real value terms that you encounter with s(t) and so, this is what is the
expression of sl(t) right and s cap of t is basically the other component which is the j
component. So, what we have over here is essentially the s of t in the desired form as we
required. So, what we get is there is that the transmitted signal there is a cosine carrier is
a sine carrier which are quadrature in nature. And we have signal bearing form that is
x(t) and y(t) which is going to carrier signal.

So, this is a basic structure on which we have to build up on for all possible future
expressions. And I think it is very vital that we abide by this framework. So, that all
representations that we will do will fall into place. So, when we have s cap of t we have
already discussed this. So, you could also write s(t) what you have done as the real part
of this particular thing right; which we have actually done it over here. So, that we could
say that it is sl(t) e to the power of j 2 pi of fc t right. So, when you say it is s l(t) e to the
power of j 2 pi fc t.

196
(Refer Slide Time: 31:57)

Also, sl (t )  a (t )e j (t )
where, a (t )   x (t )  y (t )
2 2
and  (t )  tan 1  y (t ) / x(t )
Then,

s(t)=Re sl (t )e j 2 fct 

 Re a(t )e
j  2 fc t  ( t )

 a (t ) cos  2 f c t   (t ) 
a (t )  signal envelope,  (t )  phase of signal

We could also say that we let us right s l(t) which is in general complex as a(t) e to the
power of j theta(t) in general we can write that. So, where a(t) is square root of x squared
t plus y squared t and theta is tan inversed y(t). In that case s(t) can be written as real part
of this already you have seen in the previous page and a(t) e to the power of j 2 pi theta
fc plus theta(t). So, if you are taking the real part; a is real because it is the amplitude
over here cos 2 pi fc t plus theta(t).

So, this is the familiar form which we are generally used to when we are discussing
signals. And this clearly brings out all possible ways of handling the particular signal
because here we have a(t) which you can modulate and you get amplitude modulation
you modulate theta you will get phase modulation. You also access to carrier that is and
you get frequency modulation.

197
So, we would like to stop the discussion of the signal model over here now. And in the
upcoming next lecture; we will carry on with this basic framework to develop the
structures that were there earlier. As well as it will provide us the premise to look into
the structures or the signal model that have been there in the IMT-Advanced, as well as
that are going to appear in IMT-2020.

Thank you.

198
 Evolution of Air Interface Towards 5G
Prof. Suvra Sekhar Das
G. S. Sanyal School of Telecommunications
Indian Institute of Technology, Kharagpur

Lecture – 11
Fundamental Framework for Waveform Analysis

Welcome to the lectures on Evolution of Air Interface Towards 5G. In the previous
lecture, we have started discussing about the basic framework or the signal model which
is the primary framework based on which we will study the different waveforms.

(Refer Slide Time: 00:36)

And what we have done in the previous lecture summarily is to discuss about how we set
up the system model and we have started off with writing the expression for s of t as is
shown in this particular slide, we have discussed this in the previous lecture.

199
(Refer Slide Time: 00:51)

sl (t )  x (t )  jy (t )
s (t )  x(t ) cos(2 f ct )  y (t ) sin(2 f ct )
s ^ (t )  x (t ) cos(2 f ct )  y (t ) sin(2 f ct )

Also s (t )  Re  x(t )  jy (t )  e j 2 fc t 
 
 Re sl (t )e j 2 fct , Re  real part

And from which we were able to get the expression of s(t) which is the band pass signal
in terms of the expression which is here where we have the quadrature carriers cosine
and sine and we have information bearing signals x(t) and y(t). So, and the h s cap of t
which is the Hilbert transform, you can clearly see its the cosine becoming sine and sine;
there is a mistake over here, they should be cosine and so on. So, essentially we have set
up the basic expression that will be required in all future expressions. So, we will follow
this part.

200
(Refer Slide Time: 01:28)

We also said that sl(t) being complex as was shown in this particular slide.

(Refer Slide Time: 01:33)

201
(Refer Slide Time: 01:35)

And the one before that sl(t) is in general complex as it looks over here and therefore, we
could write it as in terms of x plus j y.

(Refer Slide Time: 01:39)

And hence we could also write it as a(t) to the power of j theta t.

202
(Refer Slide Time: 01:42)

Also, sl (t )  a (t )e j (t )
where, a (t )   x (t )  y (t )
2 2
and  (t )  tan 1  y (t ) / x(t )
Then,

s(t)=Re sl (t )e j 2 fct 

 Re a(t )e
j  2 fc t  ( t )

 a (t ) cos  2 f c t   (t ) 
a (t )  signal envelope,  (t )  phase of signal

So, a(t) in that case would be related to x and y as square root of x square t plus y square
t and theta t is tan inverse y(t) upon x(t). So, by which we could also write s l(t) in this
form. Now, once you write sl of t in this form then you could write s(t) as real part of s l(t)
e to the power of j 2 pi fc t. sl(t) you replace by a(t) e to the power of j theta(t) as given
over here and the rest of it comes in this part. So, since you are taking the cos, we
discussed this earlier that a(t) you take the real part; therefore, we get the cos a(t) is real
cos 2 pi fc t plus theta(t) and a(t) is the signal envelope and theta(t) is the phase and when
you do all kinds of modulation, will be concerned with these two things and the
characteristics of the signal are dependent or you can describe them through the
expression as given in this particular equation.

So, now, will again briefly look at the baseline simulation sorry baseline modulations
because we would ramp up from almost ground 0, but we will do them pretty quickly so

203
that we finally, arrive at our destination and look at the key features what we want to aim
at.

(Refer Slide Time: 03:06)

So, a basic one, that we all know that, there are different kinds of modulation, that is with
memory, without memory less modulation and with memory modulation. And in
Memory Less Modulation every symbol or every group of symbols or rather bits go into
a symbol duration and the next symbol duration which takes the next few bits are
independent of any previous output. So, that is a memory less. So, the current output
does not depend on what has happened in the past. And, usually I mean they are linear
system, so, you have a Linear Superposition theorem applying on them and things are
more or less quite easy to analyze and they have their own issues along with that.

So, this Pulse Amplitude Modulation is one such method; whereas, there are other
methods which use memory in the modulation and they are generally the class of non-
Linear Modulation and so they have distinct features, although this is generally followed.
So, what you will find is that when we talk about the fourth generation system that is
IMT-Advanced, they would be they are using the class of memory less modulation.
Whereas, if we look at the second generation, it is with memory modulation because of
certain constraint and as we were discussing in the previous lecture that the upcoming
that is the next generation beyond what is probably in 5G, we also expect with memory
modulation.

204
So, that is why we would like to go through this basic structure so that we are equipped.
So, the basic framework to handle both of them and get insights about how and what is
the benefit of different kinds of these systems and how do they influence these IMT-
Advanced and the next generation communication system?

sm (t )  Re  Am g (t )e j 2 fct 

So, the pulse amplitude modulation is straightforward where you have the amplitude and
this is the gating pulse or the pulse shape and this is the carrier. So, this Am carries the
signal and this is the sm(t) that is the m-th signal going in the pass band is represented in
this form, which is straightforward extension of what was before. So, in the expression
here we had a(t). So, a(t) is essentially Am which is the fixed amplitude and g(t) is the
pulse. So, it is the pulse amplitude modulation, amplitude of the pulse getting modulated
pass band signal; therefore, we have the real.

(Refer Slide Time: 05:39)

sm (t )  Am g (t ) cos(2 f ct )

And the g(t) is real valued and we can also look at the standard amplitude modulation
with this and more or less how the signals would be is you have the pulse, there is a
certain carrier given by the cost 2 pi fc t which is due to the real part of this and as the
amplitude changes, either it could be small amplitude or large amplitude. So, this is s 1

205
this is s2. So, for 0 you could have s1; 1 you could have s2 and so on and so forth. And if
you have more number of bits coming into one symbol; so, if there are 3 bits that go into
one symbol, then you have 2 to the power of 3 different waveforms or 8 different
combinations or 8 different levels, 8 different amplitude values and we look at pass band
signal.

Ts  kTb

There will be different amplitudes, 8 different amplitudes; all having the same carrier
frequency. So, that is how the thing is and the symbol duration will be k that is number
of bits per symbol times the bit duration. So, that means, if I increase k, then effectively I
am increasing the symbol duration. So, if I am increasing the symbol duration, I am
effectively reducing the bandwidth right. So, if we have a smaller bandwidth, then in
order to send more and more bits; you would have to go for higher and higher bits per
symbol duration and have more number of amplitudes. You could use quadrature
amplitude so that you could pack more bits into the system.

But overall the structure remains the same and hence to increase the spectral efficiency
that is one of the terms which we have seen before that means, if you are interested in
increasing the spectral efficiency, we have seen this term before bits per second per
hertz. So, in this case our bandwidth if it is constrained; that means, it is a fixed
bandwidth then simply to increase more bits you keep increasing k and thereby, you can
increase the spectral efficiency. Of course, the energy consumption also goes up. So,
when if you are looking at energy efficiency, then these two things are probably at
conflict and there is suitable design has to be done out of this ok.

206
(Refer Slide Time: 07:55)

Am   2m  1  M  d , m  1, 2,..., M
k  log 2 M

So, now moving down further, again this framework will be useful finally when we get
into the more complex waveforms. So, Am that is what we have mentioned earlier will
take different values according to the changing values of small m which can go up to
capital M and number of bits that go per symbol, it can typically be represented in this
format ok. Log base 2 of capital M and you could assign the amplitudes as per the
expression which is again pretty standard and well known expression, available in
generally textbooks for digital communications.

s1 (t )  d g (t ) cos(2 f ct )
s2 (t )  d g (t ) cos(2 f ct )

So, in this we will find that 2d is the distance between the adjacent amplitudes. For
binary case, this is the simple structure that is this is the 0; this is a symbol s1 which is
having an amplitude of d. s2 having a symbol amplitude of minus d. So, the distance
between them in this particular picture is 2d and this is a very basic implementation and
as you can see if I put s 1 as d and s2 as minus d, our s1 of t and s2 of t that means, sm of t;
m is equal to 1 comma 2 is what we get minus d. I mean it has got swapped over here
times g t. g t is the pulse shape we will see the effect cos 2 pi fc t and the other one is d

207
cos 2 pi fc t. So, this is a basic framework which can be simply extended and the spectral
efficiency can be improved.

(Refer Slide Time: 09:29)

sm (t )  Re  Am  g (t )  jgˆ (t ) e j 2 f ct 

So, when we when you are doing carrier modulation with pulse amplitude modulation,
we get DSB that is Double Side Band and in order to reduce the bandwidth occupancy,
you can go for a single sideband and in case of single sideband your signal would be like
Am and the pulse shape folded and you have a real part of it. So, thereby you have single
sided spectrum.

So, you can clearly visualize this particular picture with respect to the signal
representation that we had done earlier for s s of t which had s s(t) plus s lt plus j s cap l t
and that is similar to what we are representing over here. Only thing is that on both the
real and imaginary it is the same information, then only we are able to do it and in
basement transmission, it would appear in this form.

208
(Refer Slide Time: 10:28)

So, these are some of the things which we already know and then, the next important
thing that we are going towards and it is very very valid in terms of our discussion for all
the things is the phase modulated signal. In phase modulated your g(t) is the pulse shape
and you have a constant amplitude. So, in this representation, it is 1. Whereas, there is a
phase that is theta m which is being used over here fc is untouched. So, we said earlier
that theta t could be modulated. So, here a(t) is constant; whereas, theta t in our
expression is basically over here.

So, as we take different values of m; m going from 1 to capital M, we get different

phases and you get phase modulated signals and in digital domain, it is the phase shift
keying; that means, the phase shifts from one phase value to another phase value. So, as
you are seeing that theta m can take these phases the 2 pi total phase available, unique
phase available is divided by the number of possible signals and then you simply
multiply by m minus 1 with varying values of m and you get the different phase values.
So, for each phase value, you get a different waveform S m of t and you have as many
waveforms depending upon the value of m and you can generate your signals.

So, if k is equal to 1; meaning 1 bit per symbol, then capital M is equal to 2 ok. So, in
that case for m equals to 1 and m equals to 2, we get two different signals S 1 and S2. For
m equals to 1 clearly the phase is 0 and for m equals to 2 the phase is pi because that is
what you get divided 2 pi divided by 2 multiplied by 1, it is pi.

209
So, clearly we have binary phase shift keying and again this particular waveform would
have similarity with whatever we discussed in binary pulse amplitude modulation as
well. So, they are identical in that sense; however, as we increase k ok. So, the a(t)
remains constant. There is no change over here; only the number of phases increase; so,
at the receiver side, if I am able to distinguish between the different phases.

So, clearly as we see here the phase difference between the two signals is pi radians;
whereas, here naturally it would be pi by 2 radians ok. So, the error probability here
would be more compared to error probability over here because, the constellation are
more closely spaced over here than this case. However, in this case every demodulation
or every detection results in 2 bits of information thereby it increases the spectral
efficiency.

(Refer Slide Time: 13:28)

sm (t )  g (t ) cos(2 f ct   m )
 2 (m  1)   2 (m  1) 
 g (t ) cos   cos(2 f c t )  g (t ) sin   sin(2 f ct )
 M   M 

So, what we see over here is the generic expression that is S m(t) a signal is written as g(t)
times cos two pi fc t plus theta m and you do not have any amplitude term over here. So,
indicating it is a constant amplitude you can put one or any other value of your choice
and if you expand this term, you are going to get g t which is the pulse cos 2 pi m minus
1 upon m plus cos theta and another term over here.

210
So, what we see this can also be represented in terms of quadrature carriers because this
is the carrier frequency fc ok. So, what we had seen is Quadrature Amplitude
Modulation. In this case it is a kind, it can be seen in terms of quadrature amplitude
modulation, but the amplitude modulating signal is different than what is used in the
other case. So, here this is the amplitude modulating signal and rather it comes
effectively from the phase value ok.

sm (t )  sm1 f1 (t )  sm2 f 2 (t )

So, now, S m t that is the signal that we have can be written as S m 1 f 1 t plus S m 2 f 2
t, again from classical way of writing down digital modulations. So, here what we have
is f 1 t and f 2 t are the two basis functions ok. So, basis functions one indicating the
cosine carrier; one indicating the sine carrier and then, there are different phase values.
So, effectively you have your signal constellations on the unit circle. If you increase the
number of modulations to number of bits to 3, then you get 8 such things and you have 8
PSK which we are going to see shortly.

So, if it is. So, here what you clearly see is that this is one of the modulating signals; this
is the other modulating signal. This is one of the pulse shape sorry this is one of the basis
functions; this is the other basis functions and through this you are able to generate the
signal in terms of modulating the basis function.

(Refer Slide Time: 15:43)

211
So, as we move ahead what we see in this particular picture is the 4 PSK diagram and
there are certain basics which I can skip for the discussion in this particular series.

(Refer Slide Time: 15:56)

So, what we have over here is the 8 PSK model. So, what we see is that at every signal
interval there are 3 possible bits that can be used because you have 8 possible levels if
you have 8 possible levels, then you need 3 bits to identify the 8 different levels and
thereby, you have the 8 PSK constellation. Now, this signal constellation is available for
use in edge systems which is an enhanced version of 2G in order to use in order to
provide better spectral efficiency because the general second generation communication
system is not very spectrally efficient although it is bandwidth efficient.

Now, one of the advantage of using an 8 PSK is that it is compatible with the bandwidth
occupancy of a typical 2G system. So, it does not play around with that. One of the big
things is that you can see it is a constant amplitude, the amplitude is not changing. So,
the big advantage because of this is the peak to average power ratio is controlled in this
kind of a constellation; whereas, if we take a constellation where if we have let us say 4
constellation points over here and some more 4 constellations some more signal points
like this.

am (t )e j m (t )
g (t )e jm (t )

212
So, this constellation if I compare this with a 16 PSK that means, if I put in additional
constellation points, what we find is that both these systems after drew with the red
color, it can take 16 different signals and this can also take 16 different signals both can
be represented by a cos 2 pi fc t plus sine 2 pi fc t. That means, both have quadrature
carriers ok, but when I compare this and this there is lot of fluctuation in the signal
amplitude. So, this mode is to be written as am(t) e to the power of j theta m t; where, a
m and theta m both vary. Whereas, in this system you would simply of course, there is a
g(t) term which is associated; whereas, if you look at this system it will simply be g of t e
to the power of j theta m t. So, here there is no amplitude fluctuation.

Now if you have a constellation which is of lower amplitude fluctuation because here if
you see some average level would be somewhere here ok; whereas, there will be
fluctuations of peaking amplitudes whenever these constellations are selected right. So,
whenever these constellations are selected the amplitude peaks and this would result in
non-linear distortions if the power amplifier is operating near saturation. Whereas, here
such problems are generally avoided when we are getting into systems where there is
constant amplitude such as this particular constellation. So, this particular constellation is
more suitable to use along with the second generation system.

So, when second generation systems started providing access to data, they introduced
this kind of a modulation so that it is compatible with the earlier modulation format with
the bandwidth as well as there is not extra requirement of PAPR. So, the signals can
easily be decoded within the same receiver structure. Whereas, if you look at IMT-
Advanced like systems, they use constellations which look like this with this this
particular picture is a 16 QAM picture and PAPR requirements are higher.

So, it is a its a more relaxed system design, there is a more constraint system design and
what you will see is that future generation systems are looking towards design of
constellation and signal space where there is lower PAPR and lower bandwidth
occupancy. So, that means, the foundation or the constraints that were experienced by
the second generation system are also being looked at as vital configurations and which
could serve as a basis of course, with lot of enhancement and extension towards the next
generation systems which have broadband and much larger bandwidth to operate, but
overall constraint properties remaining the same.

213
So, from this at least we get a basic idea of what are the factors which trigger higher
PAPR or which triggers the need for more bandwidth and how you can conserve the
bandwidth and things like that ok.

(Refer Slide Time: 20:59)

So, at this point we move now beyond whatever we have discussed to something known
as multi-dimension signaling. So, in the previous expressions what we have seen is that
there are 2 basic dimensions right. So, there are 2 basic dimensions. So, in case of PAM,
there is only a single dimension, one-dimensional. In case of PSK, we can think of two-
dimensions and in case of QAM which we have described earlier; we can also have two-
dimension.

So, what we have seen in this particular picture there are two-dimensions that is one
along this axis; one along this axis; this is also two-dimensional. So, what we are going
to discuss is something just beyond two-dimensional. Yes, you can have multi
dimensional signaling. So, let us look at the framework because that is again the basis for
the next generation systems.

So, in multi-dimension systems the concept is not very complicated, but we look at a
time duration let us say a T 1 which is represented over here and we divided it into
smaller chunks of duration T. So, it is effectively there are N number of such chunks
available and you have N such signals that you can choose from and which are
orthogonal to each other. They may not be orthogonal to each other, but you can choose

214
them to be orthogonal to each other as well. So, here if I am sending a signal in one of
the intervals and in this case I am sending a signal in another of the intervals, then we are
able to detect the signal by virtue of being present at a particular time slot. It can also be
looked at as a pulse position modulation if you want to put it in that framework, but it is
a generic framework of representing things.

Now, instead of writing it in this form; instead of time you could also replace this with
frequency. That means, that in this axis which is the frequency axis. So, there will be
multiple such frequency options available and one could choose to use any one of the
frequencies in every signaling interval. So, what we see in this particular picture as is
over here is that in this time interval only frequency f 1 is chosen. In the second time
interval only frequency f 2 is chosen and just for the sake of diagrammatic representation
in the next interval f 3 is chosen.

So, in a similar manner you could extend to in other dimensions. So, here you are you
are having more than one basis function to describe your entire set of signals. One could
also choose to use a linear combination of these different basis functions at the same time
as well. It depends upon the type of application, but with this framework, we are now
geared towards looking at systems where multiple carriers may be present or different
frequencies may be used to separate or identify the information bearing signals.

(Refer Slide Time: 24:27)

215
B  N f
k  log 2 N

So, the this is this is the basic architecture that we are talking about that there is a
frequency axis and center frequencies and the frequency axis is divided into sections
where the bandwidth of each section is delta f and the total bandwidth is N delta f and
overall you would have to select the different frequencies in different time intervals and
the number of bits that may be required to select the particular signal is log base 2 of N.
Because I have N possible signals and I choose any one number of bits required to
represent is simply log base 2 of N ok.

(Refer Slide Time: 25:11)

k  log 2  N1 N 2 

So, you can combine the time frequency together and you can have the frequency
domain and time domain together; overall it is number of bits that you can signal over
here is log base 2 of N 1 N 2. So, this is an extension of whatever we have discussed in
the previous thing and you could use these modulation methods to signal to transmit
information from one point to another.

216
(Refer Slide Time: 25:37)

k  log 2  N1 N 2 

So, what we see over here is again the same thing, but here what we want to point out is
that the transmitted signal is represented in a form which is very familiar to us that is real
part of s l that is the low pass equivalent of the m-th signal e to the power of j 2 pi fc t;
where, we can see that we have 2 pi m delta f indicating the message. In other words, by
choosing an appropriate value of m, we are in turn choosing the frequency of operation
or in other words which particular band to be chosen and thereby, we are deciding our
signal right. And every choice is composed of k bits and k bits depending upon the type
of system, it could be log base 2 of N 1 or log base 2 of N 1 comma N 1 times N 2
depending upon whether its multi dimensional both in time and frequency or only in
frequency.

Now, if we look at the structure as is represented here where the baseband signal can be
having a constant amplitude that is we are describing s l of m over here and its only the
frequency component which is changing because of values of m, where the values of m
is selected based on the bit sequence right. So, if there are 3 bits in the system, then we
have 8 different frequencies to choose from and such a system if there are capital M
number of such frequencies to choose from, we have M-ary-frequency shift keying.

217
Now this is a basis for the next important thing which we are going to see. So, in this M-
ary-frequency shift keying what we would like to do is to look at a very specific form
which has certain special properties. So, typical frequency shift keying, there is some
relationship how to choose the different frequencies and frequency separation; but then,
there is an interesting form where you could choose the frequencies of your choice; that
means, of in the frequency shift keying in such a way that the frequencies are orthogonal
to each other. If you are choosing the frequencies as orthogonal to each other, in that
case you will be finding that you can operate with the minimum separation between the 2
different frequencies.

So, we would take up the conditions under which the 2 different frequencies can be made
orthogonal which will lead us to the basic premise of the next generation of the second
generation communication system which is also a fundamental. Or, for this particular
discussion framework that we are looking at is also the fundamental framework based on
which the fourth generation system or OFDM is also designed.

Thank you.

218
 Evolution of Air Interface towards 5G
Prof. Suvra Sekhar Das
G. S. Sanyal School of Telecommunications
Indian Institute of Technology, Kharagpur

Lecture – 12
Fundamental Framework for Waveform Analysis (Contd.)

Welcome to the lectures on Evolution of Air Interface towards 5G. Till the previous lectures
we have seen a background of the way we have built up till the requirements of 5G.

(Refer Slide Time: 00:38)

And now we have started discussing the signal model or the basic framework based on which
we will discuss the first issue of discussion that is the air interface or the modulation or the
waveform strategies. So, to do that, we have said in the previous lecture that we would look
into the baseline model as well as look at the some of the earlier generation systems, because
there lies the basis towards the future generation systems.

And we have developed the low pass equivalent as well as a band pass format of the signals,
how they are connected. And we have looked at some of the very basic ways of modulating
signals we have done it pretty fast assuming that you had some prior knowledge of it. It was
just a revisionary approach. And thereafter we have moved to multi-dimensional signaling
which forms the basis for waveforms even in IMT-Advanced or the fourth generation system.

219
So, what we were discussing in the previous lecture is basically that you have a set of
frequencies right, you have a set of frequencies, and in those set of frequencies you can
choose one of the frequencies to indicate signal carrying information, and let there be a delta
f be the separation between the frequencies. And along with that if you have time domain, so
then you have basically N1 times N2 number of resource elements and log base 2 of that is
the number of bits that are required to identify the selection of a basic resource element by
which you are communicating information.

k  log 2 N1 N 2

So, we move beyond that and we said that let us consider only one time slot that means, when
there is multiple frequencies available to choose from, but for every time slot. So, in that
case, we had also said that the amplitude remains constant that is one of the important
features while we can choose the frequency by having a multiplicating factor along with the
multiplicating factor along with the delta f which is the frequency of separation.

sm (t )  Re  slm (t )e j 2 fc t  , m  1, 2,..., M , 0  t  T ,
2E
sm (t )  cos  2 f c t  2 mf ct  ,
T
2 E j 2 mf
slm (t )  e .
T

So, this kind of a signalling system is known as the M-ary FSK because you have M-ary
PAM. So, here you have M-ary selecting M possible options and this particular signal which
is in the pass band, you could find the equivalent low pass in terms of root 2 E by T and e to
the power of 2 pi m delta f, because that is what appears over here and this, this form this one
comes if we have j 2 pi fc t, so this is due to the pass band conversion. We are left with only
the baseband part. So, this is the low pass equivalent form of the corresponding signal.

So, what we see is that every fc, I mean for an f c, it gets modified by m delta f right. So, it
could be plus minus around fc, and you could choose different frequencies and hence you are
left with frequency shift keying, this is what we said earlier. Now, if you have M possible
frequencies log m base 2 that is the number of bits that would be communicated for every
selection of a particular frequency. So, in the same manner, if we have 8 different
frequencies, we will require three different bits to choose from them.

220
Now, amongst all possible frequency shift keying, we are looking and looking at and are
particularly interested in one special form where we would like that the frequencies are
orthogonal to each other. Now, if they are orthogonal to each other, then we have a special
advancement towards from the original frequency shift keying in the form that the
frequencies can be placed next to each other in the closest possible way that means, the
separation between the frequencies will be the smallest possible separation and although the
signals will overlap still we will be able to decode.

T
Orthogonality   slm (t ) s*lm (t )dt ,
0
T T
j 2 mft  j 2 k ft
 e e dt   e  j 2 ( m k ) ft dt ,
0 0

So, with this basic premise, one would like to have the orthogonality orthogonal frequency
spacing, and by definition of orthogonality. What you have is the slm that means one of the
baseband equivalent frequencies or the signals along with slk right. So, l indicating the low
pass equivalent, and m is the m-th frequency, k is the k-th frequency indicating two different
signals that is the m-th signal or the k-th signal that means either I choose one particular
frequency over here or I select another frequency over here, so it is between these two.

So, in the time interval T, which is the symbol duration. We would like to see that these two
signals are orthogonal. So, like we have two pass band signals which we would like them to
be orthogonal. So, if we work this out this is the part of slm, this is the part of slk, we directly
get from here, and in this equation we are not putting this in the expression I mean if you
even if you put it will be 2 E upon T, where E is because of the energy of the signal. And here
we have taken equal energy, so we are not considering the scaling factor in this expression.

So, what we are left with is e to the power of j m minus k delta f and integrated over 0 to T.
So, if you solve this particular thing, what we will get is that in order for this to be 0, we get a
certain condition on delta f, which will lead us to the answer of what is the separation that can
be allowed. Now, in this situation usually two different ways are looked at. So, when we are
looking at the situation where it is only a selection of frequencies, then we can take only the
real component and, we take the real part of this, and set it equal to 0. And then whatever we
get is the condition for orthogonality of signals, when we are only selecting the frequencies.

221
(Refer Slide Time: 06:53)

T
 e j 2 ( m k ) ft  j ( m  k ) fT  e
j ( m  k ) fT
 e  j ( m k ) fT 
  e  ,
 j 2 (m  k )f  0  j 2 (m  k )f 
sin   (m  k )fT  j ( m k ) fT
 e ,
 (m  k )fT
sin   (m  k )fT 
Re(  km )  cos   (m  k )fT  ,
 (m  k )fT
sin  2 (m  k )fT 
 ,
2 (m  k )fT
1
 0, if f  ,
2T
 1, if m  k

So, that is what we have set up over here, so you have e to the power of j expression divided
by the term as a result of integration integrate over 0 to T. And substitute T into this, and
substitute 0 into this, you are going to get the expression on the right, and then you solve it.
Solve it in the sense that you take out away pi m k minus m minus k delta f T, which is over
here this 2 is not here. And you are left with a term inside where from the first term you will
be left with the pi, and the second term will obviously be minus j pi, and the rest of the term
as it is, and the denominator remains as it is.

So, you have e to the power of j alpha e to the power of minus e to the power of minus j alpha
roughly the expression or the expression turns out to be in terms of this where alpha is equal

222
to this entire value. And if you work this out, it turns out to be sign of alpha whatever we
have defined alpha upon this expression. So, basically in the denominator, you have alpha
upon T, because if we consider T as part of alpha.

And then we take the real part of it, because we are we are concerned only with the selection
of the signal and nothing beyond that. So, when you take this you take the real part of the
product of the two expressions, so you are left with sinc kind of an expression over here as
well as a cosine term. And when you solve this and set this equals to 0, basically you have a
term over here and here.

So, sine a cos b if you multiply that, you get two sine sorry sine theta cos theta you are going
to get two sine theta and half the normalizing factor because of this comes in the
denominator, so you get a sine two times this expression. And if we set this equals to 0 to
maintain the orthogonality, then what we get is delta f that means this particular term which
is the delta f should be equal to 1 upon 2T.

So, if m is equal to k that means when we are having the signal, and that means m is this, and
k is also equal to this the same signal. We get the value of one, whereas when m is not equal
to k, we will get a value of 0, because by setting this equal to 0, we get this separation of
frequencies. so it in turn it means that if you let delta f take the separation values of 1 by 2T
in that case the if the signals are not the same signals, you are going to get at the receiver a
value of 0, when we are using correlation receiver.

So, if we see the way we have developed this construct is that we have chosen a particular
signal to be transmitted, and at the receiver we are correlating against the k-th signal. So, this
is kind of matched filter what we do not have over here, of course you can already consider
what we have missed out over here is the g of t should come in so g t will come in over here,
g conjugate t would come in over here, and that would result in the mod of g squared t mod
of g t squared. So, mod of g t squared being a scalar number, so that would appear in each of
the multiplicating factors.

So, in this particular expression we have taken g t to be rectangular that means, it is 1 in the
interval 0 to T, you could also have it normalized, so that means we are as if saying that one
particular signal is sent out of the different frequencies. And at the receiver you are
correlating with some other signal as a result of typical matched filter operation. So if the

223
signal is not same as the original signal that is if it is not matched to the signal, then what we
get is a 0 right.

Whereas, if the signals are matched to each other the same signal, then you are going to get a
1, indicating that only one of these will give a value of 1 at the end of the matched filtering
operation, and others are going to give a 0 right by virtue of orthogonality condition. So, if
we set delta; delta f is equal to 1 by T which is by orthogonality condition, although the
spectrum will overlap still we will be able to distinguish between the different frequencies by
virtue of orthogonality criteria ok. So, this is the prime way of developing a orthogonal M-ary
FSK, which is the basis for the next set of discussions that we are going into.

(Refer Slide Time: 11:45)

T
Orthogonality   e j 2 mft e  j 2 k ft dt , k  1, 2,..., M ,
0

 0, if k  m,
 1, if k  m.
1
f  .
2T

So, effectively this is what we have roughly explained that we would choose one particular
frequency and if this matches, then the result is 1 else the result is 0. And what we have is
orthogonal frequency shift keying with a minimum separation of delta f right. So, in digital as
you all know this PAM or Amplitude Shift Keying is kind of equivalent or correspondingly,

224
you can map to amplitude modulation for analog communications, PSK can map to phase
modulation, FSK can map to frequency modulation, but these are completely digital. And we
have seen one way of doing FSK with orthogonal frequencies, and with minimum separation
ok.

(Refer Slide Time: 12:32)

So, moving down forward, so there are if if instead you are taking QAM kind of signaling, so
this is a slight a different slightly different discussion from what we had before. So, what we
discussed in the previous section that means just a few minutes back is that we are selecting
one of the frequencies, and communicating the choice of selection whereas, one could also
think of instead of selecting, since these frequencies are all orthogonal, since these
frequencies are orthogonal to each other. So, at the receiver side or at the transmitter side, I
can probably send them simultaneously. And each of the frequencies can be used to carry
some data either via pulse amplitude modulation or via quadrature amplitude modulation.

Now, why we say this, because as we know if we have e to the power of a t e to the power of
j theta m t, so theta m can be chosen by virtue of phase or by virtue of frequency rather by
virtue of phase or via frequency and if we do both, then we will not be able to distinguish the
information bearing signal. Whereas, if we are only handling this amplitude, and we use these
phases or these frequencies, which somehow separate the signals, or which forms as the basis
for the signal, then we are still able to decode the signal.

225
So, again since I have used the word basis, we can also go back. And see that all these
different frequencies that we have used over here are can be thought of as basis functions,
and they are orthogonal to each other, so these are orthogonal basis. So, now since they form
the orthogonal basis instead of just selecting them, because they are orthogonal. We can
actually use them to send data, and we have N number of orthogonal basis functions.

So, we can actually use N dimensional signaling and not only that we can go beyond that in
each of the dimensions, we can go for amplitude modulation or a PAM pulse amplitude
modulation or we can also go for quadrature amplitude modulation. To this will be the basis
for the orthogonal frequency division multiplexing, which we will see in more details later
on, but this particular discussion is the foundation for whatever we take up at a later stage.

So, now, if if one is using QAM right, Quadrature Amplitude Modulation that means, we are
going to have a we are going to have let us say X of t plus j Y m of t, which is the low pass
equivalent of the signal or which carries the information bearing signal. And they are chosen
from the, or QAM constellation, so this is the QAM constellation.

 km  0,
sin  2 (m  k )fT 
 km  e j ( m k ) fT ,
2 (m  k )fT
1
 0, if f  , m  k,
T
1
 1, if f  , m  k .
T

So, in that case to find the orthogonality, we cannot use the real part of the orthogonal
projection. So, when we are taking the orthogonality criteria, simply the real part is not going
to help us, because there is a imaginary part which carries information. So, in that case once
we find the correlation, you can say or the inner product of the two functions. We would like
to set the modulus of it or the absolute value of it to 0, in order to get the points or the
condition under which orthogonality remains.

So, here what we had seen is the rho k m is an expression, which is given by this. Now,
instead of taking real part, if we take the mod, because we are not interested only in selection
but also in the real and imaginary part of the data, we cannot simply use the real we have to
let the real and imaginary both go to 0. So, if you have to let the real and imaginary both go

226
to 0, then we can set the modulus of the same to go towards 0. And you can have the rho k m
expression, which was shown in the previous slide, the whole thing the absolute value of that
going to 0.

So, we clearly see that this expression will go to 0, if this numerator goes to 0. And this
numerator can go to 0, when delta f is equal to 1 by T, and m is not equal to k correct.
Whereas, even if delta f is equal to 1 by T, but m is equal to k we are going to get a value of
1. Now, this is very very important. And we can also see from the point of view that if you
take the modulus of this, you are going to be left with this entire term. So, if I take the
modulus, since this is e to the power of j, it goes out we are left with the modulus of this and
the modulus of this is equal to one effectively. So, it is a product of the two.

And what we see is that this term is a sinc expression, and this sinc expression is equal to 1,
for the argument of sinc being equal to 0 right. An argument of sinc can go to 0, if m is equal
to k correct. So, under m is equal to k condition, this will give us 1. And under the condition
that m is not equal to k, if we set the additional condition that delta f is equal to 1 by T or in
other words what we see inside over here is pi T m minus k delta f being equal to some
integer multiple of pi.

In that case, we clearly get and the minimum separation is m minus k equals to 1, we clearly
would get delta f is equal to 1 by T, as the condition under which this would go to 0. So,
again if we try to realize how this is working at the receiver end is that all these signals they
are going simultaneously, right, and as your frequency as your m increases, since we have m
times delta f. Since, we have m times delta f, we have pictorially represented as higher and
higher frequencies.

So, if at the receiver we are correlating with m is equal to k that means, if we are relate
correlating with this, we are going to get a peak value for this, whereas others will be 0. So,
in other words, the receiver even though it gets all the signals in this case, we have to have m
number of correlators, each correlator will be correlating with e to the power of j 2 pi delta f
times m times t ok. And hence each of them is going to produce a magnitude of 1, because
our correlation expression we have taken as slmt, slkt.

slm (t )   X m (t )  jYm (t )  e j 2 mft

227
slk (t )   X k (t )  jYk (t )  e j 2 k ft

But, now we would also have this additional X m plus jY m term along with that that means
our s l m should have X m of t plus j Y m of t multiplied by e to the power of j 2 pi m delta f t
right, so that should be the term for slk. All the m terms get replaced by k. And what you are
left with is this particular term at the receiver. So, this term you can now decode or demap
using typical QAM demodulation procedure.

So, now if we observe, what we are doing carefully. We are actually sending all the signal
simultaneously that is the additional discussion that we had in the previous few minutes.
Now, if you are sending all the signals simultaneously, so you are kind of using all the
frequencies. And you are sending the signal using frequency division multiplexing, but in this
case it is orthogonal frequency division multiplexing right.

So, what we see is that from the same basic framework, we are able to look at FSK as well as
OFDM. Whereas, FSK is variant of this particular orthogonal, FSK is what is used in very
earlier generation that is the second generation, which we will see very soon. And the other
format, which has the same background or the same fundamental basis is used for the next
generation system, so that is why whatever we have analyzed over here forms the foundation
for whatever we are going to discuss in the future lectures ok.

(Refer Slide Time: 21:33)

228
 1
FSK : f  ,
T
m
In FSK, frequency sepearation of m-th carrier, f  ,
T
FSK : k  log 2 M ,
Multi-carrier Orthogonal Frequency Divsion Multiplexing:
k  M (carriers )  log 2 M ' , M 'obtained from QAM.

So, now at the receiver side as we have clearly said, we are going to do this operation. And
although these frequencies are overlapping right, still because they are orthogonal to each
other by virtue of orthogonality criteria, what we are seeing is that they can be decoded
without any interference right. So, this is orthogonal frequency division multiplexing, which
have just explained in the previous few minutes.

So, now what we see is that at any one interval that is T period earlier, when we are doing
FSK, we were sending k bits which were equal to log base 2 of N or log base 2 of M, which
was the number of carrier or the sub-carriers that we had. Whereas, here what we have, is at
every time instant T, you are sending M number of parallel signals. And each parallel signal
is going to carry k bits, which is equal to log base 2 of some M prime which is in this
discussion by virtue of QAM signaling.

So, if we do 16 QAM in that case, this value would be equal to 4. And if we have let us say
16 carriers, then this value is 16, so together what we have is 64 bits being sent
simultaneously. Whereas if we compare the earlier system of FSK, in that case if M was 16,
then k would be only 4 bits.

So, what we see there is a huge improvement in data rate that is possible that means, because
here you are simply selecting one possibility of the M possibilities. Here you are letting all
the M possibility is getting used, and in each of the parallel signaling, you are allowing some
kind of modulation to go along. And mostly it will be the amplitude domain modulation. And
we are using QAM, because it is very compact. And you can send higher number of bits in
that, so this is the way.

Of course, I should mention that instead of sending QAM, you are also free to go for some
real signaling like pulse amplitude modulation. In that case, what is going to happen is your

229
separation in frequencies, delta f, will be as per our earlier discussion that it will be 1 by 2 T.
And in each case this M prime, which we said QAM, you are going to use a PAM signaling
over there right, so that means although we are going for a different lower spectrally efficient
signaling format. But, since we are using a narrower bandwidth, so we are packing a larger
number of carriers in that situation. And hence we are not losing any spectral efficiency in
this particular case as well right.

So, going ahead further, what we see is that N-dimensional signaling framework that we have
studied gives rise to the M-ary orthogonal FSK, which is a basis for discussion of waveforms
for the second generation system as well as it forms the basis for discussion of OFDM, which
is again a fundamental waveform for the fourth generation system not only that based on this
signaling structure. The other signaling structures can also be studied, which were also
investigated as a forerunner towards 5G.

And they are known as the generalized frequency division multiplexing, which we will see in
due time also filter bank multi carrier, which will also see in due time as well as unified-filter,
unified-frequency multi-carrier, unified-filtered multi-carrier systems which also we will see
in due time. So that means, we have looked at a fundamental framework on which a large set
of waveforms are standing in today’s context. And these set of waveforms which we have
listed down over here, and we will see in details later on, form the basis of multi-carrier
waveforms ok.

So, when we say multi carrier, what we mean is that you are actually sending all these
carriers simultaneously while maintaining the orthogonality criteria that they are although
overlapping, they have 0 correlations amongst them. So, this is the basis for multi-carrier
signaling, and in fact in some form of 3G there are multi-carrier CDMA was also proposed.
Whereas, how do you place this multiple carriers was also investigated in quite deep details,
there are a huge amount of literature available in terms of multi-carrier signaling.

So, what we see is that we have looked into the premise or the framework based on which the
2nd generation even some forms of 3rd generation, 4th generation as well as the next
generation waveform systems can be studied. We conclude this discussion over here we will
take up the next set of discussions starting with the second generations system using this
framework from the next lecture onwards.

Thank you.

230
 Evolution of Air Interface towards 5G
Prof. Suvra Sekhar Das
G. S. Sanyal School of Telecommunications
Indian Institute of Technology, Kharagpur

Lecture – 13
Waveform Design Aspects for 2G

Welcome to the lectures on Evolution of Air Interface towards 5G. In the previous
lecture, we have discussed about the framework for waveform design and we have seen
the structure through which we are able to address a wide variety of waveforms and we
have seen the baseline structure through which we can address multicarrier waveforms.
So, we will quickly revisit whatever we have discussed in the previous lecture and we
will continue with our discussion.

(Refer Slide Time: 00:47)

1
FSK : f  ,
T
m
In FSK, frequency sepearation of m-th carrier, f  ,
T
FSK : k  log 2 M ,
Multi-carrier Orthogonal Frequency Divsion Multiplexing:
k  M (carriers )  log 2 M ' , M 'obtained from QAM.

231
So, what we have discussed in the last lecture is that there would be multiple different
carriers and these carriers can be orthogonal to each other in the way that the frequency
separation is spaced so that it is 1 upon T and the m-th carrier is m times 1 upon T. And,
there are two possibilities, one is the selection of one of these carriers and that is FSK
and the other option is that you can choose to use all of them while each one of them you
can choose to do QAM modulation and the second form translates to orthogonal
frequency division multiplexing as well as this gives rise to the structure for the multi-
carrier communication systems.

And, we have also highlighted that this particular structure gives rise to various different
waveforms which were contending waveforms for the fifth generation communication
system. So, this with this base line structure when we revisit these details we are better
equipped to discuss them in a more detailed manner.

(Refer Slide Time: 01:57)

M-ary PAM: k  log 2 M ,

M-ary FSK: k  log 2 N ,
OFDM: k  N  log 2 M .

So, in the M-ary PAM case, what we have said that each of the signals they occupy
different amplitude values. So, instead of here as we all have been saying that each of the
values are simply different choices and we have also discussed the bit rate that could be

232
taken forward by this multicarrier waveform and also have compared that it is several
times more than the bit rate that can be carried by M-ary FSK.

(Refer Slide Time: 02:31)

s (t )  Ac cos i (t ),
i (t  t )  i (t )
f t  ,
2t
1 i
Lt f i (t )  Lt f t  ,
t 0 t  0 2 t
PM: i (t )  2 f i t  k p m(t ),
FM: fi (t )  f c  k f m(t ),
t t
i (t )  2  fi ( )d 2 f i t  k p  m( )d ,
0 0
t
 
s (t )  Ac cos  2 f c t  k f  m( )d  .
 0 

So, this is also what we have discussed in the previous lecture and now we move forward
to the next important class that is the one which is based on angle modulation. There are
some details which act as a fundamental triggers to the change or the waveform design
for the next generation. So, in angle modulation we all typically know that the phase
angle of this signal is modulated whereas, the amplitude is kept constant. Now, in the

233
frequency modulation we have seen on FSK the frequency is modulated, but here it is the
angle.

And, the rate of change of phase is the indication of the instantaneous frequency. So, in
this manner if we do frequency modulation we also have some kind of a phase effect. So,
I mean they are very difficult to distinguish and hence we have said that you do either
phase or frequency along with that you can also do amplitude modulation. So, in phase
modulation simply the total phase of the carrier or the instantaneous phase is consisting
of the carrier terms which is 2 pi fc t, along with an additional phase term which is taken
care of by the m that is the modulating signal.

And, we have discussed the 8-PSK structure before. In the frequency modulation there is
this fc and along with this there is the message signal which gets modulated with the
particular sorry, the frequency gets modulated with the message signal and there is a
certain scaling factor which decides the depth of the modulation.

So, if you look at the phase of the signal which is given by theta i t that is the
instantaneous phase, you integrate from 0 to t 2 pi instantaneous frequency d tau and this
results in 2 pi fc t which is the carrier term; that means, this term which is common with
the phase modulation along with that we have 2 pi k f which is the frequency modulation
index along with it an integration of the modulating signal. So, the difference with phase
modulation and frequency modulation is in this particular term in one case it directly
appears as a signal and the other case that is an integration of the term.

So, when we look at the s of t which is the pass band signal as we have been discussing
since the since we have been discussing the signal model we have 2 pi fc t that is the
carrier term and the modulating signal which contributes to the phase in this particular
manner, ok.

234
(Refer Slide Time: 05:13)

Conventional FSK: m f  different frequencies,

1
f n  f I n , I n  1, 3,..., (n  1), M  2k , k  log 2 M ,
2
PAM: d (t )   I n g (t  nT ),
n

I n  mapping k bits binary blocks,

1
g (t )  rectangular pulse with amplitude & duration T,
2T
 t 
j  4 Tf d d ( ) d 0 

2E  
Low-pass equivalent form,  (t)= e   
.
T

So, when we look at the conventional FSK: in conventional FSK as we have been saying
the m delta f are the different frequency values which are used and hence the f n that is
the choice or the chosen particular frequency is decided based on the modulating signal.
So, what we can do over here is we can have a pulse amplitude modulation of the initial
bits. So, if there is a 0 1 bit stream that keeps coming those bit stream you can send it to a
pulse amplitude modulation and whatever signal you get out of it or the discrete signal
you can use it to choose the frequency through this particular relationship.

So, these values as in PAM can take plus minus 1 plus minus 3 plus minus M minus 1
and there could be another scaling d that gets multiplied and once you multiply with
delta f then accordingly you can switch between the different frequencies what we have

235
been discussing. And, this delta f can be chosen to be 1 upon T or 1 upon 2T depending
upon the particular realization.

So now, what as we have just discussed, we consider d t indicating the signals I n as

described over there along with it, let there be some pulse shape which is denoted by g t
and T is the duration of the pulse and n indicates the n-th signal or the n-th symbol, and
here when we choose this I n it has the k bit binary block and this k-bit will depend upon
the number of different frequencies that you are going to have in the system. In case of
rectangular pulse shape you can take g t to be 1 by 2T is basically constant in the
duration of T and then you can set up your entire signal.

This signal d t can be used to modulate the carrier frequency and then we can have our
conventional FSK can be realized in this particular manner. The low pass equivalent
form of the signal because whenever we are discussing the signals we are always
considering the low pass from which we have said since the beginning. So, what we see
over here is the low pass equivalent form when f d indicates the frequency deviation
corresponding to the k f notation that we had used in the previous page. And, what we
see over here of course, there is no modification of the amplitude and the instantaneous
frequency is dictated by the data signal.

What you can also see is that the baseband or the equivalent low pass form does not have
any f c term which is quite obvious and pretty natural and expected. So, when you do an
up conversion you simply multiply this by e to the power of j 2 pi fc t and then you take
the real part of this, right and then you can generate your entire signal, ok.

236
(Refer Slide Time: 08:23)

The carrier modulated signal,

2E
s (t )  cos  2 f ct   (t , I )  0  ,
T
t
 (t , I )  4 Tf d  d( )d ,

t
 
 4 Tf d   I n g (  nT ) d , nT  t  (n  1)T ,
 n 
n 1
t
 2 Tf d I k  2 f d I n    nT ,
k 
n 1
 2 Tf d I k  2 f d I n  t  nT  ,
k 

  n  2 hI n q (t  nT ),
n 1 n 1
where,  n  2 Tf d  I k   h  I k ; h  2Tf d ,
k  k 


0, t  0,

 t
q (t )   ,0  t  T,
 2T
1
 ,t  T.
2

237
So, the carrier modulated signal you could write as we have just said that after you take
the real part you get the cos 2 pi fc t term and there was this initial phase component
which was available over here. So, this initial phase component is present over here ok.
This initial phase component is available and this is the phase due to the modulating
signal which we have captured over here. So, this is the expression which you have seen
in the previous slide and then you can expand and see how this thing works out.

So, when you look at this entire signal the constant term is over here, we expand d t by
definition as we have described over here we have defined d t in this particular line. And,
hence we use the same d t over here we have expanded it over here which includes the
pulse shape as well as the index of the modulating signal. So, now, if we are interested in
the time interval which is between the n-th and n plus 1-th symbol; that means, the end
of n-th symbol and it is moving to the next symbol, we can expand or we can solve this
expression and we are going to get 2 pi fd T and a summation of all the previous symbols
I k from k equals to minus infinity to n minus 1 and the rest of the term is integrated
from 2 pi fd I n and nT to t correct.

So, this particular thing we get because g t we have said is equal to 1 by 2 T this 2 and
this 4 cancels to give a 2 term which we get over here this T and this T cancels out. So,
there is no T term in this particular expression. There is no T over here if you are
focusing on this particular part pi comes as it is, fd is present as it is I n because we are
taking the n-th signal. So, I n and what you have is integrate d tau because it is 1 by 2
tau. So, you are left with integration of d tau. So, integration of d tau would be tau from
nT to t. So, hence you have the particular first part which is as it is.

The second part 2 pi fd I n and you replace T over here you get a t and when you get
when you replace tau with n T you get this particular form. So, this part which is the
prior part can be represented as theta n which is kind of the accumulation of the phase
due to all previous modulations. Whereas this part what we have over here is the one
which influences the current symbol. Now, this q t if you analyze for t less than 0, this
has to be 0 because q t is integration of g t and g t is simply 1 upon T for the duration 0
to T, correct. So, there is a constant value below this before the value of 0 it is a value of
0 and here it is some constant value, ok. So, this is 0 less than for t less than 0 and for t
lying between 0 to capital T it is t upon 2T and that is what we have utilized in getting
this particular value.

238
Now, beyond t is equal to capital T, you get a value of half with a replacement of the
variables. So, therefore, what we can see is that the accumulated phase component is
simply the expression which you have written over there and in this expression you
integrate this T 2 and fd together and you represent that by the term h that is small h
which you also call the modulation index. So, this is how we will expand the expression.

(Refer Slide Time: 12:33)

 (t , I )   n  2 hI n q(t  nT ).

So, what we have is the phase term contains an accumulation of all the previous memory
as well as the term on the right what we have over here where the h term what we just
saw in the previous slide is the modulation index. So, depending upon different values of
h you can get the different terms. So, in this manner what we have actually arrived at, is
something known as continuous phase FSK signal.

So, if we go back a few steps what we will find is that if you are doing instantaneous
frequency modulation; so, if you are doing instantaneous frequency modulation through
this; that means, simply you are choosing it in this manner then what would happen or
rather if we were switching between the different frequencies so, at any one instant of
time one would have to switch from one frequency to another frequency. In a very short
duration, that is the duration of time when the pulse is changing from 1 to the next which
is almost tending to 0, there is a huge shift in the frequency so, which gives rise to a huge
amount of sideband. So, that is what is reflected over here.

239
So, if we see over here that the instantaneous frequency would go to very large values if
we suddenly change the frequency from one point to another. So, if we do a conventional
FSK communication then the bandwidth requirement is usually larger. Now, to reduce
the bandwidth requirement what is done is the phase is kept tried to be made continuous.

So, to maintain the phase continuity what is done is the steps that we have visited; that
means, we do a PAM signaling first, once we do the PAM signaling then we follow it
with a frequency modulation. So, there is PAM followed by frequency modulation which
would give raise to continuous phase frequency shift keying. So, if we do continuous
phase frequency shift keying we are avoiding the abrupt changes whenever the signal
changes from one signaling interval to the next signaling interval. So, we will see the
consequences of such of modulation format and such a modulation style very soon.

So, this CPFSK comes under the general class of continuous phase modulation systems.
So, if you have a continuous phase modulation system the overall thing implies that there
is no phase discontinuity. Now, the lack of phase discontinuity or rather if you have
phase discontinuity then at every instant whenever there is phase discontinuity the
bandwidth becomes pretty large and when we have to use the spectrum very efficiently
we would like to have the signal part which goes outside the desired band of frequencies
to be as small as possible.

So, typically you would have a certain spectrum of a signal which would appear let us
say like this, this is your f axis and this axis is your gain or the spectrum of the particular
signal. So, if you are doing instantaneous then your out of band emission is larger and if
you would do continuous phase then you would have avoid abrupt changes and you
could restrict your signal to a spectrum which is pretty well contained.

Now, if your signal is pretty well contained then the neighboring channel which one has
to send the next neighboring signal that will not have much interference from this
particular signal; now you can clearly see from this diagram that if your spectrum would
have been like this, then there would have been a huge amount of interference due to
adjacent channel interference. So, if you have to reduce the adjacent channel interference
then you have to place these two frequencies much further apart. So, now if you would
have placed instead of here you would have placed this particular frequency over here

240
then your channel would have appeared like this and then the portion of interference
would have been restricted to only this much.

Now, if we could contain our signal to a sharper transition bandwidth right, in that case
we could have the carrier frequencies which are in adjacent channels much closer to each
other. So, this is one motivation why one goes for such modulation method. So, when we
look at this second generation modulation schemes it is a class of CPM signal which was
used. When we go to the future generation; that means, the fourth generation it comes
under the orthogonal frequency spacing which also results in a very closely packed
signal and if you look at some of the contending waveforms which were fighting for his
position in 5G maybe they appear in 6G.

They include the orthogonal spacing; that means, the spacing maintained is orthogonal.
However, along with that they use certain filtering techniques by virtue of which the
signal one of the main objectives is to maintain the signal within a certain defined
bandwidth, ok.

(Refer Slide Time: 18:19)

1
f  ,
T
f n  mf .

So, what happens here is kind of can be seen over here that instead of having
instantaneous jumps from one frequency to another frequency what we have rather is a

241
continuous sweep from one frequency to another frequency. So, if you have this kind of
a transition there is more smoothness into the whole transition, obviously, it is expected
that your, the bandwidth or the excess bandwidth or out of band emission would be much
lower than the system where you would have instantaneous frequency transition as in a
conventional system, ok.

(Refer Slide Time: 19:01)

n
 (t , I )   2 I h q(t  kT ), nT  t  (n  1)T ,
k k
k 
t
q (t )   g ( ) d .
0

So, if we look at this CPM system now; so, the continuous phase modulation system has
a generic form, you can easily see that this generic form captures from k equals to minus
infinity up to k equals to n where as there we had separated out to k equals to minus
infinity n minus 1 and we had an additional term. So, this is a more generic way of
representing the whole thing where this is the modulation index and here as you can see
that this particular h is also written with the sub k indicating that each symbol may also
have a different modulation index.

So, the scheme that we will be looking at is the one which has the constant modulation
index, right. So, that is what is used in the most commercial systems. However, if you

242
have very specific requirement you can have a varying values of h if you want into the
system for specific characteristics of the signal, right.

(Refer Slide Time: 20:03)

Rectangular pulse of duration LT, L=1:CPFSK (LREC)

 1
 , 0  t  LT ,
g (t )   2 LT
0, otherwise.
Raised cosine pulse of duration LT (LRC)
 1   2 t  
  1  cos    , 0  t  LT ,
g (t )   2 LT   LT  
0, otherwise.

Gaussian Minimum Shift Keying (GMSK)
   T    T  
  2 B  t     2 B  t    

g(t)= Q   2  Q  2  ,

  ln 2   ln 2 
    
  
2
1  x2

Q(t )   e dt.
t 2

So, now these signals can have different pulse shapes; that means g t. One of the
common pulse shapes which is used is the rectangular pulse shape and which is one we
have considered in the previous discussion, the pulse shape could also be raised cosine
pulse shape, ok. So, this is also a pretty standard and more easily acceptable pulse shape

243
the advantage of this pulse shape is that it is much more compact in frequency where as
this is less compact in frequency. But, it has its own other advantage this has its own
advantage; this is easier to process and this requires a little bit more complex processing.

However, the overall gain in this particular system is much superior, but again if you
look at multicarrier systems, a rectangular window helps you maintain orthogonality. So,
each has their own pros and cons and one has to choose the pulse shape based on the
application and overall scenario.

Amongst this there is also another very important pulse shape which is Gaussian pulse
shape and what we have along with that is the minimum shift keying we will very soon
see that. So, the Gaussian pulse shape uses g t which is described by this expression
where Q is the Q function it is the very well-defined Q function. And in this expression
there is this B term which has been introduced which is the bandwidth parameter or the
minus 3 dB bandwidth of the Gaussian pulse.

So, here when we talk about the second generation system the parameter BT where you
can see that B and a T term over here which is the time bandwidth product is usually
restricted to a value around 0.3 which results in one of the best possible spectrum
occupancy of the signal.

So, to summarize in all the previous discussions we had a g t in place you would easily
remember that all the discussions that we did there was g t in place and this particular set
of results is one where we have taken g t to be rectangular. So, instead of that you could
also take g t which could be the rectangular as we have said, it could be the raised cosine,
it could be the Gaussian pulse shape also. And, another important factor which would
like to point out is in these cases the pulse duration need not necessarily be restricted for
a duration of T. You can see from here that this pulse shape can go up to L times T ok.
So, that is why it is called LREC and you can have more than 1 pulse duration; that
means, you are having the longer pulse duration. The advantage you have is that you can
have narrower and more sharper transitions.

So, that is why you have an extra multiplication factor and such systems where the signal
portion is extending beyond T duration where T is the symbol duration. So, when the
signal pulse shape expands more than that you usually call those systems as partial
response signaling and whereas those signals which are restricted to within the duration

244
of T you call them as the full response signaling. So, this is classically available in
textbook you can refer to them, but we would we are revisiting them because they are
our basis for understanding the wave form structure for second generation as well as
fourth, fifth and other future generation systems.

(Refer Slide Time: 23:41)

If g (t )  0, t  T ,CPM, full response CPM,

g (t )  0, t  T , CPM, partial response CPM.

So, in case of g t being for the full response signal we have g t equals to 0 for t greater
than 0 and it is not properly written for t less than or equal to sorry g t is equal to 0 for
this thing and g t is not, this is well written, sorry. I made a mistake over here. It is rather
this is absolutely right whatever is written over here that in case of g t being 0 for t
greater than 0, what we have is that it is called full response signaling which is what you
just described and g t not equal to 0 for t greater than 0 is what you have partial response
signaling which I just described.

So, in this case if it is rectangular pulse shape g t would appear in this form and q t which
is the integration of g t would appear in this way alright which you can clearly see that
once it reaches the value of half, after integration of this thereafter the value remains
constant because this portion the signal is 0, ok. Now, if we look at the LREC for 2T;
that means, where it spans two symbol duration then the integration of g t is going up to
this value half till the duration of 2T. Because if you keep integrating this signal the

245
signal is going to integrate like this and there after it is 0; that means, no more
accumulation is happening and hence it is maintaining that same value, ok.

(Refer Slide Time: 25:15)

So, if it is raised cosine you can see a smoother transition, you can also see a smoother
transition, but; however, in all cases the continuity is maintained, ok. So, in this case the
raised cosine is up to a time duration T in this case it is up to a time duration of 2T.

(Refer Slide Time: 25:31)

Now, this particular figure is one for the GMSK pulse shape or the Gaussian pulse shape
we will talk about the MSK very shortly. So, in this case what we see is that the pulse

246
shape for various values of BT values, ok. So, BT equals to 1 is the one which is shown
over here and BT equals to 0.1 is what we see over here.

So, what we see is that as the bandwidth increases factor for the same value of t the pulse
becomes more and more closely packed, alright. Whereas, so to find out tradeoff
between the bandwidth occupancy and the pulse duration and spectrum efficiency, BT
equals to 0.3 is the one which is used in modulation and in such systems you can also see
that around t equals to 0.5, one could truncate at least this particular 1 in such a manner
that you can have minimum errors, right.

So, since these ultimately stretch to infinity there will be a certain truncation point which
has to be followed otherwise your signals maybe out of you it will be difficult for one to
process and it will be unnecessarily long versions of signal which required to be
processed at the receiver.

(Refer Slide Time: 26:57)

So, now let us look at the MSK part of the representation of GMSK. So, one of the things
to be remembered is that it is the MSK signal has g t which is rectangular. So, when we
go to GMSK it becomes a Gaussian pulse shape instead of a rectangular pulse shape. So,
in a standard MSK it is a CPFSK signal with modulation index of half and the carrier
phase in the interval whatever we have written in the previous slides you can easily recall
that it is written in this form.

247
  
 (t , I )   I k   I n q(t  nT ),
2 k 
 I n (t  nT ) 1
 n  , nT  t  (n  1)T , h  , g (t )  rectangular.
2 T 2
  I n (t  nT ) 
s (t )  A cos  2 f ct   n   , nT  t  (n  1)T ,
 2 T 
  I   
 A cos  2  f c  n  t   n  I n n  , I n   1 ,
  4T  2 
1 1
f1  f c  , f 2  fc  .
4T 4T

And, it is a special form of binary FSK; that means, only two values of I n are selectable.
So, as discussed earlier theta n is given in this expression and the corresponding
expression over here translates to this one, which also we have discussed in the previous
few pages, if you go back again to them you want to easily get them.

So, now, we remember that this was inside the cosine function, so again we have got
back s t which is the modulated carrier there is fc t, there is previous accumulated phase
as well as the particular term which we have just seen in the previous step. So, if we
process if we process this particular set of algebraic expressions what we find is that s t
can be written as a cos 2 pi fc plus I n by 4T along with this 2 pi term. So, if you look at
this if I take out 2 pi over here I am going to get I n by 4T as representation of this, there
is a t because of this and there is a t because of this. So, you have this particular term.

Now, I n can take either plus 1 or minus 1, right. These are two values that I n can take. I
n can take plus or minus 1 because we are talking about binary FSK, right. So, if you
take I n as plus 1 or minus 1 your f 1, one of the frequencies will be f c minus 1 by 4T
and the other frequency f 2 would be f c plus 1 by 4T, just if I replace this one this whole
value as plus 1 and minus 1. So, we have two different frequencies. So, as if we are
switching between the two different frequencies and one frequency is fc minus 1 by 4T
and f and fc plus 1 by 4T.

248
(Refer Slide Time: 29:33)

si (t )  A cos  2 f i t   n  0.5n (1)i 1  , i  1, 2

 1   1  1
f  f 2  f1   f c     fc   .
 4T   4T  2T

v(t )  I 2n g (t  2nT )  jI 2 n 1 g (t  2nT  T )  ,
n 

 t
sin , 0  t  2T ,
where, g (t )   2T
0, otherwise.

Now, if you look at the frequency separation in this case what you get is that f 2 minus f
1 you would equate it to be 1 by 2T. So, what we can see is that when we choose MSK
we are landing up in a situation where the frequency separation is turning out to be 1 by
2T and what we have also seen before is that this is the minimum separation of
frequency that is required in order to maintain orthogonality.

So, this is why we usually referred to this as the minimum frequency shift keying and if
we add the Gaussian pulse shape along with it then we are going to get the GMSK
signaling and hence the primary reason for doing this is that the spectrum occupancy of
this is much lower compared to traditional communication systems and we can have a
much compact system.

249
The other advantage is that the peak to average power ratio is also low because you are
not changing the amplitude, but you are only changing the frequency or in other form the
phase. So, the amplitude is remaining constant and hence we are getting a constant
amplitude or a constant envelope signal with only frequency shift that to the minimum
separation along with the continuity in the phase which would give raise to lower out of
band emission.

So, in the next lecture we will look at the spectrum occupancy of such signaling
techniques and appreciate the importance of maintaining continuity in phase or choosing
the appropriate pulse shape which is again a motivating factor for the future generation
air interface or waveform design.

Thank you.

250
 Evolution of Air Interface towards 5G
Prof Suvra Sekhar Das
G S Sanyal School of Telecommunications
Indian Institute of Technology Kharagpur

Lecture - 14
Waveform in 3G

Welcome to the lectures on Evolution of Air Interface towards 5G. So, in the few
lectures we have seen how the evolution of requirements have happened. And, we have
also been seeing the basic signal structure which has helped us in understanding the way
of representation and, how it lays the foundation for the second generation as well as for
the fourth generation and the future generations.

(Refer Slide Time: 00:41)

251
Rectangular pulse of duration LT, L=1:CPFSK (LREC)
 1
 , 0  t  LT ,
g (t )   2 LT
0, otherwise.
Raised cosine pulse of duration LT (LRC)
 1   2 t  
  1  cos    , 0  t  LT ,
g (t )   2 LT   LT  
0, otherwise.

Gaussian Minimum Shift Keying (GMSK)
   T    T  
  2 B  t     2 B  t    

g(t)= Q   2  Q  2  ,

  ln 2   ln 2 
     

2
1  x2

Q(t )   e dt.
t 2

So, what we have seen till the previous lecture is that in the different pulse shapes. We
have actually talked about a g t, which is the pulse shapes and there could be a various
forms and the well-known form is the LREC the REC tells us that it is a rectangular
pulse shape and L tells us the length. So, it could be L equals to 1, it could be L equals to
2 and so on and so forth.

And, we have also said that how the value of L would affect the representation of the
signal. So, we also said that when L is equal to 1 it would be the full response signaling;
otherwise if L is more than 1 then it will be called partial response signaling. So, we had
talked about 3 different pulse shapes, one is the rectangular pulse shape, then we had
talked about the raised cosine pulse shape, and we also talked about the Gaussian
minimum shift keying pulse shape were the pulse shape is Gaussian in nature, which has
a bandwidth parameter and the T parameter. So, B T product which was optimized.

252
(Refer Slide Time: 01:53)

If g (t )  0, t  T ,CPM, full response CPM,

g (t )  0, t  T , CPM, partial response CPM.

And, in this slide we had seen the how the pulse shape g t; that means, this is the g t and
q t is the integral of g t, because we discuss that in a typical FSK one shifts from one
frequency to another, and because of which there could be huge amount of increase in
the side band. So, to avoid that one would do the PAM followed by FM.

So, when you do PAM you have to choose a certain kind of pulse shape. So, this is the
pulse shape we are talking about and when you do FM with the PAM signal, then this
integral of the signal comes in and which results in q t. So, what we clearly sees for
rectangle if you do the integration with 0, then as time increases the integration
increases. And, then after time t time small t equals to capital T there is no longer no
other value which gets added and hence this value remains constant, with 2 T duration of
pulse; that means, l is equal to 2 what we will see is that the integration will increase
slowly. And, after this point the value is going to remain constant which is depicted over
here.

253
(Refer Slide Time: 03:04)

What we see over here is the raised cosine pulse shape and this is the one corresponding
to l equals to 1. And, this is the 1 corresponding to l is equal to 2 and accordingly as you
integrate slowly it rises I mean it rises slowly and the rise is not that fast, because the
value decreases and at time T equals to small t is equal to capital T, there is no other
value and hence it remains constant at that value.

So, that the difference that we see from here is that, there is a linear increase and there is
a sharp change whereas, here we see that there is a smoother transition of the q t.
Similarly, this one extends for 2 T the more or less the same shape, but it is just
elongated longer. So, when things are over longer duration of time you would expect that
the pulse to be to be the spectrum to be narrower.

254
(Refer Slide Time: 03:59)

Now, this is the one, what we see for the GMSK. We had also discuss this and what we
had pointed out is that for the for the BT value of 0.3, this is very critical value. And, it
provide us good tradeoff between the bandwidth and the pulse duration and helps us
have a good shape which is used in the GSM modulation.

(Refer Slide Time: 04:22)

255
So, at this point we also reviewed the MSK, where we looked at the same signal
structure which we had started off with and in the same signal structure, we were able to
establish that the signal that goes out can be represented in a form as is written in this
particular equation.

And, in this particular equation what we also saw is this particular term which is of our
interest, which can be studied as if there is a particular frequency f 1, which is fc minus 1
by 4 T depending upon the value of I n. And, it could be f 2 another frequency which is
fc plus 1 by 4 T depending upon the value of I n. If, I n takes minus 1 you get this value
otherwise it takes this value.

256
(Refer Slide Time: 05:12)

And, then we computed the difference between the 2 frequencies which turned out to be
1 by 2 T, which we also said is the minimum separation required for the orthogonality
criteria which we discussed in the previous lectures. And, hence we could also call it the
minimum shift keying and you could also represent it as the 4 phase PSK as well. So,
there are different ways of representation whereby in that case your g t would appear as
sine of pi t by T.

257
(Refer Slide Time: 05:49)

So, this is the basic structure on which the GSM modulation stands. And, in this picture
we are trying to show how the waveform would look like.

(Refer Slide Time: 05:56)

258
And in this context it is sometimes interesting to look at QPSK can offset QPSK. So,
QPSK as we all know that there are this 4 constellation points, which are very vital. So,
these 4 constellation points and in every signaling interval that there are 2 bits which are
sent right. Depending up on the bit value if it is 0 1 this constellation is sent, if it is 0 0
then this would be sent, if it is 1 0 this if it is 1 1 this. At every signaling interval edge if
both the bits would change simultaneously as you can see that there will be 180 degree
phase reversal. And, hence there would be a 0 crossing.

Now, this causes distortion in the signal as it passes through the high power amplifier.
And, hence to avoid such sudden fluctuations what was suggested is that, instead of
letting the 2 bits change simultaneously, what if we offset one of the bits compared to the
other.

(Refer Slide Time: 06:59)

259
So; that means, instead of doing both the transitions at the same time.

(Refer Slide Time: 07:04)

One could think of sending an offset; that means, a d 0 is for duration 2 T is for the entire
duration 2 T and d 1 is also for the duration 2 T. So, in the unlike the previous case
where both were for duration 2 T, but both were transiting at the same point in time,
whereas here what you can see is that, when one is changing the phase the other is
remaining constant and when another one is changing phase the other one is remaining
constant.

So, as a result what happens is that one is not changing from one of the constellation
location to another, where there is 180 degree phase shift. So, one can avoid that and one
would restrict to only 1 bit change; that means, from this constellation either it would go
to this point or it would go to this point. And, from any other constellation again this one
it would either go there or it would go there, and avoid a direct transition to this. This
particular path is avoided.

And, hence the signal shape is restricted. The phase change is reduced to the phase
change is reduced then out of band is expected to be lower, but due to other factors also
the overall spectrum requirement does not change, but the signal characteristics as it goes
out into the RF section is now improved.

260
So, with this we have this called as the offset QPSK. Now, you could also see MSK in
the same form whereas the pulse shape instead of being rectangular, you would
recognize it as the sine of pi T by 2 T. So, you could also write the representation in this
manner and the other form is that your pulse shape would be Gaussian in nature and then
you have the GMSK modulation.

(Refer Slide Time: 08:52)

So, these modulations ultimately influence the spectrum. And, what we see is that a

261
typically for the rectangular pulse shape we all know that it results in a sinc spectrum;
that means, we have the sinc expression over here correct. And, the sinc expression gives
rise to large side lobes, the side lobes does not decrease very fast whereas, if we have the
raised cosine pulse shape which is much smoother, it is naturally expected that the side
lobes would be lower compared to that of the rectangular pulse shape.

And, hence one usually goes for the raised cosine which you generally study in a typical
course of digital communications and we just revisit here for the sake of going back to
the basics. And, also gives us a impetus towards understanding how this pulse shapes
and the spectrum is related. And, we have already seen the pulse shape for the Gaussian
pulse shape in the previous slide.

So, more or less what we are trying to show is that the choice of pulse shape is very very
critical depending upon the spectrum occupancy and out of band reduction. So, this
would typically influence the out of band emission would typically influence your choice
of pulse shape. And one would like to restrict the pulse shape in a manner in a manner
which is pretty tight.

However, when we go to multi carrier systems like the fourth generation and beyond, it
becomes imperative that the orthogonality criteria is also maintained. So, will have a
look at that as we go into details in the next few slides.

(Refer Slide Time: 10:28)

262
So, this particular rough sketch a compares the spectrum of the raised cosine and that of
the rectangular, where it kind of depicts that raised cosine in a relative performance has a
lower out of band. Although the main band is slightly wider, but finally, the out of band
emission is lower compared to that of the raised cosine pulse shape.

(Refer Slide Time: 10:52)

So, here what we have is the comparison with the MSK right and this is the one for the
offset QPSK, whereas this is the one for MSK. Now the difference is that in MSK your
pulse shape would appear like sine pi t by 2 T, where as in offset QPSK, it would still
remain as the rectangular pulse shape.

263
(Refer Slide Time: 11:18)

And, as a result we get MSK it is lower and in this particular one, what we see is
comparison of MSK with a GMSK with a BT product of 0.5, 0.3 has a different GM
spectrum. So, here what we see is that compared to MSK, GMSK has even lower out of
band and over all smaller bandwidth occupancy.

So, this is the this is why GMSK modulation is used for the second generation, where we
have cited that the peak to average power ratio is low as well as the out of band emission
is low it is a pretty tight and very efficient spectrum, but the spectral efficiency is not
very high, which is given rise to use of different modulation techniques and pulse shape
for the future generation and next generation systems.

264
(Refer Slide Time: 12:04)

So, next what we look at is the third generation system, essentially the direct sequence
spread spectrum, which is very much different compared to that used in the second
generation system. So, we will take a brief look into how this things is structured and
what is done and what is the advantage and how things are processed at the receiver? So,
that we get to see the distinction between them. So, here what we see is that there is a
data signal? Ok.

Data signal is our original message signal that is containing plus or minus 1, which was
the I n in case of our analysis for the GMSK system. And, there is a pseudo random
sequence or a pseudo noise signal present along with the original signal. So, this pseudo
noise signal is a sequence of plus and minus ones in this particular case. So, it can be
complex values also. So, what is done is the original signal is spread using this pseudo
noise sequence. So, one can think of a direct EXOR at the bit level. So, one is doing the
bit level processing, one can do the EXOR operation.

So, whatever is the signal that is present, one would multiply it in the time domain I
mean if you are doing it in the base band signal processing domain, if you are doing it in

265
the in the zeros and ones in the bit level 1 can do an EXOR, otherwise you will have this
multiplication. So, there is this information sequence at the transmitter, which goes to the
channel encoder.

So, the channel encoder would be the forward error correction code, which would
include the forward like convolution codes or turbo codes followed by the modulator.
Now, in the modulator, one would have this conversion of bits into the signals here in
this case it is depicted plus and minus 1, pseudo random generator would also generate
the signal in the same domain as the data signal.

So, if we are processing at the bit level this will also generate at the bit level, where as if
we are processing at the base band signal level, that is in the real domain it would also
generate in the real domain or correspondingly the complex domain. So, if it is in the
base band as in the bit domain we have said there will an EXOR operation whereas
otherwise it will be a multiplication operation.

So, if we see carefully what happens is that the small duration; that means, this duration
as has been identified over here is usually known as the chip duration, Tc. And, we had
earlier stated when we were describing the specifications of third generation, there was a
chip rate 3.84 mega chips per second MCPS. So, this chip duration is such that 1 by Tc is
the chip rate, whereas this is the signal rate.

So, now, what we see is that the number of chips that go into the signal period would be
termed as the spreading factor. Now, why it is called the spreading factor? Simply,
because you can clearly see that T b, which is the bit duration, is related to the band
width in an 1 by T b fashion. So, the band width is 1 by T b. Let us say here the band
width is 1 by T c or the bit rate is 1 by T b and here the chip rate is 1 by T c. So, T c
being much much smaller. So, this is R c and this is R b. So, what we see is that T c is
much much smaller than T b. And, hence we can write that R c is much much greater
then R b right. So; that means, that rate of chip is much higher than the rates of the bits.

And, hence there is an effective increase in bandwidth from the bit domain to the chip
domain. So, when you are going from bit domain to chip domain there is a significant
increase in the bandwidth factor right. So, this can be used in multiple ways. So, here in
the third generation system, this chips are actually assigned or the codes, the sequence of
chips that are present are usually assigned to different user, whereby the they can identify

266
their bit sequence by the reverse operation of what happens at the transmitter side. So,
we will see it here shortly.

So, at the transmitter side your input bit stream is multiplied by the PN sequence and
then one can send it to the modulator. So, after the multiplication one can do a pulse
amplitude modulation, where by whatever signal you get you can modify the amplitude
and you can send the signal out. Through the channel it goes to the receiver.

Now, at the receiver you again use the same PN sequence that has been multiplied with
the data source right. So, now, a user should know its PN sequence or the code that is
associated. So, it is also called the code ok. And, because this is called the code we also
call it the code division multiple access. The reason is that here if we have the same
code; that means, the same pattern and we accumulate it. So, what we see is, when we
multiply a 1 with the 1 it is a 1, when we multiply minus 1 with a minus 1 it again
becomes 1. So, effectively we have all the values in the entire duration to be plus ones.

And, hence we can recover this particular signal when we add it up right. Whereas, if the
code is of a different type; that means, instead of having plus 1, if let us say we draw
another sequence, which let us say is minus 1 over here, and it is plus 1 we just have the
reverse sequence let us draw the reverse sequence ok. So, if you have the reverse
sequence in that case the original signal is plus 1 whereas, at the receiver we are
multiplying with minus 1.

And, hence at the end of the entire thing what we are going to get is 2 sequences which
cancel out each other to produce a zero sum. So, generally the codes which are assigned
to users, the codes which are assigned to users can be generated in various different
forms, and one of the way of generating the codes is to provide orthogonal codes.

So, orthogonal codes would have the property that if I have the code sequence C m and
at the receiver I multiply with the code sequence C n, and I just put a conjugate to write
the generalized expression of k let us says k-th chip right. And, sum over k and sum over
k equals to 1 to L L c, which indicates the chip length, I will be getting a value I can use
I can normalize the entire thing 1, if m is equal to n and this could be defined to be 0, if
m is not equal to n right. If such happens then if let us say the transmitter generates with
the code sequence m and the receiver decodes with the code sequence n. So, when will
this happen?

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This will happen because if the transmitter has created the signal for m-th user, but n-th
user tries to decode it then the end result at the receiver of the n-th would be 0. However,
if it is the same m-th receiver in that case it is going to get a 1 right. So, that is the
property of orthogonal codes. So, in that case only the desired user can decode the signal
and undesired users will not be able to decode the signal. So, this way there is an
inherent privacy or secrecy, which is included into the mechanism. So, if one wants to
have a secret or private communication 1 gets the benefit of that by virtue of using code
division multiple access.

Whereas, if we consider this with respect to other schemes there just different time and
frequency slots are used; so, if 1 user knows or decodes all time and frequency slots, one
is able to decode all the other signals, but here they mal intention user needs to know the
specific code that is been assigned to a user. So, if it is the orthogonal sequence of codes
then one may be able to try using all possible combinations of codes and able to decode
the signal finally. But, then there were other codes which are known as the pseudo
random codes, which need not necessarily be orthogonal in that case the code sequences
can be made very very large and one in to find the particular code that has been used by
another user will not necessarily be a easy task.

Now, here when you decode such a thing amongst a several problems, one of the issue is
to synchronize the code. So, now, just look at the whole thing, if the user who is the
desired user instead of using the code which is the which is kind of depicted in this
picture, one tries to use let us say let us clean up some of the earlier things here. Let us
say one tries to use the same code, but it is shifted ok. Let us take another color. So, let
us say it is shifted and instead of that it is shifted over here ok.

So, if it is shifted version them it would appear that we are kind of doing a delayed
correlation. So, here again different properties of the codes are necessary the code should
have very good autocorrelation properties as well as very good cross correlation
properties. Cross correlation properties would mean that when you are cross correlating
with other codes. It should be producing a number which is as small as possible.

Whereas, you are correlating with itself it would give you the peak. So, if it has good
autocorrelation properties then that can also be used in code synchronization. So, code
synchronization is a very vital property of such schemes. So, if you are not able to

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synchronize the code properly and the delayed version of the code somehow is very
close to another code then the end result would be pretty much futile. So, these are some
of the vital things that one has to remember, when operating with such a scheme.

(Refer Slide Time: 23:43)

So, there are different modulation techniques also. So, this particular one shows the
direct sequence QPSK modulator. So, where we have the encoder and 2 parallel streams,
where one goes with the cos, one goes with the sine. So, one has the data which is split
from serial to parallel and it goes in 2 different directions. There are 2 different PN
generators and after processing one would go through the balance modulator. And, one
with the cosine and one with the sine in quadrature with respect with each other and you
generate a QPSK signal. So, what you see over here is only one of the channels.

What you see in this particular picture is one of the channels. What you see in this
particular picture is that one of the channel is part of it. So, that is the part which was
depicted in the previous slide, but in this slide we have both the things together. Now, the
demodulator part one would have a matched filter. So, in the matched filter one is using
a complex version of the matched filter, because you have the complex signal over here,
and then there will be a sampler.

The clock rate that will that will be given over here would be at the rate at which the PN
sequence is generated. And, again typically you would multiply with it and produce the y
bit that is output and goes to the decoder. So, it is a little bit more complicated version of

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what is mentioned in the previous slide, but this is what would be typically used in the
communication system.

(Refer Slide Time: 25:23)

Moving at further so, what we have over here is description of or rake receiver for
multipath. So, what it does is that before we discuss this is that, when signal propagates
from one point to another. So, let us say this is the transmitter and let us say this is the
receiver.

So, in a typical wireless link there would be multiple reflections before the signal can
proceed to the desired direction, there could be to the desired intended user there could
be reflections and it proceeds. And, if one things of sending an impulse just for the sake
of doing it, at the receiver what we will find this is the delay axis we will discuss this
again later on. The first path let us say let us identify this as path number 1 would take a
certain propagation time and it would show up at a certain distance.

What we will find is that the next path would appear at a certain delay, which we can call
it as tau 2 and it will appear over here from the second path and so on and so forth. If this
path takes time tau 3 for propagation as you know this is a little bit longer path, it will
appear over here and this is even a longer path as we can see over here what we see is
that the signal is going to appear over there. So, now, what we see is that the signal
which has been sent is received as if there are echoes at multiple delays; that means a
same copy is received over several delays and like an echo.

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So, in this case a typical architecture known as rake receiver which has the signal going
for further processing, and the signal is delayed through several delay units and again
sent for processing and it is delayed further and sent for further processing. So, this
particular structure would be a three finger rake receiver will be a three finger rake
receiver and each figure would be hooked on to a particular delay of the path.

So, in this kind of receiver the delay estimation for each of the path is also important. So,
at each of the fingers the entire processing as shown in the previous slide can be done
and combining can be done later on. So, there are different kind of combining techniques
which are also used. So, effectively what it does is it captures the signal that arrives
through multiple paths through a combining procedure.

So, when it combines the signal which arrives through multiple path, it essentially
retrieves the energies, which has been scattered in different directions right. So, the
energy gets scattered in different directions by virtue of wireless propagation, because
when it radiates it radiates in all direction. And, some of the paths get reflected and
finally, it arrives at the receiver. So, the receiver all it tries is to individually track the
different most powerful signals and process them and combining them.

So, otherwise if one would have processed the entire thing together they would have cost
a heavy amount of inter signal interference. So, when there is lot of interference this
signal quality degrades. Whereas, here what we are trying to do is to extract the different
paths individually and combine them in a phase coherent manner. So, that we are able to
maximize the energy that has been received at the receiver end.

So, in the next few lectures we look at one or two more interesting points and which are
related to the to the third generation air interface, especially about the other additional
things which go beyond the signalling, and then we will move into the fourth generation
which again will form the basis for the fifth generation or the NR or the fifth generation
new radio.

Thank you.

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 Evolution of Air Interface towards 5G
Prof. Suvra Sekhar Das
G. S. Sanyal School of Telecommunications
Indian Institute of Technology, Kharagpur

Lecture – 15
Waveform in 3G (Contd.)

(Refer Slide Time: 00:25)

Welcome to the lectures on Evolution of Air Interface towards 5G. Till the previous
lecture we have discussed the Waveform for 2G as well as of also laid the foundation for
the waveform structure for 4G and beyond and we have also started discussing about the
waveform for 3G. So, we will briefly conclude the air interface properties that are there
in the 3G and will soon translate into the foundation for the multi-carrier systems, which
is essential for understanding the 4G wave air interface waveforms as well as the 5G
waveforms.

So, what we were discussing in the previous lecture was essentially the transmitter
structure, which we have laid down over here. And, we talked about the modulation part
then there is the channel and the receiver part, which we have identified over here.

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And, we have discussed in details how the signal which is of duration T b gets multiplied
by chips, where each of the chip is of duration T c and we talked about the expansion of
the bandwidth, because T c is the chip duration is much much smaller than T b duration.
And, hence when we look at the rate of bit compared to the rate of the chip.

So, we will find that the chip rate is much larger than the bit rate. Effectively the signal
that goes out into the air has a much larger bandwidth compared to the original
bandwidth of the base band signal for a particular user. And, hence there is an expansion
of bandwidth, and typically these kind of systems are known as spread spectrum
communication, and this is an example of direct sequence spread spectrum. We also
discuss briefly upon the codes very very briefly upon the codes, where we said there
could be orthogonal codes, which has the property like if one uses 2 different codes with
different code indexes, then only if the code indexes are same you get the end result of
summation as 1 otherwise it is 0..

And, we also said that there could be other ways of designing codes where by the same
code is used you get a very high value, whereas when other codes are used you do not
get a 0, but you get a very small value that is very small cross correlation properties and
very good auto correlation properties.

(Refer Slide Time: 02:36)

We have also extended the same structure towards the QPSK modulation, where we said
that they would be one channel and another channel in 90 degrees with respect to each

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other by virtue of having 2 different carriers; one is the cosine one is the sine so that is
the quadrature carriers. And we have also represented a typical receiver structure.

(Refer Slide Time: 02:59)

We also discussed about the possible receivers we did not go into the details, but briefly
outlined the way it captures multi path signal. And we briefly said that it uses the rake
receiver architecture, we do not intend to get into the details because that is a complete
discussion and a detailed architecture in self. Our intension is to go into others other
models, but just to know about the differences that is present in the other systems.

(Refer Slide Time: 03:27)

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So, going beyond whatever we have discussed there is also a method for allow allowing
variable spreading factor. So, when we say variable spreading factor, what we mean is if
you look back into the signal model. The number of chips that are available during a bit
period can be modified; that means the code length in other words, the code length can
be varied.

So, instead of having a fixed code length where by R b sorry R c by R b is constant

otherwise, we can have a variable factor ; that means, the code rate is not constant it can
be a varying code rate. The only advantage that we have is that in in such a situation I
can use a higher data rate.

So, for example, the original codes can be split I mean I mean if you have 1 if you begin
from 1 you can generate 2 code sets, which have the first code as 1 1 and the second
code as 1 minus 1. And, if you see what has been happening with the previous discussion
at the receiver side, if we correlate with 2 different codes as we were discussing, we get a
1 multiplied by 1 and 1 multiplied by minus 1.

So, 1 multiplied by 1 is 1, 1 multiplied by minus 1 is minus 1 when we add together if

we add them together you are going to get a 0. Whereas, if if this was your original code
and you multiplied by the same code; that means, plus 1 and minus 1, your multiplication
would result in a 1, here it would also result in a 1, and if you sum them it would result in
2, which you could normalize by the number of chips. So, essentially if it is the same
code you get a 1 otherwise you get a 0.

So, here now what we are discussing is that instead of using a code length of 2 right,
which is described over here; that means, as given over here instead of using code length
of 2. If we use code length of 1 what happens is that the bit duration is the same as the
chip duration. So, if chip duration is my fundamental entity. In that case my bit rate is as
good as the chip rate whereas, if I use a code rate of 2 my bit rate becomes half that of
the chip rate.

So, proceeding further this particular code can be split again into a code of 1 1 1 1 and 1
1 minus 1 minus 1. So, once again what you see is that, if we correlate these 2 codes; that
means, multiply the chips against each other. For the first, we are going to get 1, for the
second we are going to get 1, for the third we are going to get a minus 1, the fourth we
are going to get a minus 1. So, when we add up all of them you get a 0. Whereas, if you

275
correlate with the same code, once again you get a 1 1 1 and 1 and when you add up
together we get a 4 normalized by the number of chips you are going to get the end result
as 1.

So; that means, once again cross correlation results in 0 and auto correlation results in 1
in this particular case as well. So, this way in this particular branch what we have seen is
that the code is 4 times larger than that of the bit. And, hence we have one-fourth the bit
rate.

Similarly, this code can also be enlarged and you have 2 other codes. So, 1 minus 1 we
have 1 minus 1 1 minus 1 expanded further with the 1 minus 1 and minus 1 1. So, if you
do the same procedure as discussed over here; that means, we multiply these two, cross
multiply, the end result will be a 1 a 1 a minus 1 and a minus 1 if you add them up you
going to get a 0. Whereas, if I multiply by the same code you are going to get a 1 minus
1 minus 1 will give a plus 1, same as with all others you going to get a 4 add them up
divide by 4 again you are going to get a 1.

So, this property is maintained. However, at this stage where your spreading factor or the
code rate or the code length has become 4 times that of the original bit length; that
means, the code has to be 4 times faster or in other words the bit rate will be 4 times
slower than the chip rate. So, now, you can proceed further and go to stage 3, where you
have the spreading factor of 8. So, this may you can proceed further and make variables
and make many number of codes, which are orthogonal to each other.

So, if we are in this stage and we allocate different codes to different users; let us say this
is user 1 this is user 2 and so on this is user 8. What we will easily find that if any one
user’s information is correlated with any other user’s information the end result would be
a 0. Otherwise when you correlate with the same user’s information you are going to get
an end result of 1 whereby you can decode the data, that is first stage.

The second stage now what we also have we can look at is that, here at this level, one
can think of assigning users these few code words; that means, there are 4 users who will
be using a code length of 8. Whereas, here we can give to 2 users each having a code
length 4 each; that means, we now have a total of 6 users into the system whereby 2
users; that means, these 2 users there will be using a code of 1 1 1 1 and the second one

276
over here 1 1 minus 1 minus 1. And, the other 4 users sorry this will be 4 users so, 8 is a
chip length 4 users.

So, they will be using the corresponding codes if I call it C 5 C 6 C 7 C 8. So, they will
be C 5 C 6 C 7 C 8. So, in total there will be 6 users these users will be having one-
eighth the bit rate of the chip rate. Whereas these 2 users would be having the bit rate of
one-fourth the bit rate of the chip rate. Same way what one can also do is instead of
giving to 2 different users in this stage, one can think of giving this code 1 1 code to 1
user and giving these 4 different codes to 4 users. So, in that case we are going to have C
5 C 6 C 7 C 8 along with it we are going to have the code 1 1 only and we will not use
these 2.

So, in that case we will find 1 and 5 4 over here which will give us 5 users. What we will
find is that this 1 1 code will remain orthogonal to these codes always. Because, you can
check with this, when 1 1, that is what we have over here. We have 1 1 over here, this 1
1 if you multiply by the first 2 ok. If, you multiply by the first 2 it will always result in a
0 because they have 1 minus 1 1 minus 1 1 minus 1.

Again, if you check the the second 2 what we going to get 1 minus 1 1 minus 1 minus 1
1 minus 1 and so on and so forth. So, in that manner whenever we take the second this
particular users code 1 1 and we try to correlate with any other users be it C 5 C 6 C 7
and C 8, it will always result in a in zeros.

Whereas when we correlate it with 1 1 it will always result in a 1. So, effectively here
what we have to do is in the first 2 chip durations this particular user’s code will be 1 1.
The second 2 chip durations that user’s code will be again 1 1 in the third duration again
this user’s code will be 1 1, and again in the final set that user’s chip will be 1 1.

So, effectively the first user let us call this as the first user or U 1 in this case. It will be
orthogonal with all other users, the second time interval, it will again be orthogonal with
all users, third time inter interval it will be again orthogonal to you all users, fourth time
interval it will again be orthogonal to all users.

Now; however, if you assign this particular code which is 1, which is actually not a code
to any use one user, then one will not be able to use any other codes, because all other
codes are generated from the parent code. So, if we remember the structure then we can

277
easily generate a combination of users, whereby different users can different can get
different data rates. Now, why would at all one do this because this would depend upon
several factors among which the link quality is one of them. So, if the link quality is very
bad or is in the situation is in a heavy interference in that case the particular user can be
using a larger code length.

So, when one uses a larger code length, one can when one is accumulating the entire
energy, one is able to get some bandwidth expansion gain or a spreading gain, which is
also another term which can be used instead of the word spreading factor, by which one
can increase the signal to interference ratio or signal to noise ratio, where by the
receivers signal strength is increased and by increasing the signal strength one is able to
finally, decode.

So, it is kind of one can also look at it as taking benefit of the diversity combining. So, as
we discussed in the previous lecture, that there are different combining strategies which
are also possible when designing the receiver, but end of the day where we stand is this
gives us a flexibility in allowing different data rates. Even the same user can be allocated
different code rates, at different connections at different duration of time, whereby the
user can achieve different data rates. This is one of the vital factors that was introduced
in 3G; however, if we look at the second generation or when will go to the fourth or fifth
generation such facilities are not available.

So, this is a unique facility and is it has it is own advantage, but; however, if we look at
the complexity of processing for such things. It grows tremendously as one increases the
bandwidth. So, if one increases the original signal bandwidth let us say to 20 megahertz
or even to 100 megahertz. This particular method of receiver processing becomes
impossible or becomes very very complicated which will cause lot of other problems at
the receiver. So, for other reasons as well, this got restricted to use in the third generation
system. And, we should be open that this particular methodology has various advantages
and special features, which are not possible in other systems, which are TDM, FDM
based architecture.

So, we should be open towards using the facilities and combining them towards
providing newer access schemes, newer multiplexing schemes and new radio access
technology. Now, this spreading can be used on top of other mechanisms and at some

278
point of time there was the concept of over-loading. So, if one uses over-loading
mechanism; that means, there is already some kind of signal which is going through.
Then one can use a spreading mechanism in order to put another data layer on top of
whatever is existing and which will cause minimum interference to the others. Because
these codes as we are seeing it is generated from a pseudo random number generator
pseudo noise generator.

So, when it is generated through pseudo noise or if we have pretty large lengths it can
appear noise like, so, in that case other signals to other signals this would appear like
noise. And, only to the desired signal it would appear as if there is some message content
in it. So, when it now when it comes to this particular method, this will see other users as
noise and it can recombine it is signal using the spreaded code in order to capture
maximum energy.

So, whereby even under heavy interference conditions this can work in a pretty good
manner. The other advantage is that this can also work in an asynchronous manner which
is difficult in case of TDM OFDM based system.

So, there is various advantages. So, it is strongly recommended that if one has to actually
make certain contributions towards or one has to investigate look into future generation
systems, one must understand the basic methodology how this kind of systems work so
that, that can be taken advantage of in a significant manner.

(Refer Slide Time: 16:32)

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Moving ahead further there is also possibility of soft hand over; that means, because it is
the single frequency network, the user equipment simultaneously combine with more
than one base stations. And handover failure probabilities are significantly reduced in
this case, because they can be assigned different codes, from different base stations and
they would the receiver simply has to switch the code and it can translate to the next base
station.

(Refer Slide Time: 16:57)

The next another important thing which was introduced in this system who was the
HARQ turbo codes was already introduced. And, the HARQ mechanism what it does is
that, we have already said that ARQ is a mechanism of automatic repeat request, but
when we talk about hybrid repeat request. It can do multiple things amongst several other
things what it can be do is when you are asking for a repeat transmission ; that means,
say the receiver has failed to receive proper amount of data. So, what typically it does is
that it rejects the data what he has, what it has received and it asks for a fresh
transmission.

So, if the link condition is very bad, then the probability that the second transmission is
received correctly is also the same as the probability that the first transmission is
received correctly. So, in other if the first transmission has a very low probability of
being received correctly, the second transmission also has a low probability of being
received correctly. However, it is also believe because of the randomness, that the joint

280
probability of receiving the signals correctly over multiple trials increases as we increase
the number of trials.

So, it is basically increasing the probability because they are assuming independence.
Whereas when we talk of hybrid mechanism this goes in a slightly different manner that
when we are transmitting the second time. So, some modifications are made in the link
parameters. The modifications made are such that the code rate; that means, the FEC
code rate could be reduced the modulation format could be reduced.

So, for example, one is a one is at a certain SNR condition, where the probability of error
is very high. Under that situation if the receipt packet fails; that means, fails a CRC and
the receiver asks for a retransmission. So, since it knows that with a previous modulation
and coding rate combination. So; that means, if the code rate is let us say half and
modulation is let us say 16-QAM so; that means, this would indicate 4 bits per signal
multiplied by half. So, you effectively have 2 information bits per signaling unit. So,
since you know that 2 bits per signaling unit has caused an error. So, when you are
asking for a retransmission one can think of reducing these 2 bits to a lower level.

So, one way of achieving that would be to reduce the modulation to may be QPSK,
whereby per bit you will be getting per symbol you will be getting 2 bits half and you
end up getting 1 bit per symbol, one can also think of changing this rate half to let there
be 16 QAM multiplied by one-third. So, that would result in 1 and one-third bits per
symbol. So, this is higher bits per symbol than this, but this is still lower than this ok.

So, this is greater whereas, this is kind of greater. So, one might choose to try this
particular bit rate or this particular bits per resource element unit. And, if one finds that
the probability increases one would be successful, because one not only successful in
receiving, but one is also more efficient because it produces more number of information
bits per signaling interval.

So, another way of doing it is, instead of simply changing the modulation or and the code
rate, one can even think of preserving the previous set of data. So, if let us say there is x t
or let say we say x vector with underscore we will indicate it as a vector is received from
the previous transmission. And, in the next transmission you are asking for another
transmission with the same information that is same modulation coded that is also

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possible, but you do not throw away the information which is received in the previous
instance. So, this method is different.

So, you have stored whatever is received and you ask for a retransmission. So, when you
have received the second information. So, this is in the first trail and x vector that is
received in the second transmissions. So, by 1 we mean the first transmission and by 2
we mean the second transmission.

So, then these 2 can be combined together. One particular way of combining could be
called the MRC combining or the Maximal Ratio Combining, which we will seen again
when we are discussing multiple antenna methods. So, there one can think of using x 1 1
1 1 indicating the first chip or the first data element of the first transmission, multiplied
by x. So, you can take the conjugate of it x 1 of 2.

So, this 2 would go to the this 2 and this 1 would go to this 1 plus x 2 of 1 multiplied by
x 2 of 2 conjugate plus dot dot dot dot dot up to the total length of the number of
symbols that have been received. So, in other words we are saying that if you have
received 2 sets, then let k be equal to 1 to L, L is the number symbols that got transmitted
in each of the packets. From the first packet, you take the k-th symbol. And from the
second packet also you take the k-th symbol you take the conjugate you add them
together and then you finally divide it by L, that is the normalizing factor and this
whatever you get will be the variable which can be fed to the decision factor.

So, what as happened effectively is that you have simply doubled your signal to noise
ratio. That means, whatever I mean provided the signal to noise ratio which has remained
the same in the two transmissions, the average signal to noise ratios remain the same. So,
whereby you could simply increase the signal to noise ratio and since you are at now at a
higher, let us say the double signal to noise ratio, the probability of the packet failure
decreases by a significant manner. So, we can discuss the outage probability or
probability of detecting correctly when we discuss a MRC transmission at a later stage.

So, please remember to use that same philosophy to calculate the probability of error or
probability of outage or probability of packet drop, if we are using the mechanism of
such kind of combining techniques instead of another technique where you can change
the modulation and code rate. So, here by, in summary, instead of simply asking for
retransmission, we ask for retransmission with either change in the link parameters or at

282
the receiver side we store the previous received signal. And, we combine with whatever
is received a fresh and the combined signal, the post after combining there is a post
combined signal would appear at a higher signal to noise ratio, which can simply
improve the probability of correctly detecting the entire packet.

So, these are some of the important mechanisms which have been introduced in the third
generation system.

(Refer Slide Time: 24:30)

They was also a mechanism for a fast power control at the rate of 1.5 kilo hertz and there
is outer loops slow TPC based modulation turbo coded modulation, based block error
rate measurement block error rate measurement; that means, when you are sending the
packets. Then you can check the block or the packet error rate and you can adjust the
thresholds for link adaptation, whereas you do fast power control mechanism.

Now, why is this one important this is important because if you look at the signal
fluctuation over time ok. If, you look at signal fluctuation over time then this under
mobility conditions; that means, when one is moving at high velocity we have discussed
this, that the signal fluctuates significantly ok.

So, if the signal fluctuates significantly then there are two kinds of things that happen;
that means, one can expect that as the distance increases if you talk about distance, the
average signal strength decreases.

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However, if you look at the small duration of time let us say in orders of seconds or half
a second within that period the distance that is effectively covered is very very small. It
may be a few meters. Now, within that few meters the average received signal strength
usually remains constant. If within that period the average received signal strength has
remained constant, however, because of the mobility, because of the multi-path we had
drawn the picture of a multi-path scenario. So, one can take a look at this picture and just
imagine that the receiver has moved a few meters may be 1 meter to 2 meter distance not
even that within that each of the these paths are going to change.

So, these are positions of reflection diffraction and scattering. So, obviously, when the
receiver has moved from that point to a new point this path length has become different.
So, we can take different color in order to indicate that. So, this path length will be
different ok. So, this path length will be different. So, this is the path length and this
point would also come from a different point; that means, the reflection point would be
different. So, similarly this would also come reflected from another point.

So, if all the path lengths have changed the way this signals would combined at this
location compared to the way the signal would have combined, when the receiver was
here is completely different. So, this combination keeps on happening as the user moves
from one location to another at every instant of time. So, when the user is moving from
here and it is slowly going towards this direction at every physical point these kind of
combinations are happening and which are changing at a every instant.

Now, because of such a change what we will find is that the signal strength fluctuates
over time in a short distance of 1 to 2 meters, which is also termed as small scale fading.
Now, if you look at the chip duration it is 3.84 mega chips per second effectively
indicating that the chip duration is very very short in order of milliseconds.

So, when it is very very short in within that duration; that means, when the vehicle is
moving from one point to another, the signal strength fluctuates heavily to the order of
30 to 40 dB because of small scale fading. We will discuss briefly about a little bit more
details when we go into the multi-path propagation and MIMO, before we understand
any other things in future.

So, in order to maintain the same level of average received signal strength over the short
distance, because if that is not done these this chips that we are talking about and the

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orthogonality that we have discussed or the correlation properties that we have
mentioned earlier over here, that instead of 1 0 it can be high correlation or also low
correlation. What would happen is that these properties would simply change. One can
think of that a some of the chips are getting high gain let us say a one another chips get a
low gain a 2 another gets a different gain a 3 because of fast fading conditions.

So, this orthogonality property gets destroyed and the entire design which was based on
orthogonality or high auto correlation and low cross correlation gets destroyed. To avoid
that during the entire symbol duration of the entire code it is desired that the signal level
remains constant. So, in order to do that a fast power control can help in a significant
manner in maintaining the performance of the system, in maintaining the quality of
service so on and so forth. Along with this there is the outer loop slow control, which
was also adjust the SNR switching thresholds based on which one can modify the code
rates, one can modify the modulation order, and one can even do other adaptations also.

So, with this we will stop the discussion on the waveform for third generation. And, from
the next lecture onwards we will discuss the foundation of multi-carrier especially
OFDM, which is the base for the fourth generation system as well as for the fifth
generation system. So, it is a an advice that one goes through the details of this particular
method, because we will not discuss this in any details further beyond this thing.

However, a this is every important many interesting methodologies have been have
developed, because of these WCDMA systems and we should understand that we can
take advantage of these things in few design of future generation systems. And just a
short note that at some point of time there were lot of proposals, which combined multi-
carrier systems plus spread spectrum systems. And, many schemes like multi-carrier
CDMA, multi-tone CDMA, and many others were developed which combined the
benefits of both the different systems.

So, there are several literature available. So, one should feel free to get into the details of
them to understand how the different special properties of the different schemes were
combined together to come up with a newer waveform architecture, which would meet
the demands or would have properties, which are very special and can be designed in a
way which can meet very special requirements.

So, thank you for this particular lecture we will meet again in the next lecture.

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 Evolution of Air Interface Towards 5G
Prof. Suvra Sekhar Das
G. S. Sanyal School of Telecommunications
Indian Institute of Technology, Kharagpur

Lecture - 16
Waveform for 4G & 5G (OFDM)

Welcome to the lectures on Evolution of Air Interface Towards 5G. So, till now we have
had Overview of the different waveforms that, are there in the second generation and
third generation and today has you can clearly see that we are going to discuss the topic
which is sorry this is wrong title that we have it is for the fourth generation system.

(Refer Slide Time: 00:46)

And we will be taking about the Waveform in 4G and primarily it will be about OFDM;
now, a brief few words before we get into the details of the discussion. OFDM as today
we will discuss is primary waveform. We have laid the foundation when we discussed
the multi-carrier FSK. So, when we discuss the multi-carrier or M-ary FSK we have
pointed out that the system model would remain the same which served as the basis for
discussion of 2G and the same waveform or the same structure will be useful when we
discuss the fourth generation and beyond systems.

So, we had also discussed how the M-ary FSK could be designed in the manner that the
frequencies that are being chosen for operations are orthogonal in nature and we had also
said that since they are orthogonal, it is possible that you not only use them for switching

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between the carriers and letting information flow by virtue of choice of a carrier, you can
actually use all the carriers simultaneously and that would have appear as FDM. And
since these carriers are to be chosen in an orthogonal manner, it can serve as a basis for
orthogonal frequency division multiplexing and today, we take this opportunity to get
into the details of it.

Now, other reasons why this is critical and important because this is a foundation on
which most of the modern generation communication techniques are built; so, it is kind
of a platform one can say. It is a multi-carrier technique and although it is we have
discussing 4G, but when we get into the fifth generation we will see that fifth generation
essentially stands on the same structure as in 4G, although there are certain variations in
the frame format and the way things are used compared to the fourth generation.

But the fundamental element is still fourth generation or the OFDM system and we will
again see today that it is not only the baseline for 4G and 5G, it is also the baseline for a
broad band wireless local area network. It is also the foundation for a broadband
metropolitan area networks. It is also a standard for digital audio broadcasting or digital
video broadcasting as well as for the satellite the high speed satellite communications.

So, it is a very very important waveform as on date. So, we do not know what is going to
happen after 10 years from now, but it is very important to study it and build our basics
so that we can understand most of the communication systems which are usually
available for commercial purposes.

It has several advantages and there are certain disadvantages. So, our aim would be to
understand as much details as possible and that would also give us a key inside into
developing newer waveforms based on whatever you have discussed earlier as well as
whatever we are going to discuss in this particular lecture.

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(Refer Slide Time: 04:03)

So, moving ahead when we talk about 4G, it is essentially IMT-Advanced we have
already said that and this used OFDM as it is written over here. So, when we talk about
4G the main word that comes to our mind is the OFDM technology in terms of air
interface. So, it is a very important method as we have already said because it is used for
wire-line communication. It is used for wireless communication namely Satellite. We
will see that. It is used for local area networks, we have already said that. It is used for
4G as well as its extended version in 5G.

So, not only that it is one of the primary multi-carrier techniques. So, it is multi-carrier
because we will see how these multi-carrier concepts come in. We already discussed it
once. So, the general class of multi-carrier techniques have a basis or it can be studied in
the perspective of OFDM. There are other views also where OFDM can be seen as a
subset of the overall class of multi-carrier, but this being very very popular it is also good
enough to study OFDM and, because it is easier compared to other methods and one can
digress and move into other techniques and understand them.

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(Refer Slide Time: 05:25)

Transmitted time domain signal

At receiver,

So, brief into the history about the OFDM what we can see that it was initially used in
the military systems and that was around the 1960’s. In this period it was used in
different military systems and this is the different names of the technologies that where
using them. So, it is not a new method that is the primary thing. Although it is very
popular these days, it is being used on every wireless broadband communication system,
but it has been existed for almost 60 years now.

And traditionally when it started to happen what we see is that there was a bank of
conventional transmitters and receivers. So, this is pretty normal because we had
discussed M-ary FSK as a foundation as we just said and these separations were delta f
and here found the relationship for these. So, we said that you going to use all of them

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simultaneously and in each of them, we said they had a model like e to the power of j 2
pi f k t. This is the carrier where this f k, k equals to 1, 2 so on up to N or you could also
index k as minus N by 2 up to N by 2 minus 1.

So, then there again you will be having N carriers and each of this carriers would be
getting an x k which is the signal from the constellation and will be sent out. So, what we
will get from the first one is X 1 e to the power of j 2 pi f k t. The second one is going to
produce X 2. So, this is f 1. Second one is going to produce X 2 e to the power of j 2 pi f
2 t and so on and the last one is going to take X N e to the power of j 2 pi fN of t and
each of this X 1 X 2 up to X n, these are element of sum constellation of order N.

What it means is that each will be drawn from a constellation let us say we are drawing
the constellation diagram for 16 QAM. So, each symbol will be drawn from them
depending upon the bit sequence. Now it can also be noted that each of these symbols
that are coming in, they did not necessarily be drawn from the same constellation. It
could also happen that some of this constellations some of these carriers take from let us
say 16 QAM, while the rest of them can take from 64 QAM or any other combination it
can happen.

So, this is generic model it is the generic system layout. It is a generic equation generic
framework and we have said that the same foundation or the same expressions have been
used will be useful in studying all the future things. So, here what we see is that each one
of them as a multiplication operation over here right; each one has a multiplication
operation, each one has a multiplication operation.

So, that means, there would be an oscillator in each of the lines. So, that means, there is a
signal constellation X k which is multiplied by a local oscillator which has a frequency
of f sub k and then, it goes out right that is what each of them. And finally, they go out
together. So, in the air medium you have a summation of X k e to power of j 2 pi f k t
sum over all k and this is your time domain signal that goes into the air. So, this is what
we are going to see at each point there will be a multiplication of the oscillators.

At the receiver what we see is that here we have again discussed the orthogonality
criteria where we said that at the receiver side whatever signal is received. So, if let us
say this whole signal is received and we demodulate by multiplying e to the power of

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minus j 2 pi f k prime t and we are going to integrate because it is continuous time from
0 to capital T which is the symbol duration d t you can do it in a summation format also.

So, what you will find is that when this frequency index is not equal to this frequency
index. So, that means, when k is not equal to k prime, then this entire thing would end up
in 0 and when k is equal to k prime, you will find that the entire thing will end up in X
sub k that means, the product would be 1. The sum of the entire multiply accumulate and
integrate operation would be 1; otherwise it is 0 by virtue of orthogonality.

A digression from this particular discussion, but which is absolutely in context what you
can also visualize is when we talked about these spread spectrum system. Essentially
what we are saying is that this particular signal that is what we are multiplying is kind of
acting as a spreading signal; one can think of it in that manner also.

So, here what we have is that the weights are drawn from exponential function, where as
what we discussed there is a more general one where the codes could be drawn from any
function. Hadamard is one particular way of generating orthogonal codes. Here if we
connect to this we can think of DFT matrix which we will see could act as act also as
generation of codes. So, this one can see it as a generalized picture through which one
can study either spread spectrum or even multi-carrier systems where it is kind of N
dimensional signaling as such and we have discussed the N dimensional signaling in the
past.

So, if one is a comfortable with the notations or description as basis functions; so, what
we have these as let us say we can write them as S m other way we will we not write this
on S m or let say f prime of k, this entire thing of t. So, this is a basis function. So, we
have N basis functions. The codes if they are orthogonal, they are again N basis
functions and at the receiver one can think of either a matched filter operation, I mean
here what you sees the correlations.

So, when you implement matched filter as a impulse response you convolve. So,
essentially it turns out to be an correlator receiver because finally, you will be sampling
at this time instance T. So, one can also visualize this in terms of N dimensional signal
with N basis functions and a matched filter operation at the receivers with the particular
basis function. So, we project the incoming signal on the different basis functions, read
the outputs and then process it further.

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So, if you see it in this way then it is a generic representation you can study all the
schemes in one particular platform. So, now, going back again to the way it was
developed in 1971, it was it was shown that DFT could be used instead of the bank of
conventional transmitters and receivers. So, this entire set of N number of oscillators. So,
we would have had N oscillators at the transmitter and N oscillators at the receivers we
have at the transmitter and the receiver both sides. So, those could be reduced and one
can use a DFT operation. Now DFT operations, the advantages it is it can be
implemented in digital circuit. It will be much low powered compared to this entire set of
oscillators that are to be used.

So, this was a turning point when it was not restricted to defense applications because
cost is an important factor. So, things could become easier to implement and with the
advent FFT, which which could realize a DFT operation even at lower complexity. So,
order of N log N is the complexity. So, one could finally, realize OFDM in more easier
fashion and OFDM techniques was started, were getting used, especially in devices
where power was a critical factor.

So, today when we look at things we have hand-held devices and most of them are power
critical because we would like the battery to last longer. So, we would have had this kind
of methods which use oscillators we would have been able to get only limited gain, but
because we could implement in digital circuits and we could use FFTs the gains of
OFDM became much more useful much more translatable and there was a proliferation
of different techniques which could use OFDM. So, it is started with this HDSL as we
are seeing HDSL that is what is written here.

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(Refer Slide Time: 14:50)

So, that is high bit rate digital subscriber line, where it was used. Then there was ADSL
where OFDM also used very high speed digital subscriber line and at that time it could
produce 100 mega bits per second which was very large bitrate at that instant of time and
I said earlier, it was also introduced into the wireless domain through digital audio
broadcasting. You can find these specifications in a particular reference which will point
out and it was also proposed for use in WLAN that is wireless local area network.

In wireless local area networks, there were two proposals. This particular proposal was
from European region which is HiperLAN and this is as can be seen its an IEEE proposal
and what we have today this is somehow more popular and you usually associate the
term Wi-Fi with such a technology that is wireless fidelity and there are different forums
which address it. But primarily it is the 802.11a which got OFDM into the systems.

In this series, there was 802.11b which did not use OFDM, but then there was 802.11g
which again use OFDM and it kind of superposed 11a and b in a manner that it could
interoperate with the earlier standards and it was designed for the 2.4 gigahertz ISM band
width ISM band. This was primarily for the 5 gigahertz band. So, in the 2 this basically
translated the 11 a into the 2.4 gigahertz band.

Then, there was 802.11 n standard which is basically extension of OFDM with multiple
antennas and after n, it was 802.11 ac which is started supporting MU-MIMO, Multi
User MIMO, you will get an opportunity to see them and finally, it is getting evolved in

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to 802.11 ax which is supposed to get finalize sometime next year. So, all of these are
still having OFDM as their primary baseline physical layer. So, there is the huge number
of devices which are going to operate with OFDM. There is a huge number of devices
which is already operating with OFDM. So, it is very important that we look into it
understanding it in such a details that we can take care of the problems which it is still
facing.

The wireless metropolitan area network also used OFDM. So, you can say that almost
every broadband access system is using OFDM and it is popularly known as WiMAX.
This particular name is more popular just like Wi-Fi was more popular instead of 802.11
a. WiMAX is kind of more popular in this domain and it is the 802.16 series of standards
primarily 802.11m which was the contending technology for 4G and this also branded as
the 4G technology. So, what we see is that there is a huge number of different standards
which are using OFDM because of several advantages right. So, we will get into the
details and see how it is helpful.

(Refer Slide Time: 18:16)

So, just a brief comparison of the application scenarios, what we see is that it is used
since it is used in WLAN, WMAN and WPAN. So, right from cell radius of a few
kilometers up to few 10s of meters of distance, it is useful and it could support high and
low mobility right and it could also operate in different frequency bands.

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So, these are, so it has a huge dynamics city associated around with it, as a huge
flexibility and although it is so, easily said and done. It is important that we get into the
details of how it operates and what benefit it brings.

(Refer Slide Time: 18:56)

Modulated waveform

So, since we are talking about the IMT-Advanced or fourth generation communication
systems and we have said that this particular air interface brings in a larger amount of
spectral efficiency, higher amount of spectral efficiency amongst the different things
which brings in spectral efficiency we had showed QAM. So, quadrature amplitude
modulation what we see over here is the picture of a 64 QAM signal space diagram.

So, that is also written over here it is a signal space diagram for the 64 QAM and you can
you count there are like 64 such dots 8 across column wise and 8 across row wise. So,
they are 64 in all and each position in this particular constellation diagram indicates
information carrying symbol. So, this particular signal for instance would be having the

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notation 3 plus j because this is the j-th j axis the i axis this is the j axis and this particular
signal constellation is going to be noted has 1 plus rather minus 5 j right.

So, like this you going to have all this constellations marked and depending upon the bit
sequence that comes in 0 1 1 0 0 whatever it is one has to take 6 bits; at least 6 bits at a
time because you have 64 which is equal to 2 to the power of 6. So, 6 bits are required to
select one of this points and the way this points can be arranged like gray coding can be
used where the difference between the neighboring symbols is at most 1 bit.

This is also very important because it could reduce the error probability when there is a
symbol going into error. So, if you are decoding let us say this particular constellation
point and instead of this one make some mistake of decoding this constellation point at
most one bit would go into error if you are using gray coding methodology. So, this is
something which we have studied in digital communications which you know. So, it
applies directly in such systems.

(Refer Slide Time: 21:14)

So, now, when we start discussing OFDM in details as the name reads out the most
prominent part is to be remembered is a frequency division multiplexing. This is very
very important. So, what it means is that there are different carriers and these carriers are
multiplexed. So, since we are talking about carriers it is a frequency carriers there
frequency division multiplexing.

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So, when we look at classical frequency division multiplexing system, we have one
carrier here let us say f 1; another carrier here f 2 and this is the spectrum occupancy or
the spectrum characteristics of each of the carriers. So, to avoid signals from leaking one
into another; one would specify a certain amount of guard band. The reason one has
guard band because let us say the signal dies out like this right.

So, when one is demodulating this particular desired signal, one can get a significant
amount of adjacent channel interference. So, one can get adjacent channel interference.
To avoid adjacent channel interference if I increase this separation to a good amount,
then the amount adjacent channel interference can be reduced. Because under all
circumstances it is never possible to have a ideal Nyquist filter; that means, one which
falls down vertically this kind of a thing is not possible.

So, one would always get a stretch in the frequency domain. So, one way to reduce the
stretch one way to reduce the overlap is to increase the separation through guard bands.
So, if one does this one can clearly see that this is something which one has to use only
to improve the signal quality and why are we looking at this because it is band, it is a
band of frequencies, spectrum is very very costly, we all know this thing very well.

So, better ways to improve or improved ways to utilize the spectrum is very much
important and we have said that spectral efficiency is one of the terms. So, we will talk
about spectral efficiency what we effectively mean is that given a certain bandwidth. So,
this is a certain amount of bandwidth it given in hertz. So, if I am using spectrum like
this. This is simply wastage, we can call this as wastage because you are not using it to
send information or rather you are using it to increase the signal quality which you have
to in order to maintain the QoS.

So, when we look at OFDM, things are better its one reason for using OFDM because it
is the best possible modulation or multiplexing method which will give the highest
possible spectral efficiency.

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(Refer Slide Time: 24:01)

Orthogonality

So, if you look at OFDM what we find is that this is again the frequency axis as the same
as in the previous picture and the spectrum overlap what you see is that this spectrum,
there is an overlap clear overlap. So, if this is my desired frequency of operation what
you see is that this portion there is an overlap of the adjacent channel frequency and
there is an overlap of the adjacent channel frequency on the left and right hand side both.

Also the other components that means, if we take this particular carrier; this carrier is
also going to produce interference. So, there will be a lot of overlap. But now, although
we are doing this so, compared to the previous picture, the advantage here is that if this is
the desired peak as has been pointed out the sub-carrier peaks; what we see is that the
null occurs at this point, there is a null.

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So, null means all the different sub-carriers they have a zero crossing at this point. So, if
they have a zero crossing, when we are using this particular carrier to demodulate the
signal, we are not going to get any impact of the adjacent channel interference. So and
why can this happen because we have already discussed the orthogonality criteria. We
discussed in a previous class and we also mentioned in today’s beginning part that each
of these carriers which you are calling as sub-carriers, they are e to the power of j 2 pi f k
t and the neighboring carrier is e to the power of j 2 pi f k prime t right.

So, if we try to see the projection of one on another and take the integration over the
interval 0 to T and this is exactly what we have done to check the orthogonal, we have to
find the condition for orthogonality. So, the condition for orthogonality met, gave us that
if f k minus f k prime should be equal to 1 upon T. This is the same symbol duration T
that we are talking about this is basically the sub-carrier spacing.

Then, one can get orthogonality. So, we have used this criteria to get our signal. So,
since we have used this criteria to get our signal this would obviously, mean that they are
overlapping with each other because the sub-carrier band width is kind of spreading on
both the sides; whereas, we are placing the sub-carrier at half that interval.

So, although they are overlapping by virtue of orthogonality one is not getting any
influence of any neighboring sub-carriers. So, this way one can save a huge fraction of
bandwidth and this is the smallest spacing that one can think of when we discussed MSK
we did say that minimum term comes because of this smallest separation that is possible
and that is by virtue of orthogonality.

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(Refer Slide Time: 27:06)

So, this is a animated picture which helps us understand what is actually happening. So,
this particular version is kind of general FDM you can say and if you will let change then
what you will find is that now these are orthogonal to each other. That means, the peak is
coinciding with the nulls of all other sub-carriers and then what we result is in OFDM.
So, basically in this blank this orthogonality has come in to give us this particular result
and as you can clearly see that there is a huge saving in bandwidth by virtue of using
orthogonal carriers and although they are overlapping, they are not interfering with each
other and one can decode the signals.

So, this is one of the main reasons why OFDM is so, popular and its being used as a
major technique in all possible broadband wireless communication systems, where
spectrum is very very costly and one would like to make the best use of such a spectrum.
So, we close this particular discussion over here and we will take on further discussions
in the future lectures.

Thank you.

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 Evolution of Air Interface Towards 5G
Prof. Suvra Sekhar Das
G. S. Sanyal School of Telecommunications
Indian Institute of Technology, Kharagpur

Lecture - 17
Waveform for 4G & 5G (OFDM) ( Contd. )

Welcome to the lectures on Evolution of Air Interface Towards 5G. So, we are at present
discussing the waveforms for the 4th generation as well as which is applicable to beyond
4th generation that is the 5G the foundation for the waveform for 5G and which is
essentially OFDM. So, we have discussed some parts of OFDM in the previous lecture;
let us continue with the discussions on OFDM and see more details about its features
properties and structures how the transmitter signal flows what happens at the receiver in
this particular lecture.

(Refer Slide Time: 00:52)

So, in the previous lecture we were discussing about the spectral efficiency that OFDM
brings with this particular animation where we saw that it can give us a wide a huge
increase in spectral efficiency. So, clearly there is a bandwidth saving and high spectral
efficiency, in other words I mean you can also think of high spectral efficiency would
result in bandwidth saving. So, it can be read in that manner as well alright.

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(Refer Slide Time: 01:21)

Orthogonality

So, now we see the next picture which is about the orthogonality again because, in
OFDM orthogonality is main thing and our interest is to visualize, picturize the things.
So, that we can even create further things in future so, what we are trying to see is that in
the time domain how does it look like. So, what we have over here are three wave forms
and basically we have three different carriers first second and the third. So, they are
essentially e to the power of j 2 pi f kt and rather the real part of it there would be the
imaginary part as well. So, we have real and imaginary and which is seeing only one of
the parts. So, this is one of the carriers, this is the second carrier, this is the third carrier.

So, the first one we see in this snapshot there is only one fundamental part of the
frequency, the second one which is this black one we see that there are two such cycles

302
ok. So, it is an integer multiple of the first one that is what we are seeing that it is an
integer multiple of the first one and then we have the third one that we are seeing there
are 4 cycles 1 2 3 and 4, but you can have any other. So, primarily what we are seeing is
that there are integer multiples of the fundamental frequency and if we do the integrands
multiply each one of them, if I multiply this with this throughout and add them up you
will find that the area under the curve goes to 0 and that is that is that is going to happen.

And one of the reasons that is happening which is kind of implicit in this picture is along
with these things there is a g of t which we did not write in the previous slides when we
are discussing, but it was already present when we are discussing the fundamental base
line signal model of M-ary FSK and we discussed orthogonal M-ary FSK, then we
discussed the OFDM structure in quite a few lectures back where we said that let this be
the foundation on which we will build.

And we had X k in each of the frequencies so; that means, each of this carriers are going
to carry a certain X of k which will be an amplitude and a phase term. So, phase term is
going to simply the chase the starting point and the amplitude factor will simply change
the amplitude, what we see over here is that all of them have the same amplitude. So, this
could indicate choice of using PSK kind of structure of QPSK kind of structure that
could be imagined to be associated with this particular waveform ok. So, so essentially
what it means is that if we have integer number of cycles of the fundamental frequency
then they would be cancelling out each other when you are processing at the receiver
side and one would get orthogonality and this is the corresponding time domain picture
of whatever we have seen in the frequency domain.

So, this gt that is what you were seeing this gt if it is rectangular this is very very
important. Rectangular means that it is constant over this entire period then only we get
the result of orthogonality which we have discussed earlier this result ok, because you
can clearly see in this orthogonality picture equation we should have had a g t along with
a g conjugate of t right. Now if these equations or if these expressions were kind of let us
say a raised cosine then the condition of orthogonality would be different.

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So, this is a some important things which we should keep in mind that has been
implicitly present in this and we may not have mentioned this explicitly, but that is what
we should remember. Now, if we change these gt orthogonality criteria brakes down
within this 1 by T criteria and it will be some other condition on which we get
orthogonality or it will depend on the choice of gt as well. And when we said that we
will get some opportunity to discuss some of the futuristic waveforms people have
already worked on them one of the fundamental things that people have been thinking or
spending their time upon is the pulse shape or gt along with this multi-carrier.

So, these two things together have been investigated will get an opportunity later on to
look at them. So, primarily this integer number of cycles of each sub-carrier is present
which is giving the orthogonality and this is how one should look at it when one sees the
time domain picture.

(Refer Slide Time: 06:27)

Two functions f1 and f2 are orthogonal in an interval (t1, t2) if the following condition is
satisfied

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i.e. the area under the product of the two functions in the region is zero.

So, this orthogonality expression we have already discussed this where here this f 1 2
and f 2 t are chosen in a manner that they are the basis functions that is what we have
said; that means, each one of them is e to the power of j 2 pi let us say f 1 of t and this is
let us say e to the power of j 2 pi f 2 t right. And if one would like to bring in g of t over
here and g of t over here then one would find the orthogonality criteria using the entire gt
as well. And one would think of using a certain gt g 1 of t over here a certain g 2 of t of
in the second one which is the more generic way of doing things and we will see some of
the outcomes at a later stage, but which is not relevant for 4G or 5G, but potentially
important for the future generation works.

So, yeah I mean as we have discussed that the area under the region would be 0, if they
are different and if they are the projection of one or only if they are equal to each other
then will be non-zero right. So, this also we have discussed that in OFDM the
frequencies are chosen. So, that they are mutually orthogonal, but I would always remind
you to recall that we have chosen gt to be 1 in all the expressions then only we have got
this criteria. Otherwise thus the result changes, this remains constant for all the OFDM
all discussions that we think of OFDM would be valid only with gt is equal to
rectangular or not changing within the period of interest.

Now one may think of a question about that how would one think of a windowing we
will discuss windowing some people already know about windowing at this stage. So,
there is a cyclic prefix which will also discuss. So, over the period of interest is the short
discussion before we go into finally there in the period of interest where we are actually
doing the processing you will find that this pulse amplitude remains constant. So, if we
are interested in this particular section over that period we can assume a rectangular
shape and the spectrum that we have considered to be sinc in all the discussion that we
have had is primarily because of have been considered a rectangular pulse shape, all right
moving ahead.

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(Refer Slide Time: 08:46)

So, some other important aspects of OFDM why it is used for wireless communication is
that it is well known for effectively combating the frequency selective fading, now this is
very very critical and frequency selective fading which occurs due to multi-path
reflection. So, we have discussed earlier when we were taking about the rate receiver that
if there is transmitter and a receiver. So, let us say this is the transmitter and this is the
receiver and there are reflectors all around the place.

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So, the signal from the transmitter the receiver would go via multiple paths right, it will
come via multiple paths and if you send an impulse from the transmitter. So, let us take
any other color. So, if I would send an impulse from the transmitter which is kind of
delta t what we will find at the receiver is if we draw this as the timeline and this as the
received signal power or amplitude. The first path we have discussed this thing, but we
are doing it in short is kind of arriving after certain propagation delay corresponding of
the delay of the 1st path then of the 2nd path 3rd path 4th path and so on and so forth.

So effectively the impulse gets spreaded in time right. So, when things get spread in time
things in the frequency domain would get restricted or shorter. So, if you look at the
Fourier transform of the delta function is kind of flat in frequency flat means it is a
constant value across entire range of frequencies. But if you take Fourier transform of
such a sequence and of course, there will be a phase associated with each of these pulses
we will find that the frequency response in the frequency axis will not be flat this is flat
in case of delta function a Fourier transform of the flat, but here what you will find is that
the frequency response would be fluctuating something like this will see this pictures.

So, in OFDM we will again have a picture of that that when we are seeing these narrow
sub-carriers there is the design issue involved one usually chose it in such a manner that
the band width of the carrier is such that it experiences near flat fading. So, that is what it
meant that it is kind of very resilient to frequency selective fading. So, that is in short
about the discussion we will see again later on.

So, one is to understand the propagation characteristics very well in order to understand
what the frequency selectivity and the multipath and how does OFDM take care of it. So,
if its experiences a flat; that means, nearly flat frequency response equalization is easier.
So, that is again a huge advantage for wireless communications because already you
have extra complexities this is going to only help reduce the complexity that is to be
addressed.

So, this way we will proceed towards studying the architecture of the transmitter now
that is one of the objectives, but before we get into that it is important to look at the
signal model which will again help us in realizing the transmitter architecture. So, we
have already written this kind of a expression before. So, X s of k, k is the sub-carrier
index this is the sub-carrier index which you have been writing again which is being

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reflected over here. So, what you see in this particular part is that you have k multiplied
by 1 upon T f and Tf is the same as T as we have used on the previous slides ok.

So, wherever you use T its actually Tf, but T f is the duration of the OFDM symbol right
and Tf is equal to T whatever you have done is equal to 1 upon delta f and delta f is equal
to f k minus f k minus 1. So, that is that completes the definition and what you see is that
k multiplied by this is effectively this expression is basically k multiplied by delta f that
is these frequency separation. So, if k is equal to 0 you have the DC carrier if k is equal
to 1 you have the first fundamental frequency and so on all right.

And all of them are appearing simultaneously so, therefore, there is a summation and
there is a normalizing factor this normalizing factor one can either consider or one need
not consider this it depends upon ones choice because, this is not going to matter finally,
except in mathematical notation. Because, if you are actually realizing a system you
would usually normalize the power to a certain desired value and you will send it out
only for mathematical convenience this kind of normalization factor is used. So, that one
can get the normalized power of X s of t as 1, the X capital X s of t which is the
constellation can also be normalized to a unit power. So, this normalization is something
which depends upon your actual realization and if you doing simulations otherwise it is
kind of ok all right.

So, these are all things that have been described over here amongst these one should pay
attention to this function which is the gating pulse or our g of t minus sTs this is basically
the gating pulse s is the OFDM symbol index and Ts is equal to T g i which is the guard
interval which will talk about plus Tf ok. So, we have over here certain other offset
values. So, these offset values are present in order to create the signal in an appropriate
manner, we are not going into the exact details of opening up the equation, but I can
leave it as an exercise for you to work out the details of it and understand what is the
meaning of this we will see that X t which is the summation over x s its a summation
over x of s ok.

So, what is the meaning of this in this particular expression, we see that gt is essentially
an expression which is like this; that means, it is rectangular over a period of Ts ok. And
Ts we said is equal to Tf plus T g i so; that means, if we say that this duration is the
duration of Tf which is equal to 1 upon delta f right Ts is actually larger than that and the

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extra portion is the cyclic prefix, now one can easily see that we can have some shaping
over here and some shaping at the end without effecting the rectangularness in within the
region of a consideration ok all right.

So, we will discuss again some more things there. So, this essentially helps us in writing
this notation over here whereby we have like the 1st OFDM symbol’s pulse shape, the
2nd OFDM symbol’s pulse shape and then the 3rd OFDM symbol’s pulse shape, then the
4th OFDM symbol’s pulse shape and so on, so these are all orthogonal to each other in
that sense. So, although it appears like a summation, but it actually a sequence; so, these
are again some things of notation which one should remember to use appropriately so,
that things do not get mixed up.

(Refer Slide Time: 16:56)

So now we look into the transmitter structure it is very important to understand the
structure because this is something which will be used throughout. So, there are binary
input bits which are coming in at this point and these binary bits are sequence of 0s and
1s which are converted from serial to parallel now why it is done so, will be cleared once
we look at it. So, here if we look at the output of OFDM what we have is X k e to the
power of j 2 pi fk t right and there are sum over all this different sub-carriers so we just
take a look at this expression. So, these are the constellations and these are the carriers
all right. So, that is what we have over here and these are happening in parallel that is
why we have this kind of a summation ok.

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So, now, what we should see is that each of these sub-carriers should be loaded
simultaneously right. So, if they have to load it simultaneously, these ones 1 2 upto N are
the different sub-carriers we have said that this summation this thing would be realized
as the DFT. So, now, for clarity if you look at this particular expression we can clear all
the markings that that has been put on this particular slide ok and things will be easier
now ok.

(Refer Slide Time: 18:41)

So, if you look at this t is continuous time, we can change this continuous time into
sample time where let us say T samp where T samp is the sampling period and t is the
time where it is equal to n times T sampling ok. So, if that is so, we can realize this entire
thing in the discrete domain in the digital domain with index n. So, instead of putting t
we can index this as n and here instead of putting t will be again indexing this as n and

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this Tf will be some multiple of this T samp ok. So, effectively when we look at this
particular expression one will be getting X k sorry notation s-th OFDM symbols kth sub-
carrier e to the power of j 2 pi ok.

So, now, N multiplied by T samp so, we have this 2 pi of course, then k multiplied by 1
upon N times T samp and you have the t part with this n times T samp I am just only
taking this particular t this offsets and kind of neglecting as of now in order to
understand this offsets I am neglecting. So, one can of course, bring them back it is not
going to affect your expression. So, this cancels out you have a summation over k and
you are going to have x of n. So, now, if you look at this expression it is simply X s of k
e to the power of j 2 pi k n upon N sum over k this is nothing, but the DFT which can be
realized through an IFFT expression and this is what we have as x of n ok.

So; that means, this entire things can be realized in a complete discrete manner and entire
set of multiplex multiplication operation that was happening here could be replaced by
multiplication and the summation this huge processing can be simply replaced by a DFT
and the DFT can be also replaced by an IFFT operation because IFFT is very very low
complex right. So, we have to now visualize this entire expression that is happening over
here through the view of IFFT right so; that means, in IFFT all these Xks these are the
inputs of the IFFT. So, we change the pen color to mark it better. So, these are the inputs.
So, we have Xks as the inputs and xns as the outputs and in between we have IFFT right
through IFFT it produces the time domain. So, now, why we call it IFFT of course, there
is a direct similarity and then what we see is that these were actually modulating the
frequency as the sub-carriers and this is the time domain signal.

Although this is the common way of explaining such things one can even visualize the
entire thing as time domain operation, but since there is a huge similarity with IFFT one
can take frequency domain as input and time domain as output, that is also another way
of viewing things. So, whatever way is comfortable you can see that end of the day one
has to ensure or one knows that its finally, a time domain signal that is one is handling
with. But more popular description is that this is the frequency domain and this is the
time domain and that is how you will find it most of the notation in most of the
discussions ok.

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So now we are back to the transmitter structure. So, what we see is that each of these are
the index of the sub-carriers. So, they must be filled with these different constellations.
So, it is x n. So, rather as per the notation in this particular slide it is one and s we are
kind of is equal to 1 or we are kind of omitting s your omitting s a for ease. So, we are
just noting the suffix for this one particular OFDM symbol and symbol mapping can be
anything depending upon the signaling from higher layers or the choice and as said the
symbol mapping can be different in different sub-carriers. So, now, if you are using 64
QAM this would be having 6 bits if let us say we are using 64 QAM in all there will be
all having 6 bits and if the value of N is let us say 1024. So, you will be sending 1024
multiplied by 6 bits simultaneously correct.

So, so, many bits from here 1024 multiplied by 6 bits have to be read and they have to be
sent 6 bits to each of the branches and there will be 1 2 up to 1024 such branches they
will be doing symbol mapping fitting into IFFT and here we are going to get their
outputs small x of 1, small x of 2 up to small x of N minus 1 and finally, we are going to
get small x of capital N, N number of samples. Then we will be reading them out in a
manner x 1 x 2 up to x capital N and they will go out to the analog section of course,
there is an addition of cyclic prefix we will discuss the addition of cyclic prefix and it
goes to the analog part and then to the RF chain.

So, this is how the signal flows and the equations that we have written maps to this kind
of a structure.

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(Refer Slide Time: 25:06)

Orthogonality

So, moving ahead what we see is that there are some critical parameters one of the
parameter is the sub-carrier bandwidth that is or sub-carrier spacing, sometimes it is also
called the sub-carrier bandwidth and the other parameter is the guard interval which we
will discuss sometimes or most of the time it is also called cyclic prefix. So, guard
interval is a more generic term, cyclic prefix is a very specific implementation of the
guard interval and one would remember that this sub-carrier spacing which is effectively
or essentially written as 1 by delta f sorry its delta f one could rather specify it by delta
fsc indicating sub carrier spacing and this was equal to 1 by T or 1 by Tf whatever is the
notation we have been using.

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So; that means, one chooses the sub-carrier spacing the symbol duration gets decided
this is very very important to understand and there is also another thing the guard
interval. Now why we are saying that these are important parameters for 2 2 reasons or
multiple reasons one is that this is the diagrammatic representation of the channel
impulse response.

Now in a typical single carrier system single carrier system if it has an large a certain
amount of bandwidth, pulse duration which is indicated over here clearly there is inter-
symbol interference, the echo is larger whatever symbol is being sent in this part gets
stretched to this part and to this part. So, there is ISI. So, in OFDM what we are doing is
that the symbol duration is usually made large and this is that T which is equal to Tf in
the notations that we have been using till now, I am just warning that we will probably
have some change of notation later on is made large enough so, that this channel impulse
response CIR length is much much smaller than T or T is much much larger than channel
impulse response ok.

So, we said at some point that these sub-carriers individual sub-carriers their width
should be decided in such a manner that they are smaller pretty much small, so that it
experiences nearly flat fading. Now we have to go to the details of the propagation
characteristics which we will do later on that these 2 are high inter collect connected.
Now a flat fading effectively means that the channel impulse response is perceived as an
impulse, it is not a stretched version of the impulse response, its not a stretched version
of the impulse; that means, echoes are not present.

So, to allow echoes to vanish one and to make this T sufficiently large, now although
you make T sufficiently large what do you will find is that end of it, it still stretch and
there has to be a next symbol that comes in. So, basically this is one OFDM symbol you
have made it pretty at large compared to channel impulse response this is already being
made, but still because of the channel impulse response this will become the end will
become something like this.

Now the next OFDM symbol is suppose to start from this point. So, there will be some
amount of ISI which is present over here. To avoid that what one can usually do, is one
can choose a design where the symbol duration whatever is present and the next symbol
there is some guard interval. So, we are using the term interval instead of band over here

314
right. So, this is the beginning point, this is the end point for small n and one can see it I
mean; that means, there is this guard interval between the two, what is done is this
signals which is coming afterwards they put some kind of information which we will see
what is called this cyclic prefix, but effectively there is a filler or a gap between these
two signals.

So, this channel impulse response is going to die out over here. If it dies out over here
there is ISI free system and one can have a communication. Now, one can argue that one
can design orthogonal system in time like one have designed an orthogonal frequency
system in frequency, but we must be very very careful at this point to note that when we
design the orthogonality in frequency or orthogonality within a symbol we had used
integrate 0 to T e to the power of j 2 pi fc t e to the power of minus j 2 pi sorry fk t f k
prime t dt correct.

We did not have any other thing between, but now what we have is the channel impulse
response. So, orthogonality can be brought in if we bring this channel impulse response
into the picture, if we bring this channel impulse response into the picture then we must
also have a convolution with the channel impulse response as the basic signal and overall
we can bring in an orthogonality. But that would mean that this channel impulse
response information is required at the transmitter it requires to be available at the
transmitter. So, that being made available and then being used kind of makes things very
very difficult, that is one of the aspects we cannot avoid it and hence its better to choose
a guard interval a loss which you cannot help.

But then there are mechanism which people have working on to reduce this guard
interval we will get an opportunity to see that. And now coming back to the other
important thing if we make this T very very long then because of mobility there is a
factor called Doppler which comes into play which we will see again later, because of
Doppler or because of mobility we have said that channel fluctuates in time. We also
require that the channel remains constant in this entire period so that means, T or symbol
duration must be smaller than something known as the coherence time of the channel.

315
And the sub-carrier spacing delta f must be less than the coherence bandwidth; that
means, the band width across which channel remains flat. So, these are the two important
conditions that are required to be satisfied, now delta f as you can see it is equal to 1 by T
which is from this and this is another condition. So, we have two conditions over here 1
by T must be less than coherence bandwidth and T must be less than T c or 1 by T must
be less than 1 upon Tc. So, these two conditions have to be satisfied simultaneously in
order to make the system work as well as the other thing which is the T GI which we
have been referring to while looking at the equations.

So, now, this is clearer T GI should be greater than the maximum channel impulse
response length or tau max as we call it. So, tau max is the maximum length of the
channel impulse response in this picture it is tau max over here. So, this is the 3rd
important condition that one should consider. So, one let us change the color of the pen.
So, this is 1st condition, this is the 2nd condition, this is the 3rd condition that one must
keep in mind while designing such a system.

So, we stop this particular lecture over here and we will continue more on the
fundamentals of the OFDM in future lectures because based on this as we have being
saying the 4th generation system stands the 5th generation system stands. So, it is
essential that we understand it thoroughly. So, that things becomes easy whenever we
discuss the air interface for the next generation systems and its although kind of not
required to mention, but you should see that OFDM in the wireless system has been
popular over last 2 decades it has been used even beyond that it is going to be there for
another decade.

So, it is going to live for a very long period compared to the history of wireless
communications. So, it is essential that we understand the details and we hope that with

316
this you will be able to design future things improve upon this basic structure that exists
to an extent that we can have even more advanced system in future.

Thank you.

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 Evolution of Air Interface towards 5G
Prof. Suvra Sekhar Das
G. S. Sanyal School of Telecommunications
Indian Institute of Technology, Kharagpur

Lecture – 18
Waveform for 4G & 5G (OFDM) (Contd.)

Welcome to the lectures on Evolution of Air Interface towards 5G. So, in the previous
lecture we have been discussing about the structure of OFDM, the signal flow and we
have mentioned over the diagrammatic representation of how things happen, what things
go on we will briefly represent the analytical flow or way to write it down so, that when
we are designing we can handle it in a direct manner.

(Refer Slide Time: 00:45)

So, here what we have is the analytical representation of OFDM. So, and I have said in
one of the earlier lectures that I leave this particular part for you to find out and plot it in
time and see how does it work out. This is not difficult and it will take some time for us
to do it here. So, I am consciously avoiding that, but I guess it is doable by most of you.

We will provide the link which is there is a famous paper by Speth two papers OFDM
transceiver design, fundamentals of OFDM transceiver design part – I and part – II
where, one can find such a system model and it is necessary to understand such an
integrated model. This helps us in writing one equation which can help consider all
possible aspects.

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After passing through the channel, the signal can be represented as,

(Refer Slide Time: 02:00)

319
So, so, here we have x s of t, this module we have already discussed which is the
constellation point, complex constellation point. This part we have also discussed this k
multiplied by delta f, where delta f is equal to 1 upon T and k multiplied by delta f is
equal to one can think of it as f sub k, and this is the time unit which is resulting in
continuous generation of signal. This is the gating pulse we said it will be rectangular,
but since this pulse is stretching over time T s and T s is now since you have seen guard
interval T g i, T useful sometimes it is written as T f and as per our earlier notation it is
T.

So, this entire duration is T s and we have said that one can easily do a pulse shape
which is not rectangular, but slightly tapered at the end ensuring that a duration of T u is
equal to T f is equal to T s as per our notation is rectangular. So, in this period one will
find it rectangular ok. So, that is what is ensured and this one is when we have
accumulation of OFDM signals OFDM symbols, this is what it is and it is gating pulse
function as we have said is going to ensure orthogonality amongst the different OFDM
signals next to each other just a diagrammatic way of representing. So, this is the
sequence rather it is not a sum ok.

So, after passing through the channel what is happening is h of tau which is the channel
coefficient and x s of t, we are looking at one particular signal they gets convolved. So,
as you can see this is the equation of convolution, and what we have here is noise added.
So, this is the received signal, alright and what we are seeing over here is the convolution
operation. So, here tau max is the maximum tail of the channel impulse response, ok.
And, delta f c; so, with the perfect timing synchronization the residual carrier frequency
delta f c of the receiver symbol goes to 0. So, otherwise with imperfect it is going to be
represented in this manner, ok.

So, this is the overall signal structure. So, if we have received the signal with a certain
amount of residual carrier frequency we have to whatever is received r t; r t has to be the
model has to include this residual frequency offset and here what we have indicates the
different tau delays that are present in the signal, .

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(Refer Slide Time: 05:02)

So now at the receiver the received OFDM signal is now passed through the Fourier
transform at the receiver and as a result you are able to get back your signal. So, what we
have is the Fourier transform operation is happening over here, ok. So, most of the time
when we are discussing the basic structure we will assume that the residual carrier
frequency goes to 0 and what we have over here is due to the Doppler associated with the
tau-th path. So, f d is the Doppler associated with the delay of tau.

So, in that case this particular part which is a complex cannot be distinguished from h t
which is also complex. So, together one is going to get complex coefficient and what we

321
have here is effectively the residual carrier frequency and a certain amount of Doppler
which is associated with the signal and as we said under ideal condition delta f c goes to
0 and in near static condition f f d tau is almost equal to 0,.

So, if we now write down the signal model under idealistic conditions at the receiver you
are doing the integration operation going from sT s; that means, the previous entire
OFDM symbol including the cyclic prefix and you have additional shift of guard interval
and then this portion is as the denominator part and you only have integration over the T
f. So, that means, the previous OFDM symbol then the cyclic prefix which is the T gi
and then you are actually integrating the T f portion or the T u portion this is what we
have been doing and we have mentioned them as T. So, if you do this operation with this
signal model with whatever signal model.

So, R s we have you have to take from here if you take R s from there and you replace in
the equations what you are going to get is that so, one minor thing what I would like to
point out is we are trying to decode at the k prime-th sub-carrier, right. So, we had sent
we had the signal model in terms of k, but at the receiver we are using k prime so that we
can find out what happens when k is not equal to k prime and when k is equal to k prime,
right.

So we know that when k is not equal to k prime because of orthogonality things are
going to go to 0. So, only when k is equal to k prime we are going to get our desired
result. So, if you put this equation inside this you will find out that we are able to write
down the expression in a manner that the k-th sub-carriers received signal is the
constellation point sent on the k-th sub-carrier; now, here we have k is equal to k prime.

So, k prime or k is the same multiplied by capital H s, k; s is the s-th OFDM symbol
giving us a notion of time and k prime is the k-th sub-carrier. So, s H s, k prime is the
channel coefficient for the k prime-th sub-carrier of the s-th OFDM symbol simply H s, k
is the Fourier transform of h t h t comma tau. So, t I am taking it as constant or the
particular desired time interval and instead of Fourier transform you can take this as the
DFT operation at the receiver and then it would translate to the k-th sub-carrier ok.

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(Refer Slide Time: 08:42)

So some system parameters of interest in OFDM system we have seen some of them
earlier. So, we compare WiMAX with LTE because these are fourth generation system.
What we are seeing is that there is a wide range of carrier frequency of operation. System
bandwidth – we have different system bandwidth; scalable system bandwidth for
different system bandwidth the FFT size differs, but what you will find is that with 20
megahertz this uses are 2048 point FFT. So, if I divide 20 megahertz by 2048 we are
going to get the sub-carrier spacing, ok. So now if we look at 10 megahertz it is divided
by 1024.

So, what we see is as the total bandwidth scales down the FFT size also scales down
leaving behind the same sub-carrier spacing right. So, it scales down in a in a linear
fashion same is what happens for the LTE systems. So, the sub-carrier bandwidth here is
roughly 10 kilohertz whereas, here it is 11 kilohertz by virtue of an over sampling factor,
ok. So, there is a slight difference in the parameters as you can see the useful part of
OFDM signal is different in both cases and they are usually designed for different cell
radius now that is taken care of by transmit power variation which can be easily done.
So, more or less these two are similar systems are not much variation, but slight
difference in the parameter setting.

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(Refer Slide Time: 10:14)

In this particular slide what we have is an entire range of parameters that is used for LTE
especially we are looking at the LTE factor. So, what we have listed down is that LTE
can operate or fourth generation system can operate in different sub-carrier bandwidths
and for each sub-carrier bandwidth there is something called a sub-frame duration which
we will see at an appropriate time, but what is more important for us is the sub-carrier
spacing the sub-carrier spacing which is very important. So, this turns out to be 15
kilohertz for LTE systems.

Now, how does it work out one can see that is there is a sampling frequency which is
chosen to be of multiple of 3.84 megahertz. Now, one may recall that 3.84 megahertz is
the chip rate for 3G systems. So, there is a similarity or there is some kind of a matching
with the structure of that has happened in the past, ok. So, for 2.5 megahertz the, this
sampling frequency is 3.84 megahertz and the FFT sizes 256. So, if one would divide 2.5
megahertz by 256 point FFT one would get the value of sub-carrier spacing, but then this
is the result that you are going to get over here as you can clearly see would be
somewhere around 10 kilohertz ok.

But, this is not what is used rather a higher sampling frequency is used instead of using
2.5 megahertz. Now, what does this give us? Effectively there is a wider bandwidth. So,
if this is 2.5 megahertz if this is 2.5 megahertz we have let us say 3.84 megahertz which
is wider bandwidth and then you divide this by 256; you are going to get 15 kilohertz ok.

324
And, now one would argue that 15 kilohertz sub-carrier spacing if I multiply by 256 sub-
carriers then one is going to fill out an entire set of frequencies.

But, what is done is at the edge the sub-carriers are set equals to 0 they are not allowed to
be transmitted. So, if they are not allowed; that means, if it is 0, then effectively what
happens is that one is using only a certain smaller set which fits into this 2.5 megahertz
and then there is a roll off of the spectrum and it dies out by the time 2.5 megahertz
finishes. So, there is a spectral mask which is very very clearly defined and one is able to
effectively use the available bandwidth with having as low adjacent channel interference
as possible while having sufficient guard band.

So, these are some of the interesting facts which have been brought into the LTE or the
3GPP generation of systems. So, what they have done is they have effectively used a
larger sampling factor and they have not directly sampled the bandwidth, used the over
sampling factor and then divided by the FFT size to get the sub-carrier spacing and
instead of using all the sub-carriers they are using a smaller set of sub-carriers.

And, regarding the CP length: so, there are two options of CP length available and one is
the short CP length and one is the long CP length, and these are fit into the frame
structure in a certain manner that one is able to have an integral frame size. So, we will
see them when we are discussing the fifth generation frame structure.

(Refer Slide Time: 14:05)

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 Ok. So, this is how the overall time frequency picture looks like. So, we have the
frequency axis we have the frequency axis or the bandwidth over here. So, it is written
over here frequency grows on this side time grows on this side. So, now, if we study this
particular thing carefully we have FFT operating in this entire region. So, this is your
FFT operation or IFFT operation and the number of sub-carriers N sc is basically defined
over this, ok.

So, that means, one is having N number of sub-carriers, so, when we said 2048 and we
said 20 megahertz of bandwidth so this entire bandwidth is let us say 20 megahertz it can
be different values as described in the other picture and FFT size would be whatever is
the total number of sub-carriers in this. And, then each of these elements each of these
elements over here this element and width is the sub-carrier spacing which is obtained by
dividing the corresponding bandwidth factor. So, I write it as f s indicating the up
sampling factor divided by the number of sub-carriers. So, one gets a sub-carrier
bandwidth.

And, this is the OFDM symbol duration which is T s which is equal to T gi plus T u
sorry T u or T f it is the same thing, right. So, now, we have to send signals over this. So,
as we have said that each one of these each one of these rectangles small rectangles they
are usually called resource elements resource units or they are called resource elements
each one is called the resource element because each one can carry a constellation point
X s of k ok. So, now, it will be clear why we need to use the term s.

So, these units in time correspond to different OFDM symbols, ok. So, let us say this is
the OFDM symbol number 1, number 2, number 3, number 4 number 5 and so on that is
how it is numbered. So, this is one of the sub-carriers of a OFDM symbol. This is the
second sub-carrier of the same OFDM symbol, this is the third sub-carrier of the same
OFDM symbol, now if we go down further we are going to get the N-th sub carrier of the
OFDM symbol, ok.

Now, not all sub-carriers as used as we have described in the previous slide, the edge
sub-carriers which are at the edge of the bandwidth at the both the edge of them they are
made 0 and only a smaller subset is used in order to avoid the out of band radiation in
order to avoid adjacent channel interference,. Clean these things up ok.

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So, now, each of these elements they carry complex signals. So, effectively if I have N sc
number of sub-carriers, we will be reducing the number of sub-carriers which are used
for guard band and then we have the total number of sub-carriers which can carry bits. If
each of them carry let us say k bits this is the number of bits that can be sent in one
OFDM symbol.

Now, if one has to allocate these different OFDM symbols to different users then one has
to assign resource in order to do the allocation. So, it is not possible to allow each
individual resource element to be addressed because if you do that the amount of
signaling overhead is huge to reduce that the neighboring sub-carriers are grouped
together, a block is formed. So, neighboring sub-carriers are group let us say we talk
about this group they are grouped together not only that a sequence of OFDM symbols
are also grouped together. So, these are sequence of OFDM symbols they are grouped
together. So, this entire block of OFDM symbols along with the along with the sub-
carriers are grouped together to form one addressable unit.

Now, one should also remember that there is forward error correction code. So, one has
to have a certain larger number of bits to allow the error correction code and one can
choose different modulation techniques and also want us to allocate these resources
different users. So, there is a certain minimum size of this block that includes a certain
number of sub-carriers and certain number of time domain signals to form a resource
block. So, one can think of a physical resource block and allocate the same modulation
and code rate to this particular block and also one can allocate this to a user as well.

So, this is the minimum resolution with what which one can do it, ok. So, these are. So,
then in each of the blocks in LTE systems there would be 12 number of sub-carriers and
they will be grouping up to 1 millisecond of signal in order to 1 millisecond of OFDM
symbols. So, 1 millisecond of OFDM symbols to form one physical resource block and
these resource blocks are grouped together in order to do any allocation of modulation
code rate or user allocation.

So, whenever we do any resource allocation, any link adaptation we would be doing it
over this entire block of symbols simultaneously. This will only save reduce the amount
of overhead. Further, the channel which fluctuates in both time and frequency kind of
remains constant over one such period and hence it does not make much difference to

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allocate them in a different manner. So, we have the particular representation in this
picture.

(Refer Slide Time: 20:43)

So, now we look at one very important aspect which is used over LTE and other systems
is called link adaptation. So, we briefly look at that. So, let this be the frequency axis and
let this be the time axis and this access be the channel gain given in decibels. So, if we
look at the joint time frequency picture the channel fluctuation would appear as is given
in this particular image.

So, what we see is the channel fluctuates both in time direction and in frequency
direction and we have said that sub-carrier bandwidth should be such that the channel
experienced is flat and the time duration of the OFDM signal should be such that it
experiences nearly flat fading in time or slow fading in time. So, this is your T u and this
is your delta f, right. So, and one remembers that delta f is equal to 1 upon T u.

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So, what we see is that the these factors are primarily influenced by the channel gain and
the other factors which are of consideration that B c which is the coherence bandwidth is
greater than the sub-carrier spacing we can write this as sc to be more precise and the T u
should be less than the coherence time which is due to Doppler. This is the due to
Doppler we can write Doppler spread and this is due to delay spread, right.

So, these two parameters influence the choice of sub-carrier spacing and T u as well as T
gi should be greater than tau max, ok. So, not only T u this we should replace by T s to
include the guard interval. So, that is the overall picture one should remember and what
one sees is that the fluctuation level has nearly 40 dB of signal strength variation over a
short distance or over a short unit of time.

So, a 40 dB fluctuation is a huge fluctuation and what is important is to maintain a

certain quality of service or certain bit rate. So, if the signal strength is low we know that
we will use a lower bit rate, if the signal strength is high one will use a higher bit rate.
So, in this situation what we see is that OFDM gives us the opportunity to allow certain
sub-carriers for example, here which are facing low SNR conditions and certain sub-
carriers here which are facing high SNR conditions to use different modulation orders.

So, let us say this is using 64 QAM and this is using let us say QPSK because this is in
lower SNR condition this is at a higher SNR condition, right. So, OFDM by virtue of
splitting the frequency domain picture into smaller-smaller chunks we can do frequency
domain link adaptation as well as we would obviously do time domain link adaptation,
right.

So, if we now go back to this grid picture what we will realize is that each of these
frequency bands; so, we can use different colors and say that this frequency band may
choose a certain modulation and code rate whereas, this particular band may use a
different modulation and code rate where as this particular band in the middle might
choose a different modulation and code rate and same would happen in the time domain
also. So, we can choose a different color and indicate that this particular block may use a
different modulation code rate compared to this.

So, every resource block can be given a different modulation and code rate because the
channel has fluctuations in both time and frequency domain.

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(Refer Slide Time: 25:26)

So, what we have just explained is we have the graphical representation of a similar
thing that if this is the SNR axis and this is the error probability curve and when we have
the BLER we mean the block error rate probability of an entire block going into error,.
So, these are for different modulation and code rates and generally, as your SNR
increases as depicted by this your error probability decreases. So, when your SNR is high
one can increase the bit rate by simply changing the modulation from M equals to 4 to M
equals to 16 because M is equal to 4 means k is equal to 2 2 bits per signal and symbol
and 16 means 4 bits per symbol one can increase the data rate ok.

So, similarly one can even think of going higher up; that means, one can think of going
to a different code rate. So, we erase this. So, not only not only does the modulation
increase the spectral efficiency, but also code rate increases spectral efficiency what we
see over here is the code rate has changed from 1 by 3 to 1 by 2 and by 1 by 3 means one
information bits and 2 parity bits; here means 1 information bit, 1 parity bit, so there is
increase in spectral efficiency.

But, then what we will find is if there is a threshold for block error rate; so, here we have
taken the threshold to be 10 to the power of minus 1 ok. So, then not all higher
modulations can be used; so, one has to restrict oneself to that modulation code rate
which is below the threshold and as the SNR increases one can use higher and higher
modulations.

330
So, we find there are SNR switching points; these are called SNR thresholds, ok. So, if
the SNR is somewhere here; if the received SNR is somewhere here, one would
definitely choose this modulation and this is 64 QAM with rate half as given in this
particular picture. 64 QAM means 6 bits, rate half means 1 by 2 so, which means three
information bits per second per hertz one can use over here. Whereas, if the SNR
condition is below the minimum threshold; so, this is let us say gamma 0, then one does
not find any modulation code rate to have a BER which is lower than this threshold and
hence one does not find it a good condition to transmit the signal.

So, only if the signal is higher than gamma naught which is the smallest SNR threshold
then one can start transmitting data and one would choose the maximum modulation
code rate which satisfies the SNR threshold condition and this happens for every such
resource block that we have been that we have explained over here. For every resource
block this thing operation happens, not on a sub-carrier basis.

(Refer Slide Time: 28:13)

Ok. So, at the end if we look at the SNR axis and if you look at the spectral efficiency
axis what we see over here is that if we choose a fixed modulation code rate as SNR
increases error probability decreases. So, spectral efficiency throughput increases and
throughput saturates after a certain point where no longer there is notable decrease in the
error probability, ok. So, if one chooses a higher order modulation one will find that a
spectral efficiency is very low up to a certain point near to 0 because error probability is

331
very high then it starts increasing and it also saturates at a maximum point where after
the error probability decrease does not improve this spectral efficiency.

However, if one chooses to dynamically adjust or switch between these different

modulation and coding rates then what would happen if one is at a certain point in the
SNR axis one would choose that particular modulation and code rate where one is
getting the highest spectral efficiency. So, what we see we have two kinds of curve over
here; one is link adaptation with QoS; that means, the one with this threshold one with
using this threshold and the other one where threshold is not used, but only the highest
spectral efficiency curve is used.

So, if you are using the highest spectral efficiency curve the transmission throughput is
higher in that case, but QoS is not maintained. So, one can get higher and higher error
probability. But, if one maintains the QoS then the spectral efficiency at a particular SNR
is lower compared to what one would get, but one would maintain the desired error
probability performance. So, these are some important things which happen in this
modern communication systems and one has to remember this.

(Refer Slide Time: 30:07)

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And, there is a flow of things that happen. So, the receiver measures the channel
condition. After measuring the channel condition it feeds back the channel through
something known as channel quality indicator there is a feedback. Through feedback the
transmitter adjusts the bit loading; bit loading means the modulation index and the code
rate as well as it can adjust the transmit power and then it would send back signal. This
entire flow of things should happen within a duration of coherence time again, right
because the channel should not fluctuate by the time the feedback has been given to the
transmitter and it uses the feedback towards forward transmission.

So, that means, your loop time should be less than the coherence time. So, loop time is of
course, a multiple of frame time and a frame consists of several OFDM symbols ok,
rather several OFDM blocks and so that means, the symbol duration or T s must be
significantly smaller than T c and not simply just smaller than T c that we had discussed
earlier. So, as we go deeper into more requirements and advanced mechanisms we find
more and more restrictions coming into the system. So, T s being less than T c would
also boil down to T u or T f being less than much much less than T c. So, this is
something which we should remember and it is not simply that T u is less than T c that is
used in the design.

So, we stop our discussion over here and we will move on to other things for OFDM
from this point. However, it is very important to remember whatever we have discussed
because this is the foundation based on which we will discuss several other things. The
entire physical layer or even the entire communication protocol stands on this basic grid
architecture. So, you must remember that there exists a bottom layer grid architecture on
which all these things happen and there is a frame structure we will discuss the specific
details of frame structure of the fifth generation system at a certain point, but overall this
is the skeleton on which the entire signal protocol stands.

So, it is very important that we should understand this and whenever different things
happen we should be able to connect back to this frame structure to realize how signal is
flowing, how bits are flowing, what is happening at each stage, how resources are being
allocated. So, we must understand the basic element of a resource unit which is very
critical for all these kind of broadband multi-carrier communication systems.

Thank you.

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 Evolution of Air Interface towards 5G
Prof. Suvra Sekhar Das
G. S. Sanyal School of Telecommunications
Indian Institute of Technology, Kharagpur

Lecture - 19
Waveform for 4G & 5G (OFDM) (A)

Welcome to the lectures on Evolution of Air Interface towards 5G. So, we are at present
at the middle of a very important analysis or waveform discussion, which is OFDM
which we had started in the previous lecture. And this is very very important I would
always say that its very critical to understand this, because when we go into 5G we will
not discuss the details of it will be only using the parameterization. So, it is essential that
we understand as much details as possible for this particular structure.

(Refer Slide Time: 00:50)

Orthogonality

334
So, what we were discussing in the previous lecture was about the resilience towards
multi-path and some of the parameters that are of interest. So, we were talking about the
three important parameters as we have pointed out here. So, we have actually identified
this number 1 over here, and that is the time interval for the OFDM symbol should be
less than the coherence time. We will discuss the coherence time and the 1 upon T or in
other words T should be greater than 1 upon B c which is other way of looking at it.

So, it is basically the sub-carrier bandwidth 1 upon T is effectively the delta f must be
less than the coherence bandwidth. So, this is the point number 2 that is what we were
discussing yesterday. So, the sub-carrier spacing should be less than coherence
bandwidth or this sub-carrier bandwidth is less than the coherence bandwidth means that
each sub-carrier experiences is a flat fading. That is what we were discussing here that,
this width should be less than the coherence bandwidth ok. We will understand
coherence bandwidth later on, but as of now we briefly given an explanation that there is
fluctuation in time sorry there is a impulse response which causes of fluctuation in the
frequency resulting in frequency selective fading.

And the other thing is that the guard interval which we are discussing in the previous
lecture, that is the interval that is necessary for separation between two consecutive
OFDM symbols, which is the guard interval that is what is written over here. So, this
guard interval should be greater than the tau max, which is the maximum excess delay of
the channel. The maximum excess delay of the channel has been pointed out over here
which is the maximum length of the extension of the channel impulse response right. So,
these three things we must remember and we said why these are critical, because this
coherence time comes from Doppler; we have talked about Doppler over here. So, signal
strength fluctuating with time. So, we would like that over the duration of our
consideration all that appears very very small in this particular diagram.

335
But this is an order of seconds and when we are these I mean seeing it with higher
resolution. So, we would see that the signal that the channel is fluctuating something like
this. In this scale this is the time axis and this may be in milliseconds or microseconds
and we will see that with the parameters of interest that this time in duration is in the
order of microseconds. So, when that is in the order of microseconds, when these
fluctuations appear so much changing in order of seconds, in order of microseconds, they
almost remain constant.

So, but however, when Doppler becomes very high and effective Doppler, a Doppler is
basically due to mobility. So, you have vehicular mobility, we will look at the exact
expression and the carrier frequency both influence the Doppler of course, the angle at
which the signal is arriving at the receiver is also important. So, as the carrier frequency
increases right we have discussed in the fifth generation millimeter wave is one of the
bands and also higher frequencies towards 6 gigahertz are also being contemplated. So,
there even under same mobility condition, a higher frequency causes increasing Doppler.
We have also seen that 5G requires to support 500 kmph kilometers per hour so that
means, the mobility support also increases hence Doppler is a critical factor.

So, under very very high mobility conditions are very high Doppler conditions, these
constraints become important ok.

(Refer Slide Time: 04:47)

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So, this in this particular picture we have carried forward whatever we have been
discussing earlier. So, here we have the frequency domain picture. So, we have the
frequency axis. So, this is the f axis in hertz or megahertz or whatever is the unit one
wants to use. And this bluish line that we have over here indicates the fluctuation of the
channel with respect to frequency. So, this changes and this is because if this is your
delay axis or the time axis and this is your signal gain axis.

So, the channel impulse response if it appears in this manner, then if you do a Fourier
transform of this of h of tau and you take the magnitude of it mod squared of it, you
would get fluctuation in the frequency domain which looks like this. We have discussed
this earlier and each of these units which is the sub-carrier bandwidth we can say; they
should be small enough so that each encounters nearly flat fading condition. So, this
pictorially depicts what is going on and it is kind of flat fading situation.

So, effectively when we look at the time domain has given over here, the signal as if sees
a single equivalent path. Because all of these paths get added up together by virtue of
matched filtering because, we have said that the receiver processing will do an
integration from 0 to T. So, T is this duration. So, if this is the duration of T, then all
these values get accumulated right they of course, get accumulated by multiplying with
the pulse shape. But, here again we have said that in the interval of T that is for our
consideration for OFDM, this remains a rectangular pulse, hence it is a constant value.

So, effectively all these paths get added up together. So, they add up to form an
equivalent impulse or equivalent sample value of a particular phase. So, if it is a single
equivalent delay that would result in a flat fading across a sub-carrier. So, each sub-
carrier sees a single equivalent path and hence it resolves it or it sees it into a flat fading
channel for that particular path. So now, if we take one sub-carrier at a time in that case
at the receiver side we are we will see that that X of k gets multiplied by H of k this
expression also will see in due time, that effectively this is the flat fading equivalent of
the channel.

337
So, you are received signal structure would look like this in the frequency domain. And
hence, since this is a scalar, equalization is very simple, one of the most elementary
equalization would be to if I know H let us say H cap, I could take an inverse of it and
multiply with Y cap I will be left with X cap the desired signal plus H cap inverse W k;
that means, there is some processed noise, this can be considered as processed noise and
this is the desired signal.

So, as if the signal is corrupted only by noise by additive noise and the noise is of a
certain variance. Now, H again we will see later on that H cap is basically the Fourier
transform of h tau what we are talking about here and this particular channel impulse
response is under most of the circumstances that we will consider would be zero mean
giving raise, I mean in non-line of sight conditions Rayleigh fading conditions. So, if this
is zero mean, then the mean of the processed noise is also 0 as well as what happens is
only the sigma value of noise gets changed. So, this results in only a change in the noise
variance right.

So, this way it helps one have less complex receiver. In otherwise, if we were processed
in time domain, what we are seeing is that there is ISI and one needs to take care of it by
implementing ISI canceling receiver, which increases the complexity. Because this has to
happen for every symbol and even then you would still have some kind of residual
interference because of which the error will reach an error floor it will simply not
decrease to the smallest possible value ok.

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(Refer Slide Time: 09:28)

Moving further, this particular picture is essentially talking about what we have been
explaining its rather more pictorial and this simply says that if there is a transmitter, the
signal propagates through multiple paths one could be direct line of sight. There could be
another reflected path from moving vehicle and it could be reflected from different kind
of surfaces. And, as a result of which an impulse would appear as echoes or these are the
delayed versions of the impulse that one receives and in a typical single carrier system
there would be inter symbol interference.

(Refer Slide Time: 10:04)

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So, if we again graphically look at the multi-carrier system, each of the sub-carrier which
occupies spectrum which is like a sinc and there is guard interval. So, this matches with
whatever description we have given before and this is a useful symbol duration which
has become long ok. So, there is a cyclic prefix which gets added between the guard
interval. And, since you have a long symbol duration, the bandwidth is narrow, it is a
narrow band and earlier you had a wider band and symbol durations were small right.
Symbol durations were small means these, the entire system bandwidth would have been
large and that would have experienced, select frequency selective fading across the entire
band of operation; so, we will clear up these single carrier systems right.

So now, since you are occupying a smaller band, the question arises that what do we do
with the other bands? Again the answer is very simple that you send them in parallel. So,
once you send them in parallel, this also matches exactly with a definition of the
transmitter architecture. So, each one of them are sub-carriers carrying symbol X k. So,
this is a sub carrier index k 1 this is another sub carrier index k 2, and they will all of
them would be in parallel. And this particular picture gives a complete time frequency
realization or one can extend ones imagination that this is the time axis and this is the
frequency axis.

So, frequency axis can be in this direction ok. So, overall the time frequency signal
would look like this and we had said earlier that in one of the carriers this would be the
sub-carrier frequency. The next carrier could be having the sub-carrier frequency which
goes there, the next one would be having cycles and the next one would be even having a
faster frequency, but all integer multiples of the previous one. And, what we have given
over here is that, one needs to estimate the channel coefficients. So, because this is these
are fluctuating.

In reality, these channel fluctuations are not as fast as typically represented in this
diagram and they usually remained constant over a few number of sub-carriers ok. So,
that is the coherence bandwidth over which remains constant and hence pilot carriers
need to be introduced, pilot sub-carriers by pilot we mean the sequence which is known
as the transmitter and at the receiver. So, that means, it is known both at the transmitter
and receiver which is used for channel estimation ok. So, some of the carriers are used
for pilot channel estimation, rest of them are used for data communication ok.

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(Refer Slide Time: 13:14)

So, this is just the similar picture given in a more illustrative manner that, single carrier
system with ISI on this side and frequency selective fading as you can clearly see
because the bandwidth would be pretty large. In this case whereas, when we go for
OFDM, this is the translation that happens from a single carrier system to a multi-carrier
system, this is the representation of the channel impulse response. And from channel
impulse response we have the channel transfer function, which is this fluctuation and
effectively each of the sub-carrier receives flat fading.

(Refer Slide Time: 13:49)

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So, this is a cumulative picture and one can visualize what is going on, which results in
flat fading per sub-carrier. No ISI that due to multiple reasons mainly because of
introducing a guard interval and because of flat fading, there is single tap equalizer.
There is bandwidth saving because of overlappingness of the spectrum and that not only
gives bandwidth saving its primarily because, the spectral efficiency has been increased.
And, as shown in the previous one, we have depicted all I mean the distribution of pilots
all over.

So, that in different sections of the coherence bandwidth; one can introduce a pilot. So,
roughly speaking for every coherence bandwidth there needs to be one pilot carrier. So,
one can say one pilot sub-carrier. So, this is important in order to estimator channel ok.

(Refer Slide Time: 14:49)

So, we now discuss the cyclic prefix part. So, this particular waveform structure is you
are well used to by now given all the descriptions, and we have said why the guard
interval is necessary. But, then instead of simply having a null in the guard interval what
is done is, a cyclic extension of the signal is done right. So, we will discuss the cyclic
prefix part over here.

So, if this is the entire symbol duration as it is written over here useful part of the OFDM
symbol ok. So, this is the useful part OFDM symbol. So, all your figures you must have
realized that it covers this particular part ok. So, that is the part it covers alright. And

342
now what is done is this particular portion as given over here, I would rather write it as
guard interval ok. So, this is the guard interval part ok.

So now, instead of leaving it blank, the last part is carried forward to the first part. So, as
you can see the picture, this portion this entire portion, we have indicated it by this kind
of a line and we are indicating it by this kind of line. So, that this continuity or the ease
of understanding is maintained over here it is copied in this part. So, if I say this as 1 2 3
4 this be labeled as 1 2 3 4 in that manner ok. So, if we see how it is copied, this
particular portion goes over here and this particular portion goes over here. So, this part
of the waveform which is copied the red colored one, which I am marking with a
blackish color is basically over here as you can clearly see that and the other waveform,
which is over here is being copied over here.

So that is how the cyclic prefix extension is done yes. So, with this cyclic prefix there is
a lot of advantage we are going to discuss that.

(Refer Slide Time: 17:20)

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So, let us look at what is happening in the guard interval part this channel impulse
response, as we clearly see over here the channel impulse response which is here. It is
subsumed within the guard interval that is one primary reason and we have said that the
card interval should be greater than tau max. Tau max is the maximum length of the
channel. So, this prevents inter symbol interference inter symbol means inter OFDM
symbol interference ok.

So, this one thing and because of the cyclic prefix that is what we are getting; in the in
the receiver when the signal goes to the channel what we know is that, if x t is the signal
it actually gets convolved with h t comma tau; tau is the delay and t is the time axis now
when we process it at the receiver, we use a DFT operation ok. So now, the d when we
look at the time domain convolution operation, if I take the Fourier transform, it would
appear X of f the dual of it. The X of f multiplied by H of f whereas, if I do a cyclic
extension; this convolution turns to be a circular convolution ok. So, when it turns to a
circular convolution if I do a DFT, then it would result in X of k which is a DFT of x t
and H of k which is a DFT of H t correct.

So, at the receiver since we will be implementing an FFT operation because of the
transmitter we have implemented and IFFT operation. So, at the receiver will implement
an FFT operation FFT is the realization of DFT and in the time domain, it corresponds to
the circular convolution. So, the circular convolution would be effective if we have a
repetition of the signal or as if the signal is repeated in time. I mean if it is repeated in
time and between the convolution linear convolution it appears a circular convolution.
So, what we see is that this enables us to use the DFT operation at the receiver, which
can be implemented by FFT. At the transmitter we have the IFFT operation and the
receiver we have the FFT operation. So, again we recall that we have been discussing
this DFT which gets finally, translated to FFT has a very low complexity implementation
and one of the main reasons why OFDM became popular is because of its low
complexity implementation.

It had all several advantages, but because of the complexity it was not being taken
forward. But once this thing came into being this FFT operation, OFDM became very
very popular. And since we are having this cyclic prefix; that means, extension of the
signal in the front part of it, the linear convolution which happens in the channel appears

344
as a circular convolution. So, the circular convolution if you take the DFT of this entire
operation which is the received signal.

So, this entire signal is y of t which is received if we take the DFT at the receiver
opposite operation of the transmitter, it works out as product of the corresponding
frequency components. So, everything fits into plate place and whatever ISI happens at
the receiver part, one would be rejecting this component one will be rejecting this
particular part and one will be concentrating only on this part which is the desired signal
part useful OFDM part and it will pass it through the FFT operation at the receiver. So
now, instead of leaving it blank if we bring a cyclic prefix to it, it helps us avoid ISI as
well as use a FFT operation and the receiver and provide low complexity processing as
well as low complexity channel equalization.

Now amongst several other things one we one should remember that, if one is using a
guard interval, one is actually using less signal energy. But if one is using a cyclic prefix
then some extra amount of energy is being wasted in some form and the part of
transmission over here. But that wastage is kind of beneficial by overall lower
complexity operation at the transmitter or at the receiver side, but however, there were
many works in this regard and there was a lot of work which was done to reduce the
effect of cyclic prefix or the having some cyclic prefix and this is still an important
issues still an important area, because spectrum is very very costly.

So, if one can find out methods by which we can remove or at least reduce cyclic prefix
significantly, while maintaining a low complexity operation at the receiver plus
providing low complexity channel equalization then that would be a highly beneficial
scheme. Now, one can think of that I reduce guard interval, but complexity goes up that
is not accepted because if guard interval is removed then spectral efficiency increases,
but then one has to deploy inter symbol interference canceling receiver for every sub-
carrier and then the exponential growth in complexity.

One also has to remember the FFT operation has to be utilized. So, taking everything
into consideration if one comes up with a better mechanism, then that would be highly
acceptable and highly desired by this community which works at multi-carrier systems.

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(Refer Slide Time: 22:49)

This is almost the same picture that we have, but it is much cleaner picture.

(Refer Slide Time: 22:56)

So, you have discussed more or less the important issues and this particular slide more or
less summarizes the parameter choice, and one important thing that we have over here is
especially in the last part over here which talks about a certain tolerance factor. So, what

346
it says is that, if we know that the there is a certain sub-carrier spacing this has to be
decided and we know that there is a maximum amount of offset in the carrier frequency,
we are talking about offset. Now this offset could be due to various reasons, one is a LO
performance the local oscillator performance which is kind of the accuracy of the local
oscillator. Frequency synchronization capability and then they would be accuracy would
also include the phase noise of the oscillator and there would also be presence of Doppler
which we will discuss in greater details.

So, to take care of this one rule of thumb or easy way one can one can remember or one
can understand is if one compares this ratio delta f by delta fsc; if this is a less than 0.02,
then one can more or less get around 20 dB of signal to interference plus noise ratio and
this interference is self interference. So, if one is maintaining this rule of thumb, then one
can get a good inter carrier interference and that would be a factor which helps design
this sub-carrier spacing. So, what has to see there are several factors which are usually
chosen in order to design the OFDM system parameters.

(Refer Slide Time: 24:44)

So, this is the overall flow of things. So, we have at the receiver the low noise amplifier
where the signal comes in, followed by the local oscillator which is used for down
conversion, a low pass filter they would be automated gain controller, analog or digital
conversion time synch frequency synch. Now these are very very important because we
will see that if we have the signal. So, let us go back to this particular figure and we said

347
that we are going to use this useful part of the signal for processing at the receiver by
rejecting this cyclic prefix. And the receiver you are going to reject the cyclic prefix and
process this part and send this part to the DFT operation ok.

So, now there are some possibilities which come in; one of the possibilities that there is
not a perfect timing synchronization and hence instead of starting at this point one starts
at this point ok. So, one starts at this point; however, one uses the standard length of the
OFDM symbol. So, one stretches beyond the OFDM symbol. So, if one stretches beyond
the OFDM symbol what happens? The cyclic prefix of the next OFDM symbol comes in
cyclic prefix of next.

So, if the cyclic prefix of the next OFDM symbol comes in. So, this portion one is going
to experience inter symbol interference alright. So, this is very important. So, as a result
one can think of instead of going to the left there could be going to the right, they could
be also other possibility that one has synchronized to this point and has reached up to
here because that is the useful portion.

So, if one has done it in this manner, then what is the problem? There is a problem that
this particular section which contains the impulse or the inter symbol interference from
the previous OFDM symbol from the previous OFDM symbol, then that results in ISI
right. So, there is always a problem of ISI if you are not perfectly synchronized and if
there ISI and that is huge reduction in signal to interference plus noise ratio and hence bit
error rate would increase.

Now, if the guard interval is kept slightly larger, is usually kept greater than the
maximum channel impulse response then and the channel impulse response dies out
earlier; see the channel impulse response finishes at this point then there is a certain
amount of margin which can be made available. So, even if you are synchronized a little
bit to the left, it is not much of a problem why there is not much of a problem because,
one would be receiving signal up to this part. So, one would not be getting this, because
one has synchronized to the left, but one can recall that this part is already copied over
here right. So, this part is already copied. So, one is not losing any information.

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But since there is a shift as circular shift is there in time domain, since there is a circular
shift in the time domain so, this would result in a phase rotation in the frequency domain.
Because x t minus tau would result in the frequency of e to the power of minus j 2 pi tau
by N kind of a phase rotation that can happen in the in the frequency domain. So, this
kind this frequency rotation can be corrected because this will become indistinguishable
from the phase rotation which is introduced by the channel. So, if discussed that here
there is a channel that gets multiplied.

(Refer Slide Time: 28:58)

So, if you are wrongly synchronized you are going to get some phase rotation part, which
is e to power of let us say minus j 2 pi k tau by N ok. So, this particular phase rotation
now this is a complex quantity. So, this complex quantity one will not be able to
distinguish any further, they will be integrated together to one channel coefficient all
right. So, that means, synchronization is very critical; however, one is little bit to the left,
it is not much of a problem. In terms of frequency domain synchronization, there is big
issue we have said some things and we will discuss further that, if this is the frequency
domain representation of the carriers and we have assumed that they will remain
orthogonal. Now if there is frequency offset. So, in that case the receiver would instead
of being aligned over here the receiver gets aligned at a slightly different point.

So, if the receiver is aligned at a slightly different point in that case, that desired signal
that reduces instead of being sampled over there the desired signal amplitude has reduced

349
as well as the interference signal which is from the neighboring carrier comes over here.
So, there is again heavy inter carrier interference. So, which results in loss of
orthogonality you can clearly see there is loss of orthogonality, heavy penalties paid. So,
therefore, these are very important factors for OFDM system design. After one has
successfully synchronize them the FFT operation at the receiver channel equalization, we
have already said this there is phase tracking term which are some details of it symbol
demapper; that means, you are actually finding out what this constellation means in
terms of bits for followed by forward error correction code and output bits this is the
overall flow of what happens at the receiver.

So, we stop our discussion over here in this particular lecture we will move on to the
next lecture and whatever we have discussed we will present the analytical model which
you can go through in your own time will briefly go through them and look at some other
important aspects which need to be remembered when discussing about OFDM.

Thank you.

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 Evolution of Air Interface towards 5G
Prof. Suvra Sekhar Das
G. S. Sanyal School of Telecommunications
Indian Institute of Technology, Kharagpur

Lecture - 20
Waveform for 4G & 5G OFDM (A), SC – FDMA, DFT Spread OFDM (A)

Welcome to the lectures on Evolution of Air Interface towards 5G. And as we have said
that we are at a very crucial juncture trying to understand the multi-carrier basically the
OFDM system and it is very important as we have said also to understand the parameters
and how they are related. Although we did not have a detailed discussion on the
propagation characteristics, but we have been giving guidelines and hints at every point
how do these things influence the design of OFDM. So, when we take a careful look at
the propagation, one should be able to connect these two different things.

(Refer Slide Time: 00:51)

So, before we proceed further I would like to reiterate this is I have said this thing earlier,
but like to say again that these references are very very important. Especially, if you are
working with 4G and 5G because these leads the foundation for the multi-carrier
systems, it is absolutely essential that you go beyond the typical notes or the material that
we supply and look into these references. And, especially I would say because these are
books which are available and this is also a book which is available and interestingly I
just tell you that this particular one and e-book is also available at a much lower price

351
and this one is especially relevant for our course. So, this has been made especially for
participants of the course, the publisher has made the e-book. So, you can find this in all
possible places, it is much cheaper and its soft copies of which is very easy to handle.

And however, these are the references which are especially important for only OFDM
part. This will be useful for all other things and these there are actually a pair of
references over here, which is also important for the basic expressions. So, I would very
strongly recommend you to get these references and use them, this is very easy to read,
these are all freely available in the internet. So, it is very important that you go through
them ok.

(Refer Slide Time: 02:21)

We have also discussed the structure of the transmitter and receiver in the previous
lectures. So, please get time to go through them and understand each and every process
and try to implement them also. Implementing in MATLAB is not difficult or your own
suitable platform that would give you a better understanding of things.

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(Refer Slide Time: 02:40)

And the link adaptation you may not implement, but it is for you to know and understand
the criticalities.

(Refer Slide Time: 02:46)

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This particular picture is also important in terms of time frequency diagram, because
whenever we talk about the whenever we are especially talking about the frame
structure, the frame design or any the other thing; this picture should be available in
mind. There is a time, there is a frequency, there is a group of symbols and we have as
always said this is the time duration, OFDM symbol duration, this particular part this is
the sub-carrier bandwidth. So, the entire picture should be available in mind when we are
discussing such things.

(Refer Slide Time: 03:18)

And in the previous lecture we have discussed how the OFDM affects the peak, peak to
average power ratio.

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(Refer Slide Time: 03:25)

And how the different, I mean the probabilities of getting higher and higher peak to
average power ratio increases with the sub-carrier width, we have also described how it
happened.

(Refer Slide Time: 03:38)

So, these are some things one should be noting carefully, because these are the factors
which ultimately affect the design of the system. So, we have also explained how the
clipping procedure because of these non-linearity effects of the power amplifier effects
in band modulation and there is all kinds of distortion. Again lot of results are available

355
in some of these references, and the references there in. So, it is absolutely essential to
understand details you go into those references.

(Refer Slide Time: 04:06)

We have also discussed the method to reduce peak to average power ratio.

(Refer Slide Time: 04:08)

And we have said that one method is to do a DFT spreading; that means, you spread the
signal that is going into this IFFT block. So, that the coherent combining that may
happen is kind of reduced. So, in case this there is coherence combining this kind of will
remove the effect.

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(Refer Slide Time: 04:37)

So, with that there is significant reduction PAPR we have also discussed this.

(Refer Slide Time: 04:39)

We have discussed the transmitter receiver structure. So, the DFT operation at the
transmitter is correspondingly undone by the help of an IDFT of the operation at the
receiver.

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(Refer Slide Time: 05:01)

So, this is also very important what we will do today is, we will go beyond this and we
will look at some of the important other aspects. So, we have discussed this time this
generation process.

(Refer Slide Time: 05:05)

We briefly looked at the metrics and demerits of OFDM. So, we have always started off
with that it has very low complexity transceiver simply because of because of FFT
architecture, good multipath combating capability this we have discussed in the previous
lectures. Demerits peak to average power ratio we have discussed. High out of band

358
radiation we have briefly touched upon; primarily what we have we have explained not
only in the previous slide.

But, also in the previous other discussions that a rectangular sinc rectangular pulse
results in a sinc spectrum and a sinc spectrum does not die out very very quickly.
Susceptibility to frequency errors also we have explained and we will again look at it in
details, and these are some important factors which have led to the development of newer
methods. So, always we as a researchers or engineers and look at demerits and try to find
mechanisms to overcome these problems.

So, they we have already said that there are several methods reduce PAPR and one
method we have already discussed. There are methods to reduce out of band and
primarily it is about the pulse shape, we will get an opportunity again later to discuss in
more details. And susceptibility to frequency offsets there are again various methods to
do it ok. And applications are of course, LTE downlink, WiMAX, Wi-Fi and in uplink
what is used? LTE uplink it is the DFT spread OFDM this is what we discussed in the
previous lecture. We also said beyond LTE; that means, LTE plus plus or in other words
even in 5G both these techniques; that means, this OFDM as well as DFT spread is used.

So, whatever you are discussing whatever you are studying what are you doing now, is
absolutely relevant for the fifth generation system as well. So, we have explained
thoroughly in the previous lecture that the typical OFDM structure as you can see in this
particular slide, can be used for further modification with slight changes it can result in
very significant things. So, what we said is that, this DFT spreading is done over a set of
sub-carriers and this causes these individual sub-carriers to appear as if they are
coagulated they come together and it gives the notion of a single carrierness.

At the receiver side because we are doing cyclic prefix, we can avoid ISI you get this
frequency domain equalization benefit there is also we have discussed. Now, moving
beyond this is a very interesting thing that one can think of is, if you increase the size of
DFT. now what we have said is there are N points in the DFT N point DFT right that is
what we have said over here. And we said that let this be of M point right. So, then the
number of DFTs that you require would be N divided by M and it is done in a manner
such that this is integer this is to be maintained.

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Now, if we take the options one extreme option could be M is equal to N this is one
extreme option that is highly possible.

(Refer Slide Time: 08:34)

So, if you do that then what happens is that, the DFT spans the entire length of it right.
And now you can easily see that the DFT followed by IDFT essentially cancels out each
other there is no need to do this operation. So, the DFT followed by IDFT since its
cancels out the notion of sub-carrier goes away because sub-carriers are present over
here we have sub-carriers ok. And if we go back here, the sub-carriers are still present
over here ok. So, now, if we stretch it the notion of sub-carriers would go away and
hence the sub-carrier mapping would also not required any further right. So, this is also
very very important to note.

Now if we do away with the sub-carrier mapping. So, correspondingly the receiver
operation of sub-carrier demapping would also not be required. So, now, we are doing
away with this part we are doing away with this part and we are doing away with this
part ok. So, what we see is that these things are gone from a transmitter receiver
architecture and even things become simpler.

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(Refer Slide Time: 09:52)

So, here the serial to parallel should also go away that is also not necessary and you have
a system which is a single carrier system. So, now we have a single carrier system ok;
however, we can maintain the same bandwidth. Now typically this would cause all kinds
of problems of a single carrier system. We know the typical problems have a single
carrier system that is inter symbol interference right, but what is the biggest advantage of
single carrier system is the PAPR; that means, peak to average power ratio is the
minimum or is the lowest possible thing compared to multi-carrier system ok. We can
think of a sinusoid and it has a peak to average power of ratio of a by 2 or 3 dB and if
you would assign some kind of modulation QAM modulation, the PAPR would be
primarily due to the kind of modulation that comes in. Why it is so? Because if we are
thinking of BPSK there is no change in amplitude, if you are thinking of QPSK, there is
again no change in amplitude right. But, if we go for the next higher order modulation as
given in this particular picture, what you see is that, amplitude of this constellation is
different from the amplitude of this constellation. So, the constellation itself brings in a
peak to average power ratio.

Now if we go for higher order constellations so; that means, if we go for 64 QAM. So,
this is 16 on any one quadrant you would repeat the same over here and on all the
quadrants. So, then if we compare the power with respect to this constellation compared
the power with respect to this constellation point it is obviously higher. Now this one can
easily see in one of the results that we had depicted over here is that, here it shows that

361
how as the constellation size increases the peak to average power ratio increases that
what you are seeing ok. Because, now this is going towards more of a single carrier
system whereas, when we look at OFDM system, the increase is not notable it is not
much notable because the PAPR is primarily driven by the factor N and this N is quite
large.

Because, if you look at WiFi; WiFi which is a very small number it is 64 which is also
not small. If you look at LTE, the number is around 1024, if you go for the fifth
generation the number is even larger ok, but there are different other mechanisms by
which one can think of effectively or practically having a lower PAPR. Now one another
way of seeing it let us let us carefully take a look at that. If one of the users is being
allocated only one such band of frequencies right so that means, only these frequencies;
that means, these few frequencies are going to get non zero constellation points or
symbols. So, for that user all these sub-carriers would be getting zero in the symbol value
ok.

So, effectively the active number of sub-carriers is restricted to the bands of sub-carriers
that is allocated to that user. So, when we look at the IFFT operation at the transmitter
the x n which is summing over K is equal to minus N by 2 to plus N by 2 minus 1 or let
us say it is summing over K is equal to 0 to N minus 1 or you can also sum over K plus
be 1 to N. In all these cases X k e to be power of j 2 pi k n upon n that is valid for all the
cases. So, what do you see is that, for a large number of K the X k value is 0 for one
subset this is 0. For another subset this is not equal to 0; that means, for these subset
values of K for this K X k is not equal to 0; for these K X k is equal to 0 correct. So,
what does that mean? That when we are adding these up over a smaller set when were
adding it up over a smaller set then the peak to average power ratios automatically
reduced.

So, now, if the system allows for the user to use only a small subset of the entire
bandwidth, in that case the peak to power peak average power ratio is automatically
reduced for that particular user right; so because that user is not accessing the entire
band. But now if we look the base station; the base station is allocating let us say this
chunk to user 1 this chunk to user 2, this chunk to user 3 and so on and so forth. Then
from the transmitting end at the x at the base station, what one will find is that the base

362
station has all the sub-carriers active in the worst case scenario. When there are lesser
users this will obviously, be not the case.

So, the base station suffers a PAPR problem. But look at this we have discussed in the
previous class, that in the uplink direction the PAPR problem is addressed in LTE where
is it is in the downlink it is not addressed. The main reason we have said is that uplink is
user device to the base station user equipment to base station or which is also known as
the eNodeB the name changes when you go to the fifth generation system ok. So, then
the users battery is a primary issue battery life right. So, saving or reducing PAPR make
sense whereas, in the reverse direction power is not much of a constraint and one can
implement better power amplifiers whereas, the user end you have constraints on
implementing the power amplifier.

So, as a result the PAPR problem at the eNodeB or the base station is not much of a
challenge whereas, it is a primary challenge at the user equipment. This is something
what we should remember. So, hence all the solutions and things get designed.
Accordingly in the fourth generation, the uplink has a solution at the user and in the
downlink it does not address it at all and since we have also said now that in the uplink
the user equipment need not be sending across the entire band of frequencies.

So, that also helps in the fifth generation, although it allows for DFT spread in the uplink
in order to save power, but it can also allow OFDM transmission in the uplink direction.
This is something one has to note very carefully. So, going ahead further from what we
have discussed. So, now, what we are discussing is this single carrier FT. So, what we
see over here is that, we have the single carrier the next part is what we will look at. So,
since we have addressed this problem PAPR is heavily reduced there is the lowest
possible PAPR one can think of, but the ISI problem still remains. So, how is this
handled and how is the entire framework giving us a facility is that, what we are seeing
is as we translated from a standard OFDM system; that means, this was our standard
OFDM system as we see one by one blocks are getting removed ok.

But what we are seeing is that all right. So, this part is also removed the CP has remained
this has remained. So, this remaining means that you have some guard interval which is
revealed as a cyclic prefix right. So, what does this do? This helps prevent the ISI being
manifested at the receiver right. Because the receiver does a CP removal this particular

363
part is CP the negative sign over here indicates a CP removal. So, once it removes the
CP, the entire block of OFDM symbols. So, we have a block based transmission right
and the block length is remaining N as an OFDM nothing has changed. So, basically that
same N block length will remain and there will be a CP N CP will also be added to it
right. So, that gets removed and then you have the entire block which is free from the ISI
of the previous block ok.

So, the ISI between this and this is addressed by the CP that is added and one that is
removed. Now, one would argue that one has to apply ISI cancellation, but look at this.
Since we have got this CP right our earlier discussion that convolution linear convolution
at the in the time domain gets translated to circular convolution in time domain. That
means, if we do DFT operation it would appear to be DFT of the channel coefficient
matrix multiplied by that of the DFT of the its receive signal strength all with N point
DFT; here is something we have to remember right. So, what does that help us in that,
every sub-carrier now we are seeing a sub-carrier all the sub-carrier was not present, but
we are seeing in the frequency domain with a certain resolution and the resolution that
we see is equal to the bandwidth of the system by N that remains.

So, if we can have N very large. So, now, this look at this N one can choose
independently one need not be constraint because the transmitter does not have any value
of N. So, this can be chosen independently with any finite resolution that one thinks of
and one can apply this frequency domain equalization. So, this is a very handy technique
for uplink. So, wherever power is a major constraint one can easily think of using this
particular method single carrier FDE for uplink and when one sends it for uplink, these
minimum PAPR at the receiver and this processing is done at the base station. So, where
power and processing capabilities never a constraint and one can handle all the ISI in the
frequency domain by very easy signal processing.

Now, once you have got this in the frequency domain. So, here you are in the frequency
domain one has to do the DFT operation DFT it one has to do the IDFT operation; so, in
order to get from the frequency domain to the time domain. So, what we have over here
is these pictures, these have to be IDFT at the receiver side these pictures have to be
IDFT at the receiver side and these have to be IDFT at the receiver side all these have to
be IDFT at the receiver side. So, once we do the IDFT, we get back our signal x n over
here what was the signal x n over here?

364
Free from channel only thing that remains is the noise that one cannot remove and these
can be now sent to the QAM demodulator or a better word is demapper we would not use
the term demodulator and then one can think of serial to parallel to serial conversion this
is parallel to serial conversion or one can think of bringing this module earlier and then
doing with one single QAM demapper. So, this is an extreme case of single carrier
FDMA and one can do reduce the PAPR like anything.

(Refer Slide Time: 21:09)

So, after this we proceed further this will also be I.

(Refer Slide Time: 23:14)

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And we look one interesting capability of this DFT spreading. So, what we look at DFT
spreading. This is the picture that is important for us. So, we call it DFT spreading now,
we look at little bit deeper picture of it. And instead of DFT spreading we would rather
call it a spreading system. So, we would simply call frequency domain spread it right.
So, that is what we will look at.

Sometimes these kind of things are also called multi-carrier spread spectrum. Now there
are different realizations of multi-carrier spread spectrum one realization is you have
spread spectrum communication and they happen on multiple parallel carriers. The other
way is that, you do frequency domain spreading; that means, you have a multi-carrier
system, but along with it you have some kind of spreading. The spreading codes can be
obtained as we said earlier from different combinations whatever we have studied in the
third generation system.

So, let us look at why should we do it and what are the benefits and what is it related
because we can use it in again all future communication systems. So, in a typical OFDM
system these are the sub-carriers, we are discussing we have been discussing this picture
it is not new. This represents the frequency domain channel again and let these be the
data symbols as has been written over here. So, now, what you can see is that, this
particular sub-carrier which experiences a deep fade deep fade means the signal
attenuation is very large as you can clearly read over here. This set of sub-carriers were
signal attenuation is very large what would happen is the would go under deep fading
and they will not be demodulatable at the receiver right. So, that is what happens.

366
(Refer Slide Time: 25:05)

So, these symbols get lost and you cannot demodulate and the other symbols are either
increasing in signal power or decreasing in signal power because of the fluctuation of the
channel, which is in correspondence to this curve right. So, it means different signals
experience different signal to noise ratio. We have said earlier that this is what is utilized
for link adaptation right. But now while we have seen the positive side of it the negative
side of it is like, there is a lot of loss also and these are not recoverable loss. One can
argue that yes, I can go for error correction codes and I can recover, but deep fading
losses or something which is always difficult to recover.

(Refer Slide Time: 26:02)

367
So, we look at another system which is kind of multi-carrier spread spectrum. So, now,
let us look at this picture because this sometimes helps us in creating better techniques,
there have been a lot of investigation in these methods earlier, but these are yet to be
practically used. So, we would take this opportunity to discuss these methods. So, that
one can potentially take this up.

So, what we are discussing is not something new in context of knowledge, but something
which can be exploited even within the same framework that exists. So, let us say we
have these colored symbols which are required to be spread, and they get spread as
depicted in the next picture. So, we have color coding to help us understand the picture
right.

(Refer Slide Time: 26:44)

So, now we have expanded these signals. Now, how did we do it? We had X of k let us
say, but we will be these X of k was going into IDFT at the transmitter and coming out
as x of n ok. So, now, let us take one of these and let us mark it as capital X of n and then
with this we multiply with the weight k n which is drawn from a column of the DFT
matrix. If you look at the DFT matrix of size n it is an n cross m DFT matrix. So, if we
take one particular column of it we are getting one code. One can also think of taking
them from the Hadamard matrix. The good thing about Hadamard and DFT matrix is that
both are orthogonal matrices.

368
One can also think of going beyond this orthogonal sequences and going for pseudo
random sequences as we have discussed in the third generation system. So, again when
we discuss third generation system we said that yes there are certain advantages which
you can bring from the third generation system into the multi-carrier system which is the
next generation system. So, this is one view of such a thing. So, what we see is that,
these are the data symbols which have been spread on a group of sub-carriers and they
are orthogonal in frequency. And these are the chips of the spreads. So, as we have said
let us say there is one symbol and this is spread across the entire set of sub bands.

So, and this is the spreading gain we have discussed a spreading gain, because same
information is contained in this entire set same information is contained it is simply
spread across the set of frequencies. If one wants to improve the spectral efficiency in
that case, one can assign another symbol on the same set of frequencies. So, once when
assign one if one assigns another symbol on the same frequency, if these codes that are
used to spread them have good properties then what can recover them very easily right.
We have discussed that if they are orthogonal there will be no projection on each other
and if they are pseudo random the amount of cross correlation will be very less.

So, instead of seeing them in time domain what was the in the third generation, here we
are showing the frequency domain picture. So, one can stack up different codes as we are
showing in this particular picture and hence one would get a huge benefit in terms of
spectral efficiency.

369
(Refer Slide Time: 29:13)

Now, how do we process them? So, when it goes through a fading channel, we will find
that these signals are lost as we have discussed. We have maintained the same channel
gain in the consecutive pictures, but we will find that the entire signal had been spread
across several sub-carriers. If the signals have been spread across several sub-carriers
then even a loss of one or two symbols part of the symbols fraction of the symbols does
not cause a major problem.

(Refer Slide Time: 29:44)

370
Because one can combine the chips of the code and effectively one can increase the
signal power to a sufficient level so that it crosses the decision threshold.

(Refer Slide Time: 29:49)

So, again what we see is that, there is combining of chips and the difference that we
bring in is that there is a frequency domain combining of chips. So, effectively you are
getting a frequency diversity by this method within the same time interval. So, in other
systems you had to have a time delay, here within the same time interval you are getting
this benefit.

(Refer Slide Time: 30:25)

371
Now, these chips as we said can be drawn from different mechanisms. So, there could be
a lot of other problems also like a lot of deep fades and the symbols the entire symbols
can go into error, because when we see this here what we have drawn is that there is a
narrow section of bandwidth which goes into a deep fade right in these pictures.
Whereas, it could be the case that this entire large set of bandwidth goes into deep fade
because of certain properties of the propagation channel. So, if the channel properties
such that the coherence bandwidth is large, then a large set of frequencies are above the
threshold while again a large set of frequencies can be below a threshold.

So, in order to take care of this problem one can think of coming up with mechanisms
which would overcome the outage, because a large set of symbols going into deep fade
one cannot do anything. Because what we see is that the consequence of symbols they
have all gone into fade. The previous picture was only a fraction of the symbols had gone
into fade and one could recover them, but here an entire block goes into fade. So, what
do you do now is the natural question.

(Refer Slide Time: 31:31)

So, what we find is that instead of doing them on consecutive sub carriers, one can
spread them on interleaved sub-carriers. So, this facility is also very important it is
available in Wi-MAX like systems, where you can spread them on different sub-carriers
rather you can distribute the signal on different sub-carriers spreading is not supported
over there, but we are discussing something which is beyond the existing systems. So,

372
one can spread them under such conditions what you will find is that, if a signal is spread
across in the same situation only one of the chip is not going in fade whereas, others are
not going in fade.

(Refer Slide Time: 32:10)

And hence when we have there is also another mechanism by which one can do is that,
one can think of doing a combining in terms of frequency hopping mechanism. So, if one
talks about sub-carrier hopping. Now, let me tell you although it appears that we are
talking of spreading and sub-carrier hopping right in order to overcome such problems,
the hopping mechanism is again a method which has been there in the second generation
system right.

So, we are simply taking advantage of the best features which were existing before and
combining them with the new features, that are given especially through OFDM. So, we
are maintaining OFDM applying those methods on top of OFDM so as to get benefit.

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(Refer Slide Time: 33:02)

So, if you have the hopping mechanism by which the signals are hopped over different
carriers in that case the combining after averaging over the effect. So, what happens is
that each of the signal gets averaged over these different sub-carriers right. So, this gives
some additional benefit that your frequency diversity now increases beyond the subset of
frequencies that we consider and it spreads across the entire set of frequency band. That
means, your entire band is available for diversity combining what simply happens is that
you are improving the outage.

Let me highlight although peak throughput is very important. Peak throughput is

something which is very important this is something which is one of the key advertising
factors I would say or key parameters when people are moving from one generation to
another generation, the other very important factor is the reliability. So, if we have
mechanisms like this reliability can be improved significantly and outage is a very very
critical factor. Outage determines what is the worst case performance.

So, while we want to increase the peak performance, it is very critical that one improves
the outage performance also. Because simply increasing the peak performance does not
give us as much a benefit if on the contrary we lose out in terms of outage performance
right.

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(Refer Slide Time: 34:30)

So, some of the important considerations over here is the loading factor, which means
the number of data symbols to be used to the spreading gain of the code. So, we have we
have discussed the variable spreading factor when were discussing the third generation
system. So, similar things can be adjusted over here; that means you can use a variable
spreading factor or one can think of instead of putting so many symbols, one can reduce
the number of symbols. If one reduces the number of symbols that are put on to a set of
sub-carriers, then the amount of benefit that one gets is better because the multi-user
interference gets reduced in such a case.

So, if one is really constrained with the signal to interference plus noise ratio or signal to
noise ratio, then one can think of reducing this loading factor thereby getting even further
benefit in terms of spreading gain. One can do in terms of interleaved grouping of sub
carriers, block grouping of sub-carriers, these are all very critical detailed methods inside
this multi-carrier system which are essential in order to get the best possible benefit.
Channel estimation error is also important because if one is doing kind of additional
spreading then this would affect all the symbols not just one symbol.

Synchronization is important we have discussed the effect of synchronization in OFDM.

And, to overcome this sometimes successive interference cancellation receivers are also
recommended.

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(Refer Slide Time: 35:59)

So, there are different results that we had obtained earlier and what one can see is that
through hopping one can get a significant benefit in performance and one can reduce the
outage, better error probability can be used, but when we talk of such spreading, channel
estimation error which is affecting one of the symbols if you do OFDM effects several
symbols when we do such a spreading.

So, we must take care multitude of these parameters together when you are finally,
designing or implementing a communication system. We conclude this lecture over here
and we will carry on with further discussion on how these techniques are adopted to the
to the fifth generation system in the upcoming lectures.

Thank you.

376
 Evolution of Air Interface Towards 5G
Prof. Suvra Sekhar Das
G. S. Sanyal School of Telecommunications
Indian Institute of Technology, Kharagpur

Lecture - 21
Waveform for 4G & 5G OFDM (A),
SC – FDMA, DFT Spread OFDM (A) Contd.

Welcome to the lectures on Evolution of Air Interface towards 5G. So we are discussing
currently OFDM that is Orthogonal Frequency Division Multiplexing. And, I have been
iterating that it is very important to understand the details of OFDM, how the principle
layout structure is, how the things work and most importantly: what are the different
parameters which affect the performance and how the parameters are to be chosen.

What are the channel effects or what are the environmental effects which influence the
choice of parameters. Because, when we go to 5G air interface which is primarily OFDM
but, the difference is choice of set of parameters which is essentially driven by the
different conditions under which it has to operate. So, going forward from where we had
discussed the things in the previous lecture.

(Refer Slide Time: 01:10)

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So, we had been talking about the link adaptation procedure in OFDM and we had
explained how the channel fluctuations are utilised.

(Refer Slide Time: 01:18)

So, what we have discussed I will briefly talk about it that the signal strength fluctuates
in all directions in time as well as in frequency, so in both these directions signals keep

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on fluctuating. And, we had discussed through this particular diagram is that the sub-
carrier spacing has to be maintained in a manner that it experiences flat fading for every
sub-carrier. And we had also mentioned that in the time domain the time has to be
decided in a manner that it experiences near constant channel; that means, each sub
carrier width and the corresponding symbol duration this is Tu.

So, if you draw it over here it might be visible. So, if this is Tu for us and this
corresponding to that is the delta f ok. So, these are to be maintained in a manner as has
been discussed several times like this is one of the criteria and on the other side on the
Tu side this is another criteria. So, this comes from delay spread this comes from
Doppler spread which are two different characteristics of the channel and they are on two
different dimensions; one is because of the excess path length and one is because of the
mobility. And then we said further that since this fluctuates that there is around 40 dB of
fluctuations of signal strength since these sub-carriers are different sub-carriers they are
all orthogonal.

So, we remember that they are all orthogonal sub-carriers e to the power of j 2 pi fk t and
fks are chosen such that fk minus fk minus 1 is equal to delta f is equal to 1 by Tu this is
the condition we have been using. So one can choose to use different modulations on
each of the sub-carriers and clearly from this picture we had explained that whichever
sub-carrier experiences a low signal to noise ratio can be given lower order modulation.
Whereas, the subcarrier which experiences a higher signal to noise ratio will require a
higher order modulation it can support higher order modulation effectively this can
support 6 bits as an example this is going to support only 2 bits.

So, overall instead of doing an single modulation across the entire set of frequencies one
can actually fluctuate, one can vary the different different data rates and thereby overall
increase in throughput or spectral efficiency can be achieved. So, this is one of the
biggest advantage that the OFDM brings it brings in along with other different
advantages which we have been discussing and one issue about this particular picture the
y axis is channel gain in dB. So, this is to be taken into account.

So, when we take the received signal strength, the received signal strength is to be taken
along with this. So, if you are doing in dB so, P received signal strength in dB should be
set equal to P Tx that is the transmit power in dB sorry in dBm or may be in dB watt

379
dBm, then you take away the path loss in dB and you also take away the channel gain.
So, what you see over here is the maximum channel gain is usually set to one that is
normalised. So, whereas, what one has to do is the average small scale channel gain is set
to be equal to 1. So, instantaneous fluctuations will be there dB and this is your received
signal strength. So, to translate this picture to received signal strength one must be given
the transmit power and one should also consider the path loss associated with it then one
will get the received signal strength.

So, one should not get confused that a minus 25 dB how one will support a QPSK
modulation and at 0 dB how one will support a QAM modulation this is not the complete
picture, so the complete picture has to be taken into account by taking the transmit power
as well as the path loss. So, as to take the complete link analysis and there you are
basically taking into account the link budget in total.

(Refer Slide Time: 05:38)

So, moving ahead we discussed how different modulations are to be chosen and there are
different SNR switching thresholds there is a requirement of error probability.

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(Refer Slide Time: 05:45)

We have also discussed in the previous lecture about how the spectral efficiency curves
change one when one has QoS requirement; that means, there is a threshold on BER
which can be translated to block error rate and so on and this on without QoS that means,
there is no constraint. So, one keeps on transmitting the best possible signal that gives the
highest spectral efficiency; however, the problem is no criteria on error probability is
maintained ok.

So, these curves are without having without having any throughput computation
considering repeat transmission repeat Tx is not taken into account. So, if you take
repeated transmission into account these lines which appear to be higher than these green
lines they are going to be even worse. So, they will shift to the right because when you
repeat transmission the spectral efficiency loss is huge. So, to avoid that some prior link
threshold is prepared and that is through this BLER threshold. So, over a over the last
mile over the last that is the link between the base station and the access sorry the access
point and the user device 10 to the power of minus 1 or 0.1 block at the rate of threshold
or packet error rate is well accepted. We have also discussed this flow of things we have
also said that how things flow in this particular sequence of events.

So, just briefly initially there is transmission from the transmitter be at the base station or
the user equipment; that means, in the downlink or uplink direction. So, we are taking
any one particular direction the fluctuations of the channel are measured in the channel

381
estimation module. So; that means, when we discussed about channel fluctuations here
when we discussed the channel fluctuations it is assumed that during channel estimation
process this particular signal strength or whatever is the signal strength here gets
measured. That signal strength is converted to a particular modulation and code rate
whatever is supported because one can measure the SNR on this axis once the SNR is
measured then one can choose which of the supported MCS is MCS can be used and the
index.

So, the index of M modulation and code rate combination can be send back to the
transmitter. So, because otherwise if look at it we can have various different modulation
in code rates, but there is only a finite set. So, if we have let us say 32 possible
combinations if; that means, if there are 32 possible MC combinations then one will
require 5 bits to identify them. And this is some time reduced by choosing 16 possible
combinations and hence you reduce to 4 bits; that means, every signalling will be having
1 bit less, if we take the large number of resource blocks. And, large number of users
accumulated number of overhead bits would be significantly meaningful and why 1 bit is
been considered under this conditions is that we are talking about the control channel.

So, one would usually prefer to have a lower control channel than the data channel
because data channel is the one which contains the actual pay load, the data, but control
channel is necessary without which there is no meaning can be assigned to the data
channel it cannot be utilised in a better manner. So, in order to have an efficient
implementation there is limitation on the control channel.

So, would like to use lesser number of bits, but we still want to have control channel. So,
there our mechanisms which are used to reduce the control channel signalling overhead.
And so, what we find is that suppose we are using 16 levels to be fed back; that means,
every alternate level are used to fed back the other side; that means, if let us say the user
equipment feeds back information to the base station right, so it uses 4 bit feedback let us
say. So, base station knows that so that means, from 16 levels it gives a feedback, but the
base station knows that there are 32 possible levels. So, using a prior information about
the block error rate which the user has been sustaining the base station has flexibility or
the decision making capability that whether to allow the particular MCS of choice or
may be reduce it by one half step or increase it by one half step. If the conditions have
been good for the past few occasions, past few occasions means past few transmissions

382
then the base station can take things in a little bit optimistic manner and it can rather
choose one of the intermediary stage.

So, these are various mechanisms which are also deployed and considered to improve the
throughput performance or spectral efficiency performance which is directly not visible,
but when one goes to implement these things then these control channel and feedback
becomes of primary importance. And this index that is the feedback is sometimes called
the channel quality indicator. So the channel quality indicator is what we mention over
here. So, the channel estimation feeds back this channel quality indicator this is we have
briefly mentioned in the previous lecture, but today we had discussed little bit in more
details. The channel quality indicator is fed back to link adaptation unit as we have just
described and it takes the final decision of what is the value of modulation in code rate to
be used along with power control and then it sends back the data.

So, there is one entire loop of feedback and then that feedback is used for
communication of the actual information in the later cycle. So, what happens in the first
cycle when some prior data is coming to the user during that time whatever channel
estimation feedback is given to the base station is used for the next iteration. So, this
particular diagram below on the time axis indicates the sequence of events that is there is
a pilot symbol which is used for channel estimation, channel is estimated followed by
feedback and then it is used for data transmission. Now it is to be ensured that this
interval of time is less than coherence time that is what we have said the loop time
should be less than coherence time, now loop time uses several frames because when the
transmission happen it happens in frames.

So, at least one transmission followed by another transmission at least two frames come
into picture and each frame consists of several sub frames, each sub frame consists of
several symbols right. So, what we effectively see is that multiple symbols a large
number of symbols should lie within the coherence time this is very very critical. So,
effectively it means that our earlier condition that T Tu is less than Tc is not sufficient it
should be much much less than Tc is the condition that we have to use. And we have also
said that simply not Tu we should take Tu plus Tgi which is the guard interval into the
account and make much much less than the coherence time ok.

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(Refer Slide Time: 13:24)

So, at this point I would take short digression and would like to point out several
references on OFDM which are very very useful. So, because we have only limited
opportunity to discuss the things, but it is always recommended that you look for
references beyond this and which contain where you can give more time take your own
time read them through. So, that you can understand the details in much clearer manner
much easier fashion; so, this is one of the early reference books that are available it is it
has been followed widely there has been second reference which is also pretty popular.

So, one can use this particular book as well and thereafter if one is not having access to
these books there is this PhD thesis by Klaus Witrisal which also contains good details of
the OFDM system model which we have been following over here. And this particular
thesis also contains summary a very quick summary of things, there was another report
which is also publicly available the these things are freely available one need not use any
payment for them they are absolutely freely available which also contains a break down
or analysis of OFDM in much much easier fashion in very very simple words.

This particular book I have already referred to which we are mainly is the guidelines for
this particular course is also useful. And finally, I would also recommend the paper
which is given over here there is part I and there is also part II of the paper which also
provides an excellent framework for writing down the expressions of OFDM and doing
all kinds of analysis alright.

384
(Refer Slide Time: 15:03)

So, this is the typical flow and we have simply added these two parts, we have already
discussed the transmitter structure earlier where we have actually discussed all more or
less the signal flow through all these blocks. So, we will not discuss it again. So, in the
receiver side exactly opposite operation happens.

So, only this synchronization is something which is an extra part we have also discussed
about them and then the receiver processing is in the reverse order of the transmitter and
there is this feedback loop. And so, effectively cycle of events goes on in such a process
which is also a very important part of OFDM communication.

385
(Refer Slide Time: 15:46)

So, we have discussed about this particular picture where there is pilot, channel,
estimation, feedback and link adapted. So, what is effectively meant is that this period
should be less than. So, if I call it T LA this should be less than Tc. So, this condition has
to be maintained and it keeps on repeating.

(Refer Slide Time: 16:06)

So, this is the overall picture of things. So, if we look at the details of it what we see is
that we have described a channel fluctuation figure earlier. So, I will just quickly get
back to the channel fluctuation figure. So, that it helps us. So, this particular picture what

386
you see is that the unit of time is seconds and I have said this in earlier discussion and
this is of course given in megahertz. So, if we go down further now and look at the
picture based on whatever we have discussed. So, what we find it is this particular
section which is containing the channel gain in dB is effectively zoomed in version of it
where now our time scale is in milliseconds.

So, that is a big difference and since it is in milliseconds what you see is that in time axis
the fluctuation is pretty slow change in colour indicates the change in the values and a
redder colour the colour which is more red indicates a higher value a bluer colour
indicates a lower value ok. So, that is how the colour pattern or colour coding goes. So,
what we see is that in the frequency domain the fluctuation has more or less remained,
but again if you go back we will go back to the earlier picture what we will find is that
we have captured up to 15 megahertz in this particular image and here this resolution is
0.05 milliseconds 0.05 seconds ok.

So, now we are showing a picture which is only up to this much that is a much smaller
duration and the resolution in time is also in milliseconds. So, the picture looks different
over here and the fluctuations appear to be lesser and these smaller units are basically
delta f sub-carrier spacing and this unit is Tu. So, this is for representation purpose that
we have drawn this particular picture. So, these are reflecting the sub-carriers. So, that
you can clearly see that if you proceed along this line its one of the sub-carriers and any
one of the sub-carriers has a spacing of delta f and each of them are Tu durations.

And as we have said earlier that several such OFDM symbols in time are grouped
together and several such sub-carriers are grouped together to form a resource block as
has been marked by this colour and I am putting a shade on this which is the resource
unit on which all kinds of link adaptation procedure is done. So, this unit in its multiples
have to flow from transmitter to receiver for estimation, receiver to transmitter again for
feedback information and then it has to go. So, this needs to be understood, we will get
back to more detail on performance analysis again later on.

387
(Refer Slide Time: 18:59)

So, now, let us look at some other important parts of OFDM. So, if we look at typical
OFDM generation process we have said that an IFFT operation happens at the
transmitter. So, in the IFFT operation; so; this is the butterfly architecture of the
implementation. So, there is several multiply and addition operation which happens
right, so if you look at the time domain equation x of t or x of n rather if you do it in the
discrete domain x of n we had said it is sum over k Xk e to the power of j 2 pi k n upon
N for any one OFDM symbol.

So, now these are the. So, this is the you can this particular picture has small x on this
side and capital X on this side you can also reverse them and simply put appropriate
values of weight and things would be either FFT or IFFT. So, if you have taken only one
particular picture. So, what we have done over here is that we have actually considered
this in this particular representation if we see that several such X ks gets simultaneously
added ok.

So, when several such X ks gets simultaneously added there is of course, a weight factor.
So, what we see over here is summation of several such constellation points these are
constellation points chosen from the symbol mapper. So, once these are chosen from the

388
symbol mapper then what we have is that each of these numbers are random realizations.
So, if each of them are random realizations then what we see is there is an addition of
random numbers. So, this itself is a random number. So, every sample in time is a
random number and the variance would depend upon let us say I put k is equal to 0 to N
minus 1 or 1 to N upon the length or the numbers that we add, as the value of n increases
the variance becomes larger and larger.

So, what it effectively means is that the fluctuation of the signal in time increases as the
number N increases now what is the impact. So, let us look at this. So, this particular
picture of what we have is the time domain signal for is the time domain signal for
typical OFDM what we see is that there are several peaks which occur and there is a
certain average level of the signal. So, what the problem we see over here is that the peak
power to peak average power there is a peak to average power which is very high in case
of OFDM which is again a typical problem.

(Refer Slide Time: 22:02)

Now, why it is a typical problem we will see. So, in this picture it is shown as the size
increases the probability of getting higher and higher values is more and more and more
ok.

389
(Refer Slide Time: 22:12)

So, in this particular picture what we can show the signals finally, go through the High
Power Amplifier right, they go through the HPA before being transmitted outside. So,
when they go through the HPA we need to look at the characteristics of the high power
amplifier, the high power amplifier ideally speaking should have a linear curve this is the
input amplitude this is the output amplitude. So, it should ideally have a linear in that
case whatever signal goes in goes out with the same shape characteristics there is no
variation of the shape characteristics. But, in all practical systems the performance or the
characteristics of the power amplifier is not linear rather it is non-linear right the way we
have drawn other curves or the way I am tracing one of the curves is kind of non-linear
ok.

So, this curve is more or less non-linear and then what would happen is that one would
desire that the signal is operated as high input power as possible because the amplifier at
higher input power is operating with higher efficiency. And if it operates at a back-off
then efficiency of the power amplifier is less, now why we talk of back-off because, if
we are moving away towards from the saturation point then we are more or less in the
linear region of the operation. So, if you are in linear region of operation then the signal
goes out in an undistorted manner ok, but the problem is we are going to get less output
power, less output power would mean that the signal or the operation has to be sustained
for a longer duration of time in order to send the same number of bits right plus there is a
power efficiency loss.

390
So, this effectively leads to greater loss of battery power especially at the hand held
devices. So, for OFDM a PAPR causes lot of restrictions in the having large coverage
area. So, we need to have several mechanisms in order to take care of this, but for the
downlink direction; that means, for the base station to the user equipment the problem is
not much because, base station is having power supply from the electric grid whereas,
the user equipment side it is the battery. So, this is very very critical factor.

So, if one has to use a back-off there is a significance reduction of the range one would
like to have a situation where on would be using as much power as possible in other
words one who is interested to have signals which is low PAPR. So, now, if one if one
does send the signal over here then what happens the input signal goes on something like
this and as a result if we see the output signal there will be when the signal rises the gain
at the output is much less. So, the output signal we will find does not follow the input
signal so much especially in the saturation region.

(Refer Slide Time: 26:11)

Now, this clearly changes the time domain shape of the signal. So, if it changes the time
domain shape what it would result is there is obvious impact in the corresponding
frequency domain shape. So, once it impacts the frequency domain shape it causes a lot
of in band distortions, lot of in band distortions results in ultimately causing a poor signal
to interference plus noise ratio at the receiver side. So, graphically what we find is now
this overlaid blue coloured picture shows whatever signal that comes out now; obviously,

391
the spectrum characteristics of this signal is worse than this is different rather than what
is originally present in the red coloured signal.

So, if the spectrum characteristics signal content has changed then it would; obviously,
effect the signal that it carries and hence the quality of signal at the receiver would be
distorted which would lead to higher bit error rates. So, to overcome that single carrier
FDMA is proposed the single carrier FDMA is simpler in the sense that it introduces a
DFT in front of the IFFT operation. So, a DFT in front of the IFFT operation it simply
does it cancels out the effect of IFFT, now there is a genesis for this kind of studies is
that what it simply says is that since there is a combination of these weights that causes a
large variation, so, the large variation would happen if they add up in phase if by some
mechanism the in phase addition can be destroyed then the fluctuations or variations can
be made less. So, in order to do that at every point one can think of multiplying by Ck
where Ck is some code sequence ok. So, code sequence can be taken from various
different aspects one could be Hadamard code could be DFT code. So, here what we are
discussing is that instead of thinking of the DFT operation it is some kind of a spreading
operation, peak to average power ratio. But the cyclic prefix addition is still maintained
all though it appears like a single carrier system because cyclic prefix helps to mitigate
the inter symbol interference and one can operate using the FFT at the receiver along
with it one can use the frequency domain channel equalization, because frequency
domain channel equalization is much much simpler.

(Refer Slide Time: 27:42)

392
So, people have found through results that there is a significance reduction in the peak to
average power ratio if one uses different if one uses this DFT spreading mechanism.

(Refer Slide Time: 28:01)

So, will move forward and take a look at the OFDM structure. So, this is the OFDM
structure which we have discussed at the transmitter side there is IDFT operation. Now,
to change or to look at what kind of change is one can think of we have already
discussed about merits and demerits.

(Refer Slide Time: 28:16)

393
We would like to show you through a minor change in the figure how different things
can be realised simultaneously over the same kind of architecture. So, if we focus on this
picture this is the IDFT operation at the transmitter and the DFT operation at the
receiver. So, as a first step, we are simply showing that nothing has changed it is the
same IDFT operation in the transmitter and same DFT operation at the receiver, but
pictorially we have just modified it to show a translation that can be thought of.

(Refer Slide Time: 28:46)

Now, DFT spreading is introduced before it so, DFT spreading kind of over a smaller set
of bandwidths. So, if you have say 1024 carriers in the IDFT operation then one would
like to add DFT of various sizes to get various benefits. So, one could think of a 128 size
DFT. So, if one does 128 size DFT one would have M number of such 128 point DFT
that would result in 1024 point IFFT mapping. So, if this is 2 to the power of 10 this is 2
to the power of 7. So, we have 2 to the power of 3 number of that is 8 number of such
IDFT such DFT operations happening.

So, as if 1 2 3 up to 8 such DFT operations, each one is going to produce 128 point
output, and all of these will be feeding into a 1024 point IFFT operation afterwards and
then whatever we get is what we get. So, now, what we will find is that this particular
section, this particular section if we focus on this particular section the DFT along with
these carriers they smudge out each other and as a result one can think of getting a larger
bandwidth of equivalent to a single carrier system. So, as if there is there are multi-

394
carriers have gone away and a single carrier of this much bandwidth has come into play
ok.

So, now this can cause confusion that since we were talking about single carrier all the
effects of ISI in single carrier would come into play, but now what we are seeing is that
the cyclic prefix is still being added. So, this addition of cyclic prefix would maintain the
ISI free characteristics in the time domain between the different symbols and this would
also allow us to go for a frequency domain equalization ok. So, this frequency domain
equalization makes things very very easy, one can use a very simple architecture per sub-
carrier, only one tap equalization, and hence one can proceed with the things.

So, if we follow through some of the steps shown from the OFDM system to translate to
DFT spread system which has a very low PAPR because it kind of randomizes parts of
the signal, we can actually have the same system with a minor path switching. That
means, when we are doing the OFDM, we would like to use one particular set of
components when we are doing DFT spread we can use another set of components rest
of the components remain more or less the same with not much variations. And in fact,
this is used in 4G systems. So, in downlink in 4G systems they allowed to use OFDM
and it is rather A it is a multiple access part.

So, the resource block that we have discussed is to be used for different users in other
words it means that some of these carriers of this are grouped and allocated to let us say
certain user and another set of subcarriers are grouped and allocated to another user and
so on and so forth alright. So now, in downlink OFDM is used and in uplink single
carrier FDMA or SC-FDMA as it is called is used another name for SC-FDMA is DFT
spread OFDM A ok. So that means, this particular operation is as if it is doing the
spreading operation on top of the DFT or the IDFT operation.

So, this is called a DFT spread OFDM and spreading codes are derived from the DFT
matrix e to the power of j the DFT matrix gives you e to the power of j 2 pi k n upon N
because here you are going to get e to the power of j 2 pi k n upon N and here we will be
getting e to the power of minus j 2 pi k n upon M ok. So, not M sorry we can put it as M
prime indicating a different size because here I have used M, so, therefore, I am choosing
M prime over here. So, M prime times M would be equal to M so, you can see that M
prime multiplied by M should be equal to M. So, that would set everything proper. So,

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this would make the things appear like single carrier. So, what we have one single carrier
wide band another single carrier another single carrier.

So, it is still multi carrier, but each one of them are having a wider subcarrier bandwidth
only because it helps reduce PAPR. Now, at the receive at the user equipment side so,
when you are doing uplink, user equipment is sending information to the base station.
So, if one does DFT spread, PAPR is less, if PAPR is less, then one can go for the higher
transmit power, one can go closer towards saturation, plus the efficiency of the power
amplifier is higher as well as one can radiate higher amount of power and hence the
overall system improves the power budget of the system and coverage can be improved.

So, this way downlink OFDM A is preferred in uplink SC-FDMA or DFT spread OFDM
is preferred in 4G as well as the same thing is supported in 5G communications. So,
when we look into the 5G NR we do not have to revisit this particular aspect again that
this OFDM structure is followed in downlink and in uplink this DFT spread OFDM is
also supported because, it would give lot of benefit to low power devices to have a larger
coverage and a better battery life.

So, with this what we find is that our discussion on multi-carrier systems especially with
orthogonal carriers lays the foundation for the framework or waveform structure or the
physical layer signalling procedure for the 4th generation as well as the same thing for
5th generation which we have been discussing. And, which we have been saying when
we were talking about the foundation of waveform analysis or the framework based on
which we have started discussing the waveforms. We will continue on this and look into
other variants of waveforms that exists we will also look at the frame structure for 5th
generation and what are the additional benefits of the 5th generation air interface in
upcoming lectures.

Thank you.

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 Evolution of Air Interface towards 5G
Prof. Suvra Sekhar Das
G.S Sanyal School of Telecommunications
Indian Institute of Technology Kharagpur

Lecture - 22
Waveform for 4G & 5G (OFDM) Numerology Part – 1

Welcome to the lectures on Evolution of Air Interface towards 5G. So, till now we have
discussed the earlier waveforms as well of well as we have laid the foundation for
discussing the waveform for 4th generation and 5th generation. And we have also
discussed the basic framework on which the 4G and 5G stands that is the OFDM. And
upon which we have DFT spread OFDM, which is also a modification of OFDM, and
which is primarily there to reduce the peak to average power ratio.

So, this particular method we have said is used in the uplink direction, and it is valid for
both 4G as well as in 5G. Whereas, when we go to the 5th generation standard, we said it
primarily uses OFDM. So, today we in this particular lecture, we take a look into the
specifications of the 5th generation system. Especially, the frame format and how OFDM
fits in, and what are the different variations, what are the different documents that one
needs to refer to. So, we will primarily look at the main contributions, the changes, and
how does the whole thing work.

(Refer Slide Time: 01:26)

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So, today our discussion will be about the waveform in 5G, and this particular waveform
is given a new name called the New Radio, so usually you will find NR as the
terminology which is more popularly used. So, usually the industry goes by keywords
and acronyms, so NR is the name which will often occur for next quite a few years at
least in the next 10 years. And it is nothing but the air interface for the 5th generation,
which is again need not be scared about the new name, it is just a modification of
whatever existed before.

(Refer Slide Time: 02:01)

So, if we look at how things got developed, again we are looking at the 3GPP which is
the 3rd generation partnership project, which is come up with LTE the long term
evolution, and which is again proposing the next generation system that is the NR as they
call it and which will be the 5th generation system. So, as we can see that 3GPP from its
standard website what you will find is that it unites several telecommunication standards
development organizations, and this is directly from the website that is what I have taken
over here. And it is a group where many partners participate together towards creating
specifications.

And primarily there are three broad categories or classifications. One of them is the
Radio Access Network. So, what we are concerned is with the radio access network,
which is the part between the base stations and the mobile units. So, the entire network
where there will be multiple base stations, and multiple mobile units, they could be cross

398
connected, they would be interconnected. So, this last part of the network beyond which
the core network starts is the radio access network part. So, this is the radio access
network. We have described in one of the earlier lectures how does the radio access
network work, what are the different procedures and protocols.

Then there are Services and System Aspects that is another group, and the core network
and terminals is another group. So, primarily the radio access network is where we have
been mainly concerned, because this is the one where air interface comes into play.
Whereas, in the core network part, it is mostly wired network most of the time it is wired
network, and of course along with it different kinds of services and system aspects are
also present. But, as the name of the course suggests we will be in the air interface and
hence primarily in the radio access network part.

(Refer Slide Time: 03:59)

So, if you look at again the 3GPP, I mean whatever is stated in 3GPP basically we are
reading that particular out is that these generations that means, this 2G, 3G, 4G and 5G
as we have been stating. They does not come just like that, I mean it is not a sudden
release as if there is a milestone, and at suddenly at some point you reach 2G, and
suddenly at certain point you reach 3G or 4G or at 5G it is not like that it is rather a
continuous evolution from one stage to another that is what 3GPP primarily aims at, and
describes it in that manner.

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And amongst other major things, it also says that backward compatibility is very very
important backward as well as forward compatibility. So, this is also primary thing,
because it is a continuous evolving technology that means, suddenly if we find
something some new technology over here, which does not coexists or does not work
together with 2G, then it is a big problem overall huge amount of investment has to be
done and so on.

So, here what 3GPP usually does is it presents new proposal in terms of releases, so you
will find release 99, release 4, 5 and so on. And we are currently in the phase of release
15, release 16. So, these would primarily comprise what we are discussing about 5G.
Release 15 specifications are available, so one can usually go to 3GPP websites and find
the release 15 specifications usually this is called 5G wave-1 or the first part of 5G with
release 16 one is expected to get the full specification of 5G.

So, what happened in this period LTE which is release 8, we have seen earlier that it met
almost all of the requirements of IMT-Advanced right. And LTE-Advanced which is
release 10 is basically the one which meets all of them without any problem, I mean all
of them are exceeded significantly. And IMT-Advanced is essentially LTE-Advanced.
And LTE is sometimes called 3.9G. So, what again we see is that there is the continuous
development of things as things are moved on.

(Refer Slide Time: 06:34)

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So, what we have here is basically two things. One is the radio side that means the
wireless signalling side. And the other is the system architecture ok, how the entire thing
works. And this especially works with respect to the core network, the signalling, and the
other aspects. And this one primarily talks about the waveforms, the air interface, and so
on, radio access technology, radio access network.

So, what we see is that UMTS, which we have described earlier is usually coming under
release 99. HSDP HSPA, which is the High Speed Packet Access Downlink, and
sometimes it is also called HSDPA High Speed Downlink Packet Access, it is part of
release 5. High speed packet access for uplink, it is part of release 6.

So, one can see that continuous there is an evaluation evolution, and this is HSPA plus,
so on our phones when we get H plus, we would think about getting HSPA plus. And
these range of systems would be classified broadly as 4G, these systems they use a
different air interface primarily they use CDMA, which we have discussed in some
details. And these systems onwards, they use OFDM within brackets A framework. And
we have discussed the basic layout for the OFDM system.

These two systems varies significantly from each other, in terms of the physical way of
looking at the waveforms. But, when you write them mathematically, we can still find a
lot of similarity between them if we look it at an abstract level, if we think it from the
basis functions.

So, getting to the core network aspects there is IMS, which got introduced around release
5. EPC is the Evolved Packet Core, which got established around release 8. And then
there were multiple developments, next generation systems are basically the 5G systems,
which are coming into play. So, what we see effectively is that there is a gradual change
of the different technologies, gradual improvement, and not a sudden change as we go
from one generation to another. And this particular picture summarises, the change over
from one generation to the next generation especially over the last three generations of
things.

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(Refer Slide Time: 09:02)

So, when we go into the sequence of events, the 5G has we have been discussing is
primarily the main technology that are of our concern. And in order to look into the
specifications one has to go into the series of documents that is listed over here. And
what you find over here the introduction of 5G that what we are discussing is kind of
improvement over LTE, over LTE-Advanced, over LTE Pro see here you are again
seeing that they are gradually changing over with slight change in the name as well as
slight change in the technology that is why the name is changing. And the first drop of
New Radio that is what we have been described, features in release 15, whereas in
release 16 one is expected to get the entire range of 5G efforts.

But, it is be understood that 5G is not going to stop at release 16, there will be further
developments beyond release 16, which would continue to enhance the so called 5G
which we are waiting for eagerly. And we will slowly enhance and grow towards the
next generation, which is 6G. So, when we go to 6G, we will again find there is dramatic
change, slow change, gradual change, but overall between the 5th generation and 6th
generation, there will be again a dramatic change as we have seen over here like the
primarily the air interface got changed significantly in this particular case.

So, here what we have is the radio aspects for UMTS and all got enlisted in the 25 series
documents that means, if you go to 3GPP website, you will get 25 dot 301, 25 dot x, y, z
kind of documents, which describe the different specifications that are provided which

402
include the physical layer, which includes the user equipment, which includes the base
station, which includes the services, the core network everything. So, whenever you are
looking into the 25 series, it is primary with the UMTS set of documents.

If we go beyond that is the LTE and other document, it is the 36 series of documents. So,
there again we have 36 dot 201, 36 dot 104, 36 dot 101, and several other documents.
So, if you if you open, this 36 series documents in 3GPP, you will find a whole set of
documents which describe the entire operation of the network. So, when we go beyond
LTE, and especially we are talking about the radio technology beyond LTE, we will have
to look at the 38 series of documents right. So, again this is from the 3GPP website, so
all are from 3GPP. So, if you go to 3GPP, you are going to get the detailed
specifications. So, the objective of this specifications is that they are going to meet IMT-
2020 requirements right, so as it is said.

Full compliance with ITU’s IMT-2020 requirement is anticipated with the completion of
3GPP release 16 at the end of 2019 that is in phase 2 of 3GPP effort. So, we have
described the IMT-2020 requirements in all our previous descriptions using the M series
of specifications of ITU. And now 3GPP comes up with the set of specifications, which
meets these IMT-2020 requirements. And as one will find generally it has been a case
that these technical solutions meet all the requirements, and they will be branded as IMT-
2020. And we have seen that IMT-2020 and 5G this terminology, they are
interchangeably usable.

So, if we say which specifications would be meeting the IMT-2020 of five 5th generation
standard will obviously, be going to the series of documents, which are numbered in
3GPP from 38 series.

Now, there could be other organisations than 3GPP, who could also come up with such
technical specifications. And again if they meet the requirement criteria of ITU, then
they will again be branded as the 5th generation technology. Same thing happened in the
case of 4G, which was IMT-Advanced we have discussed this in details earlier. So, 36
series of documents produced a set of technical specifications, which met the 4G or IMT-
Advanced set of requirements. Same sequence of events happens, when it is IMT-2020,
and here again the thirty 38 series of documents would meet the particular requirements.

403
(Refer Slide Time: 13:49)

So, when we require the 38 series of documents, we are essentially talking about 5G
from 3GPP perspective. And we are talking about NR or the New Radio from 3GPP
perspectives. So, if one has to go into the details of these particular technology
specifications, one would find 38 dot 201 which is the NR, again we are seeing that the
name appearing often. It talks about the physical layer, so we have to go to 38 dot 201
document to get into the details as well as there are general descriptions.

And 38 dot 104 is the document, which is also pertaining to NR that is the New Radio,
and it is the base station, radio transmission, and reception. Now, what you see is that
there are two different set of documents, which together describe the NR. There are
many other documents also, which are required in order to complete the description of
description of NR.

Now, it is not possible to get into the details of all such documents in a course like this,
and our main aim is to look at the fundamental technologies how things work, and what
are the details which make things run. Whereas, this particular documents provides exact
or rather bit exact specifications. So, if one has to design, rather one has to develop a
particular equipment, which meets the ITU requirements or which is as per the 3GPP
technology specifications. Then one has to follow these along with the entire range of
other documents, which would describe the entire protocol structure.

404
There is the technical report of 912, which describes a new radio access technology. So,
if you go to the website, you will find a whole set of documents, which can be used. In
order to understand one particular methodology or the process which 3GPP would
require you to follow, you have go into the details of this documents. So, in this
particular course, we will take peak look into some of the documents as we found
relevant with respect to the new technologies. So, primarily we will be looking at 211 as
well as 104 in order to establish the physical NR.

(Refer Slide Time: 15:59)

So, what we find is that the 201 document of 3GPP is the 3rd generation partnership
project. It contains the technical specification of radio access network, NR, and the
physical layer ok. And these are some of the abbreviations I do not need to go through all
the abbreviations, you can easily understand them, and go through them as per necessary.

This User Equipment is something which we will refer to, cyclic prefix CP, which will
refer to DFT-spread-OFDM, we have already discussed in the previous lecture in the
previous topics. And physical downlink shared channel is the one which carries data,
control channel is the one which carries control information relating to the data carrying
in the downlink direction, this is the random access channel, PUSCH is the shared
channel, which carries data in the uplink direction, and this contains control information
for the data which is being transmitted in the uplink direction ok.

405
(Refer Slide Time: 17:02)

So, the general description of layer 1, what we find is that the radio interface described in
this specification this is exactly taken from this particular document ok, these few
statement are taken just to show you that how these things are mentioned, and what
exactly is in the content. So, what we find is that 201 contains specifications, which
covers the interface between the user equipment and the network.

So, user equipment is the hand held device or the last unit of the entire thing that we are
talking about it describes layer 1, layer 2, and layer 3. Layer 1 is primarily the physical
layer, layer 2 and layer 3 would conclude or would include the medium access control as
you could see depicted by the picture. And layer 3 would include the radio resource
control. And between each layer there are service access points through which each layer
gets access to the next layer. So, they communicate with the help of the service access
points. And the physical layer or the air interface is primarily described in layer 1.

406
(Refer Slide Time: 18:11)

So, in layer 1, what we find is that this is very very important statement than what I have
actually made bold with the reason, we take a note of it. The NR physical layer multiple
access scheme ok, so this is the primary thing, when we talk about the air interface which
is the multiple access scheme or the radio access technology is based on OFDM with CP.

So, this particular statement you will find exactly in the document and that is what is
something, which we have to carefully note that there has been fundamentally no change
from what was there in the previous description. But, there are certain changes which are
important and critical, which we will take a look at.

We also see another statement that Discrete Fourier Transform Spreaded OFDM or DFT-
spread-OFDM which we have described thoroughly in the previous lecture with CP that
means, with cyclic prefix is also supported in the uplink direction. This we have also
described, we have also given the reason why it is why it is so and we have also
described that under one specific case that if the size of DFT matches that of the or the
spreading in the DFT matches the size of the IFFT that is used for the OFDM, then you
get a complete single carrier system with CP.

So, in that case you get SC-Single Carrier with CP, and the receiver processing can be
frequency domain equalization, because you have a cyclic prefix ok. Both FDD and
TDD are supported, so these are some important facts which we should keep in mind.

407
Another important fact which is also essential is that the layer 1 is defined in a
bandwidth agnostic way based on resource block right, allowing the NR layer 1, NR is
the new radio to adapt to various spectrum allocations. A resource block spans 12 sub-
carriers. So, the entire definition is in terms of resource block. Resource block is an unit,
which is addressable, which can be addressed by higher layers, and every description is
with respect to resource block.

So, if you have a narrow band system, the number of resource blocks would be less. If
you have a wide band system, the number of resource block is large. And in all cases
what we find is that the resource block spans 12 sub-carriers. This description has also
remained from the 4th generation to 5th generation. And if you ask the question probably
why, one of the major reason is backward compatibility as well as forward compatibility.

Now, that would raise the question that would you do you think that the this kind of a
framework is going to remain, when you go from 5G to 6G, we do not know the answer,
but some potential overlap has to remain. And when we go from the 5G to 6G, what I
think is that there will not be as much similarity to the 4G system as well as similarity to
the 5th generation system. So, we there is there is no hope neither there is any
speculation, but it all depends upon how the technology evolves from one stage to
another alright.

So, now the modification that we see over here is the statement, now we are going by
statement, because that is very vital with a given sub-carrier spacing now, this is vital,
this is the modification that is happening over the previous system. In the previous
system, there was no such no such statement like with a particular sub-carrier spacing,
because the sub-carrier spacing was fixed, and it was described for all possible
implementations, which is constant and that was 15 kilohertz which we have seen in
some of the specification charts that we have described earlier.

Another important thing what we see over here, which describes the earlier one that the
radio frame has a duration of 10 millisecond ok, consists of 10 sub-frames with a sub-
frame duration of 1 millisecond. Now, this the sub-frame duration of one millisecond has
also been carried over from the previous generation. However, the description of slot
which is not given in this particular slide, we will see that has changed from the previous
generation to the next generation. So, we see a modification within some existing

408
structure. So, there is some kind of compatibility, and some new things which have come
in. A sub-frame is formed by one or multiple adjacent slots. So, here we have the
description of slot, each having 14 adjacent symbols.

So, now again summarily, we will of course see them in details. What we find is that
each slot having 14 symbols, so a slot has 14 symbols. And this has carried over from the
earlier generation right. Although there is some modification in terms of the cyclic
prefix, and the number of symbols on very specific cases in the previous generation
system. But, here the number of system the number of symbols is fixed to 14, but the
number of slots that fit into one sub-frame is different, and that is dependent upon the
sub-carrier spacing. And this is what our aim is to understand, and see how they fit in
each other ok.

(Refer Slide Time: 23:41)

So, this is the list of some of the documents, which are necessary in order to completely
understand the NR physical layer. We will not going to details of everything, but my
main intention to provide you this list, so that all those who are interested in the exact
specification details can follow this different documents ok.

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(Refer Slide Time: 24:06)

So, the 38 dot 202, which is one of the documents listed earlier. So, it provides the
physical layer service provided by the physical layers. And the scope is to describe the
services provided by the physical layer, and to specify services and functions, model of
physical layer, parallel transmission of simultaneous physical layer and channels,
measurements provided by physical layer that means, there could be multiple layers of
transmission, and there could be a feedback provided from the user equipment to the
base station and so on and so forth. So, all these things are described in 38 dot 202 sorry
what we find.

(Refer Slide Time: 24:43)

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Next is the 38 dot two 211, which will be our primary description document which we
intend to describe over here, it provides definition of uplink downlink physical channels.
So, these are the actual channels over which the signals are carried. The frame structure,
which we intend to discuss; we will talk about modulation at some point. The OFDM
signal generation, and all other procedures that are necessary which are part of signalling
as when the things go between the user equipment, and the base station.

So, we will see some part of the pre-coding which is due to MIMO, and there is also
something called transform pre-coding which is nothing but again the DFT-spread-
OFDM as well as there is also. So, when we talk about layer mapping, this primarily
talks about the MIMO communications. And pre-coding would talk about the pre-coding
weight matrixes right.

So, we will see some of them, although not everything that is present over there, because
our fundamental aim is to look at the way the technology works, and not into the way it
is exactly implemented on a particular standard, because there could be other standards
and other applications, where these technologies would work in a similar manner ok.

(Refer Slide Time: 26:02)

212 the next document, it talks about the channel coding. The moment you do channel
coding, there has to be rate matching in order to fit into the frame structure, and then
transport channel descriptions, control information and so on and so forth. This includes
description about multiplexing as well.

411
213 this talks about the physical layer procedures for control, and the scope is to
establish the characteristics of the physical layer procedures such as the synchronization,
uplink power control, random access procedure, for reporting control information, and so
on and so forth. So, we will not go into this document, but please find your time to get
into details, if you are really interested in the exact implementation.

(Refer Slide Time: 26:45)

Then there is 214, which is with respect to the part of data. See the previous one is with
respect to procedures for control, and physical layer control. Whereas, the next one is
with respect to data right, and there also it is the power control, and physical downlink
shared channel related procedures, so that is PDSCH and that one is PDCCH, PUCCH.
So, here it is PUSCH, which we have described earlier ok.

And 38 dot 215 is related to the physical measurements. And the scope is to establish the
characteristics of the physical layer measurements, and to specify control of UG and NG
is the next generation radio access network measurements, and capabilities for the new
radio. So, when you go into these documents, you will find all such detailed description
provided ok.

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(Refer Slide Time: 27:39)

We will primarily talk about the 38 dot 211 document, we have carried over the same
notation that is present in the document, so that when you refer to it there is no difference
in the way we are describing them. So, k, l, p, mu these are some of the parameters
which are important, because based on this everything will be defined.

So, k indicates in our notation, in our understanding a sub-carrier index. And l indicates
the OFDM OFDM symbol index. So, what you can see over here. The frequency-domain
index k, and time-domain index l for antenna port p. So, it is the p-th antenna port
through which signals are going out, and sub-carrier spacing configuration mu. So, we
will see this details in due time.

Then we have a sub k, l to the power p mu indicating the value of resource element k, l
for antenna port p and all kinds of things. So, k, l is some index in frequency axis which
is k. So, this is time axis, this is frequency axis. Some index in time axis. So, this is the
resource element for a particular antenna configuration. So, p is an antenna
configuration, so that means antenna port. So, if it is a particular layer, it would
corresponding to correspond to that particular antenna or layer. And mu describes the

413
physical size of this resource element. So, one has to understand this is the smallest
entity in the system right.

In other words, when we will describe this is one sub-carrier. So, we are drawing this
part of the sync which is important for us, so that is one sub carrier. And it is one OFDM
symbol, we are not concerned with the CP, because CP is rejected. So, one subcarrier for
one OFDM symbol forms the resource element, this is the fundamental entity ok.

And each of these are going to carry a complex symbol a k, l p mu. So, k is
corresponding to this k, l is corresponding to this, a is the variable which carries the
value. So, in other words this is corresponding to ours X s of k that is the constellation
point ok. So, this we are writing constellation point. But, if you are doing DFT-spread-
OFDM, in that case this will be some complex value which is a combination of several
constellation points, so which is some combination of constellation points.

So, in in otherwise if you are not doing a DFT-spread, you can think of using an identity
matrix inspread instead of the DFT-spreading matrix. Otherwise, if you are doing a DFT
spread, then you can have a DFT spread. So, rather what we have is a combination of
constellation points, the combination will vary according to the operation. So, if it is pure
OFDM, this will be a constellation point. If it is DFT-spread we take several such
constellation points on different carriers, and then we sum them up and that is this value.
So, this has to be understood and connected to the notation that we have used before.
Delta f sub-carrier spacing, we have also described this in all our descriptions. So, this is
also an important parameter right.

And here we have some more descriptions about T s and T c which we will see later on.
So, what is what is critical here is what we see is mu is also described, so we have been
talking about mu so long. So, let us see what is mu, what does mu mean. So, delta f is
equal to 2 to the power of mu multiplied by 15 kilohertz right, so that means, mu can
take different values. In case of 4G, mu was effectively 0. In case of 5G and others, mu
can take values 0, 1, 2, 3, 4 right. So, what we see one of the major changes that have
happened from 4G to 5G is that this delta f can take different values, which had
otherwise been remaining constant for the previous generation system.

So, we conclude this lecture over here, where we have summarized the or we have
projected a background to the description of physical layer for 5G. We have discussed

414
the technical background earlier. Today, we have talked about the documents which are
relevant, the documents one which should read and, also the parameters or the variables
which are useful in describing the 5th generation frame or the particular physical layer
which we are going to see in the next lecture.

Thank you.

415
 Evolution of Air Interface towards 5G
Prof. Suvra Sekhar Das
G. S. Sanyal School of Telecommunications
Indian Institute of Technology Kharagpur

Lecture – 23
Waveform for 4G & 5G (OFDM) Numerology Part-2

Identified the differences between 4G and 5G which are the most important differences
in terms of the air interface, also we have been able to identify what are the common
things that are present between the fourth generation and the fifth generation. And,
primarily we have said that the air interface consists of OFDM with access; that means,
the multiple access is based on OFDM and there is also support for DFT spread OFDM
in the uplink direction as has been there in the fourth generation system. Along with it
OFDM is also available for uplink direction transmission.

And, in the earlier lectures we have described that why OFDM could also be suitable and
the primary reason we have said is that when a user sends data in the uplink direction the
user need not send it over the entire stretch of bandwidth and then if it is sends over a
smaller set of the bandwidth only 12 subcarriers let us say using one resource block, then
the peak to average power ratio is not significantly high.

In that case doing a DFT operation to spread and reduce the PAPR is obviously, going to
give some benefit, but it is not necessarily that the benefit will be huge and given the
extra processing that one has to do because if one does an extra DFT processing there is
also some amount of power and complexity that adds up to the system.

So, there is an overall balance which is necessary depending upon the application and
scenario of deployment. So, there are two possible options which are available in the
fifth generation, but it is highly compatible with the earlier generation system.

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(Refer Slide Time: 01:51)

So, we have discussed this particular slide in a previous lecture, where we have
described most of the variables that are necessary and we have also seen what is a. So, in
case of OFDM it is the complex constellation point if it is the DFT spread, it is a
combination of complex constellation points.

417
(Refer Slide Time: 02:13)

So, then there are other variables which are also available. So, we are not using this
much except a few of them from here. It is the N mu CP, l which is the cyclic prefix
length and as you can see it is also configured with respect to mu; that means, mu is
described in the previous slide as one which specifies the sub-carrier spacing. We had
seen earlier that if T u is the T useful duration of the OFDM symbol then this is related to
delta f as 1 upon T u, and we have also seen that T GI is extension of the T u.

So, generally this is some alpha fraction of T u, some fraction of T u. So, here what is
done is T GI is coupled with T u through the same parameter mu. So, N CP is the cyclic
prefix length as you can see sub CP l indicating the length of it and mu indicating the
subcarrier spacing indication which is parameterised by mu, and this is the resource grid
side size we will see it at the later stage.

418
(Refer Slide Time: 03:37)

And, out of these definitions whatever we have we will again see them with example
specific things that will be clearer. So, as we can see in all cases the number of slots per
sub frame for a sub-carrier configuration mu. In the earlier lecture we have described that
the number of slots is a function of is the function of the subcarrier spacing which is
different compared to the earlier generation where things were pretty much fixed, ok. So,
we will see all of these descriptions in the next few slide, alright.

(Refer Slide Time: 04:09)

419
So, when we go into the frame structure, the way things are defined is in a very
systematic manner. So, fields in the time domain is expressed in units of T c. So, T c is
the variable which defines the unit in terms of which things are defined. So, T c is 1 upon
delta f max multiplied by N f. So, delta f as you can see is the sub-carrier spacing or the
sub-carrier bandwidth and the maximum value of it is taken in the denominators, so
when you go 1 by delta f you get the chip duration and it is. So, basically if you look at 1
by delta f max it is basically the shortest T u, our T u which we have been describing as
far as possible that is the OFDM symbol duration and this is further divided by N f which
is the number of sub-carriers.

So, if you look at this entire denominator term denominator term is delta f max that is
the maximum sub-carrier bandwidth multiplied by N f. So, we will see what is N f. So, N
f is number of sub-carriers. So, together this gives a bandwidth indication and 1 by
bandwidth is the chip duration or the clock duration which is useful. So, here delta f max
is specified as 480 multiplied by 10 to the power of 3 hertz, so, 480 kilohertz. So, that

420
means, what we will see is that if we relate it in terms of mu delta f is 2 to the power of
mu into 15 into 10 to the power of 3 hertz.

So, this factor you will find that this goes into delta f mu by a factor of nearly 32. So, 15
it will go to 32 times; that means, mu will take a value of 5 in this particular case, ok and
N f is 4096; that means, 4096 sub-carriers are possible. So, you can multiply 480 kilo
hertz multiplied by 4096 to see the total span of sampling frequency as is available. Out
of this entire bandwidth the entire bandwidth is not used, we know that from fourth
generation system, there are certain guarding guard band at the edges where there is no
transmission so as to avoid inter carrier interference.

So, here we have done a calculation of these things where we find out that the T c chip
duration is turning out to be around 50 nanoseconds it is 50.86 or it is 50 nanoseconds.
So, this is equivalent to you can think of around 20 megahertz in time I mean in the
bandwidth domain. The T s which is again another parameter is with respect to some
reference value and here what we find is the reference value is 15 kilohertz and this
reference value is the LTE value and 15 kilohertz with 40, 2048 sub-carriers. So, there
you will find that T s turns out to 325 microseconds compared to this.

So, these numbers are from LTE. So, LTE system sub-carrier spacing is 15 kilo hertz and
in the 20 megahertz it uses 2048 point FFT. So, with respect to the LTE system the new
fifth generation system is scaled in terms of time and bandwidth. So, this is a scaling
factor or kappa which is used to describe such parameters, ok.

So, now comes the one of the most important and most interesting terminologies which
have been discussed for quite some time and that is called numerologies, ok. So,
numerology is nothing, but the description of mu; mu is we have said describes the sub-
carrier spacing. So, what we see is that multiple OFDM numerologies are supported that
is one of this statement and table below. So, basically this particular table describes the
numerology, ok. So, this particular table as you can see this is table one which describes
the numerology. It effectively tells us that mu equals to 0, you can see from this
expression it turns out to be 15 kilohertz and corresponding to this we will also find a
cyclic prefix length which we will describe later on.

So, as you keep increasing the value of mu simply by using this factor like 2 to the power
of 1 is 2 multiplied by 15 is 30 kilohertz, then when mu is 2 this factor is 4 this factor is

421
60 kilohertz. So, what we find is that sub-carrier spacing is increasing with increasing
value of mu. This is in contrast to the fourth generation system and since it is also
OFDM only thing that changes is this sub-carrier spacing. So, this sub-carrier spacing
change is controlled by this parameter mu. So, this configuration of OFDM for different
sub-carrier spacing is termed as numerology in OFDM. And, we have described in the
previous slide that the cyclic prefix duration is also coupled with mu which we will see
shortly.

So, through the use of mu one can describe that T cp or T gi as per our description that is
the CP duration followed by T u which is equal to 1 upon delta f, right. So, through one
parameter that is mu one can describe the structure of a OFDM symbol and we had said
in our notation earlier it was T s here T s is a different meaning. So, this is the total
symbol duration as per our description of the OFDM symbol. So, we can say that T s o f
indicating OFDM symbol duration. So, this entire value can change based on the choice
of parameter.

Now, this choice of parameter mu and cyclic prefix are obtained from higher layer
parameters. So, basically something which is above the physical layer can provide you
choice of these parameters. So, if these two choices are given, then you can describe an
entire OFDM symbol. And, earlier we have described in several ways that how the
choice of parameters are very important for successful deployment of OFDM system and
what we see over here is that this particular aspect is exploited in the fifth generation,
things are not kept constant.

So, there is a lot of potential to exploit the capabilities of OFDM, use it in a flexible
manner as per the situation which is dependent on the propagation environment as well
as the need or the environment. We have seen several scenarios and descriptions which
have ended up in certain sort of requirements and we will see how these different
requirements can be met with this flexibility provided by OFDM.

422
(Refer Slide Time: 11:47)

So, there is some definition of resource block we will see that we have described shortly
earlier that the number of sub-carriers in a resource block is 12. So, when we have
different sub-carriers stacked against each other a group of 12 sub-carriers would be
called a resource block, ok. The next consecutive will be another set of 12 sub-carriers.

So, if there are if there are 1 0, if there are let us say 2048 subcarriers in all, of which a
certain fraction is used and we divide by 12 we will find the number of resource block
that is available. Now, if we divide 2048 by 12, then we get the certain number, but not
all those numbers are useful because out of 2048 in the entire spectrum we have said that
certain numbers in the guard band are not used. So, only a smaller subset is used. So, that
number has to be replaced in 2048 and we get the appropriate value of the resource block
and that will depend upon particular spectrum and application scenarios, right.

Further, one more thing is that as we have said that in a particular bandwidth; suppose,
there is a certain bandwidth one can have narrow sub-carriers, we will see this; one can
have wider sub-carriers, we will see this. So, accordingly depending upon the value of
mu the number of resource block is going to change, right.

423
There is also definition of bandwidth part which says that bandwidth part is the subset of
contiguous resource block for the given numerology; numerology as we have said is the
one which described through mu in a bandwidth part on a given carrier. A UE that is the
user equipment can be configured with up to four bandwidth parts in downlink with the
single downlink or uplink bandwidth part been active at a given time. So, at any one
given time although you can divide the entire bandwidth into four parts from the UE
definition part perspective, but only one of them can be utilised at any one instant of
time. So, this makes things a little bit easier from the UE implementation, ok.

(Refer Slide Time: 13:45)

So, ok from here we are at the middle of everything one can think of. So, this particular
set of expressions describes the OFDM symbol that is being generated because we have
said the 5G uses OFDM. So, what we find over here the continuous time signal s, we
have used such a s symbol earlier when are discussing the symbol structure, l in time
domain, p is the antenna port, mu is the numerology, t is simply showing the time unit.

424
So, we do not have k over here, because it is OFDM symbol. So, OFDM symbol as we
had said earlier we can connect over here x of t is equal to in our notation what we have
described earlier X s of k sum over k; k is the subcarrier e to the power of j 2 pi k t by e
to the power of j k t pi by N, one can think of this way or one can think of one e to the
power of j 2 pi k n. So, when we are doing in the terms of discrete we are going to get it
as X s.

So, our s would correspond to l over here k remains the k e to the power of j 2 pi k n
upon N and of course, there is a gate which we should always have n minus s N s, right.
This is something which always had. So, now, if we compare this we said earlier in one
of the earlier descriptions that this a corresponds to the constellation point for the
OFDM, otherwise it will correspond to the combination of these symbols. See here we
have the same thing again that X s if we compare these two equations now x t what we
had written earlier corresponds to s l of t, right.

There is certain antenna port parameterised by mu we will see that and here this
particular symbol corresponds to the complex constellation, e to the power of course, we
have e to the power of j 2 pi. So, we have j 2 pi and then we have this k which is also k
over here. So, this k is also have been a k summation over there. Now, what we find is
delta f being specified ok which is 1 upon N in our case or you can have k multiplied by
delta f in the other way. So, t corresponds to t the only difference we have is that delta f

425
is specified as 2 to the power of mu multiplied by 15 into 10 to the power of 3 hertz,
right. This is the only difference that is available in the system. So, so here you can have
delta f over here. So, which would indicate the spacing.

So, here our description was for any given delta f ok, but here what we find is that this
particular delta f can take different values which is specified by the parameter mu. Rest
of the parameters are constant parameters. These are all the constant parameters. This is
the shift which we had indicated earlier in our expression and we had said that it is for
you to figure out how does these equations fit in. So, what we see over here is there is a
N mu CP description and T c is also given in time and there is also an offset of t mu that
is also described. So, rest of the parameters are constant. So, what we essentially see
from here is that it is the same OFDM symbol, but with a delta f description which is 2 to
the power of mu 15 kilohertz.

The N mu CP description is given over here which is which can be used in order to
calculate the value of delta f and in this description it is said that the delta f is given in
clause 4 2 of the document 38 dot 211. So, if you go to clause 4.2 in the document, delta
f is mentioned and delta f is described exactly over here in this particular class. So, this is
the primary foundation on which the fifth generation system stands. So, it is very
important, let we take a look at it.

(Refer Slide Time: 18:35)

426
So, in the next particular slide we have actually given the exact description which you
have provided in the previous slide that is we have identified the exponential term. We
have identified it very very clearly that there is a k which gets multiplied with delta f and
t in order to complete the OFDM signal generation and delta f in section 4.2 we know
that it is given as this expression.

So, if we combine all of them we get the OFDM signal generation in the fifth generation
system. So, one could also replace this entire set of values with a another variable delta f
mu delta f sub mu to be defined in this manner and then one gets s l mu which is the
parameter over here being directly influenced in the equation.

So, whatever we have described primarily tells that this subcarrier spacing or SCS can be
easily read of as this particular value, ok; that means, it tells one can choose different
values of sub-carrier spacing depending upon the parameter mu and which is a multiple
of 15 kilohertz as we have been saying, ok. So, this is the primary you can say the most
important information or meaningful information in terms of the air interface for the fifth
generation, ok.

427
(Refer Slide Time: 20:07)

So, when we look into the CP length we have presented a calculation of CP length over
here. So, from which what we find is that for different values of mu we will get different
CP lengths, ok and what we see is that we have two different cases; that means, when l is
not equal to 0, ok. So, what do we mean by l not equal to 0, let us see that. So, when we
look into the description we find that CP is described in various manner; one is the
extended cyclic prefix length which is slightly longer as you can clearly see there is a
multiplicative factor 512 compared to 144, right. So, this is a larger multiplicative factor
this clearly means that CP length is longer compared to other CP cases.

So, if the channel duration or the channel impulse response is large enough. So, then one
can use the extended cyclic prefix otherwise one would use the normal cyclic prefix. But,
l which is the time index so, for l equals to 0 or l as the last symbol one will find that
there is a particular length of CP which is again larger than the case when it is not the

428
boundary OFDM symbols. If it is a boundary OFDM symbols then the length is larger
whereas, if it is not the boundary OFDM symbols it is a different value.

What it means is that there is a consecutive set of OFDM symbols that form a slot which
we will see short shortly. The first OFDM symbol and the OFDM symbol index for
which it is equal to 7 into 2 the power of mu. The value of CP length is given by this
number in the middle for all other values, it is given by this a typical OFDM symbol is
given by this. So, we have actually listed down the values of CP for the normal case in in
this and for the case where it is l is equal to 0 or 7 into 2 to the power of mu over here.

So, what we find is that in all cases the number of samples in the CP has remained
constant. However, what we find is that in the other cases the length of CP is different.
But, what we also see is that when we calculate CP there is a T c which comes into play,
right.

So, this is just a number of samples which are being defined in the CP length, but one
should also get a T c which is coming into play when one describes the CP length. So, as
mu changes the T c would change the sub-carrier spacing would change effectively one
will find that this product will give a different number and the values are going to be
different which we will see shortly.

So, what we find is that the CP length accordingly takes different values as the mu value
changes. So, what we see over here is as mu increases, sub-carrier spacing increases. So,
if sub-carrier spacing increases the T OFDM symbol duration would decrease and if T
OFDM symbol would decrease since CP length is a fraction of the T OFDM symbol and
hence that would also decrease.

Now, very simple although it appears to be very very silly, but still what we see is if we
would have kept the CP length of this value whereas, OFDM symbol duration has
become this value and have combined this, we would have find that this spectral
efficiency would be less than 50 percent because this is the useful part which is 4.16
divided by 4.69, sorry it is it is plus 4.16. So, what we find is that this fraction is less than
50 percent and spectral efficiency is less than 50 percent.

429
(Refer Slide Time: 24:23)

So, what is done is instead combination of values of T CP and T OFDM symbol is tied;
that means, they are coupled you can say that they are fixed you cannot change them,
right. So, once you choose the value of mu your value of sub-carrier spacing and your
CP gets defined; in other words your entire OFDM symbol duration gets defined, right.
So, by choosing a single parameter you can change the entire OFDM structure and we
have said earlier how do these parameters effect each other, ok.

(Refer Slide Time: 24:53)

430
So, in terms of numerology what we find is that effectively it means that there is a
variable sub-carrier spacing or variable sub-carrier bandwidth either of the terms which
would otherwise mean that it is a variation in OFDM symbol duration and along with it
there is a variation of the guard interval. Now, let me tell you that, it is not necessary to
have these things coupled together, it is not necessary to have this. This can be chosen
independently.

So, although we have said that a combination of this CP length and this OFDM symbol is
kind of meaningless, but technically speaking one may choose to do so depending upon
the situation, but whether it gives appropriate benefit in terms of actual throughput is
something one has to see.

So, accordingly one may find that this combination may not end up being fruitful in a
particular situation in that case it may be wiser to have a wider a longer OFDM symbol
than the one that is given over here. However, it is not true that this OFDM symbol
should be always coupled with the fraction of T CP as given by this number one may
also decide to do with another number where efficiency is lower, but it serves the
purpose. But, in this particular standard they have fixed up this combination of CP along
with the OFDM symbol duration.

So, at this point we stop this particular lecture because in the next lecture we start to look
at the exact frame structure based on which we have the entire air interface for 5G. So,
what we have effectively done is describe the OFDM signal generation equations. So, if
one is interested in generating the signals one should follow them and now, using all the
descriptions that we have given so far we will fit them into the frame structure and see
how does it fit together.

Once we are done with the frame structure then we will be interested in looking at the
philosophy or design issues, why this have been chosen, what are the advantages and
how what kind of gains one can get, what are the possible architectures, what is the
genesis, when where from things have started, in the subsequent lecture.

Thank you.

431
 Evolution of Air Interface towards 5G
Prof. Suvra Sekhar Das
Department of Electrical Engineering
Indian Institute of Technology, Kharagpur

Lecture – 24
Frame Structure of 5G air Interface

Welcome, to the lectures on Evolution of Air Interface towards 5G. So, till now we have
discussed all the previous waveforms, the base line structure, we have also discussed the
waveform which is used for the fourth generation as well as the fifth generation which is
the primary. We have also discussed the variation that is presented in the fifth generation
waveform with respect to the fourth generation. We have said primarily they are the
same waveform, but it is parameterized and it is called OFDM numerology.

So, after understanding whatever is the required for the basic elemental structure today
we will look into the frame structure frame format that is present in 5G and as we said
will also look at the genesis and also how these things are evolved and what is the reason
behind designing such a system?

(Refer Slide Time: 01:06)

432
So, what we have discussed in the previous lecture is the expression for the OFDM
symbol generation and where we have identified that the time domain signal, the OFDM
signal is generated like a standard OFDM generation where we have the symbol
constellation in case of OFDM otherwise, it will be the combination of the DFT spread
signal. It is summed over k that is the sub-carrier index and e to the power of k comes in
like a typical IDFT expression and frequency domain sub-carrier spacing and time. So,
these are the three important factors.

We have also identified that this delta f which is present there is essentially this factor
delta f is equal to 2 to the power of mu multiplied by 15 kilohertz. So, it is a multiple of
the basic structure that is used in the fourth generation system and what we find it is a
variable OFDM system and this variability is controlled through the choice of values of
this parameter mu which we have also described in the previous lecture. And hence it is
termed numerology that is what we have given over here it is called OFDM numerology
because this number changes the values of the sub-carrier spacing as well as that of the
cyclic prefix.

433
(Refer Slide Time: 00:37)

So, that is the only difference. So, we have also discussed the various lengths of cyclic
prefix that come along with the different parameters of mu and hence the combination of
delta f and the CP length together defines the numerology and this combination comes
from higher layer information. So, higher layer information will convey to the lower
layer what is the values to be used and it goes on accordingly.

434
(Refer Slide Time: 03:02)

So, what we have summarized is that numerology essentially talks about variable sub-
carrier spacing or variable sub-carrier bandwidth along with variable guard interval or
cyclic prefix.

So, cyclic prefix and sub-carrier spacing together they define numerology that is what we
have over there, ok, alright.

(Refer Slide Time: 03:30)

So, what we will discuss is how does it look like. So, in a standard OFDM system like in
LTE we have the sub-carrier spacing which is constant which is uniform and this is the

435
frequency domain view. So, this is this is the f-axis or sub-carrier index you can call it as
index also if we want to put it as k values if these are different values of k and these are
the different amplitudes.

So, one may remember that these amplitudes will change depending upon the modulation
that is used. So, in this picture all the values have remained the same indicating they are
carrying the same constellation or even they are carrying the same amplitude of the
constellation. So, if it is QPSK this picture matches very well. Further one should also
remember that even in QPSK in the same amplitude one could be of reverse phase that is
also possible.

(Refer Slide Time: 04:32)

And, if one uses a 16-QAM like constellations so, in that case different ones will be a
different levels. So, one could be like this and one could be like this, but the zero
crossing would essentially remain at the same point. So, that fluctuation will remain ok.

So, now in case of 5G, instead of calling it standard OFDM, they are simply changing
the name to numerology and it is a new terminology. So, if we just look at this particular
figure there is not much distinction.

436
(Refer Slide Time: 05:09)

But, what happens is that because of the concept of numerology one can change the sub-
carrier spacing to a different value as we have been discussing. So, while this is possible
in fifth generation another combination is also possible and they could simultaneously
exist at the same time. So, with this picture it gives a clearer picture of what exactly
happens with the set of equations that we have showed in the previous few lectures.

So, the description of a cyclic prefix and it is calculation we have already discussed and
we have presented it here just for a review.

437
(Refer Slide Time: 05:45)

So, when we look at the frame structure this is the next important thing that we are
suppose to discuss. So, the frame duration is defined as 10 millisecond, we have said this
earlier the frame duration is a 10 millisecond duration. In an earlier slide we are
summarized everything in one slide and now we are getting into details of it. And if you
do the calculations of putting in a delta f max and N f with the values we have given in
previous slide and you multiplied by T c which we have defined earlier you get this
particular value.

The next important thing to consider is that each frame consists of 10 sub-frames; each
of 10 of 1 millisecond duration. So, here what you see the changes instead of divided by
100 it is getting divided by 1000 naturally it is one tenth of the value and 10 such values
together combined to produce 1 millisecond.

Number of consecutive OFDM symbols per frame is defined by this parameter, at some
point we said that yes we will we are going to use these parameters we said in

438
appropriate context will be defining them. So, now, we have it. So, number of symbols
per sub-frame. So, what we have over here is per sub-frame, for a configuration mu is
equal to number of symbols per slot; so, here we have something called as slot which we
will define and multiplied by number of slots per sub-frame for a combination or a
numerology mu.

So, what is clearly means is that the number of symbols per sub-frame is a factor which
depends upon mu, as well as the number of slots per sub-frame depends upon mu. We
are just trying to look at the expression and trying to understand what is derivable from
the equations whereas, what we see over here this particular expression it tells us that
number of symbols per slot is not parameterized by mu, right. So, that means, that
number of symbols per slot is a constant value which we will see ok, but number of slots
per sub-frame changes and thereby it will produce different results. So, what we see here
is that we are given a pictorial representation of the description whatever we have given
on top.

So, each frame consists of 10 such sub-frames; 10 such sub-frames each of 1 millisecond
duration and this is called the sub-frame as we have defined and each sub-frame if we
look deeper into a sub-frame we will find consists of several OFDM symbols up to N
symbol per sub frame parameterized by mu right. So, this pictorially explains the
particular picture that one can generate and this obviously, helps in a easier
understanding of how things are set up.

439
(Refer Slide Time: 09:06)

So, now what we see over here is that for a given sub-carrier configuration mu, right, n s
mu can take such values; that means, it is indicating number of slots per sub-frame, right
within a sub-frame and n s f mu is basically number of slots per frame which is simply
multiplied by 10 because there are 10 sub-frames in a frame. So, that is what we can
remember that is 10 sub-frames in a frame is constant and number of symbols in a slot is
also constant. So, these two things are constant, that is what one can remembered.

Now, these slots as we will see can be defined as downlink slot they can be defined as
uplink slot and they can also be flexible slots. So, accordingly one can choose to
distribute between downlink and uplink and detailed description one will find in the
document 38 dot 213. So, we have described this different documents earlier and if one
has to go into details of them one should go into those documents and find out.

So, let us look at the picture once again. So, we have the different OFDM symbols
coming up and we have already seen that there are N symbols per sub-frame ok and we
have also identified that number of symbols per slot is basically constant which is 14
independent of the different numerology that one is concerned with. So, this number is
similar to the one in the fourth generation system. In the fourth generation system you
could had 12 or 14 depending upon the length of cyclic prefix which would be dependent
upon the operation situation.

440
Number of slots per frame would change according to mu, right. Now, why this would
happen? We would obviously, get to see that and number of sorry number of slots per
sub-frame would also change for the same reason that is what we are going to discuss,
but number of slots per frame is a 10 times the number of slots per sub-frame for all
cases that you are seeing, simply by virtue of this number 10 that is present in all the
cases for all values of mu right.

So, that means, we also have another situation where one can use and extended cyclic
prefix which is nothing, but a larger value of the cyclic prefix there the number should be
different. So, there you have number of symbols for slot is 12 and as we said in the
earlier generation that facility was also available. So, which is matching and there is no
reason to be surprised with this because whatever technology 3GPP comes up with they
have a basic agenda that there should be backward compatibility with the previous
technologies. So, this essentially helps to maintain compatibility with the previous
generation.

So, what we see now is we are getting a deeper picture into the frame structure or sub-
frame structure and what we have is that there are 14 symbols per slot that comes into
play and the number or the variable is depicted over here so that, a more or less
completes the picture of a frame with its sub-frame and symbols per slot. Not only that
so, now, what we have is that since there are 14 symbols per slot ok; however, this
duration has remained constant over 1 millisecond. Obviously, they would be more
number of slots or they will be multiple slots per sub-frame. So, that is what is indicated
over here multiple slots per sub frame. So, that is what is indicated in this particular chat
as well as reflected in the image next to it.

So, we go ahead further. So, this is indicating the slots per sub-frame and these numbers
are depicted over here which matches with the number as you are seeing over here right
this number matches with this number over here. So, they exactly fit into the jigsaw and
we are able to setup the expressions.

441
(Refer Slide Time: 13:56)

But, now again we will take a look at the same picture, but we will rearrange the view
compared to what we have seen earlier, so that we get a proper hierarchy of the symbols
and the frames from the bigger to the smaller number.

So, we have a frame of 10 milliseconds, in the frame of 10 milliseconds we have 10 such

1 millisecond sub-frames. In each such 1 millisecond sub-frame we have multiple slots
that is the next level of hierarchy. In each slot we have 14 such symbols which present
one particular slot and that remains constant and hence we will have multiple such
symbols in one such sub-frame. And that overall represents the entire structure that we
need to look at when we consider the frame structure.

And again for the sake of reference we have pointed out the different parameter values
that one needs to use and one should be careful if extended cyclic prefix is used if you
are using a longer cyclic prefix and earlier we have described how they extended cyclic
prefix calculation happens. So, if the cyclic prefix length increases then the number of
symbols that can fit into this would obviously, going to be different. Accordingly you get
different number of symbols per slot and the numbers are so calculated that it matches
with the earlier generation right.

So, now, we take a look at the symbol that we are talking about. Each symbol carries a
cyclic prefix that is what we have indicated over here in each of them we have indicated
a cyclic prefix and that cyclic prefix depends upon whether you are going to have a

442
normal cyclic prefix or an extended cyclic prefix most of the calculations that we have
shown over here are with respect to the normal cyclic prefix. With the extended cyclic
prefix one can change the calculations accordingly.

So, when we take a deeper look into each of the OFDM symbols; so that means, we are
looking into final and final granularity. We have started with 10 millisecond, then we
have moved to 1 millisecond, then we have moved to slots, from slots we have moved to
symbols. Now, we are going inside the symbol and we trying to see how does it match.

So, each symbol consist of a cyclic prefix as well as there is this OFDM symbol duration
and this is the basic structure and when we move beyond that what we find is that in one
of the numerologies the number of sub-frame is equal to 1, that is what we have said and
that matches with the case when mu is equal to 0 and this is what is the baseline structure
matches with whatever is present in the earlier generation system.

So, in that case number of symbols per sub-frame would be equal to 14 because you have
only one slot in the sub-frame. So, if you see the changeover of the picture that we have
drawn from the previous, this is the generic picture. Now, we changeover there is only
one slot, but since number of symbols per slot is constant to 14, so, the entire OFDM
symbols stretch to 14.

So, for obvious reasons the duration of this OFDM symbol as to be longer and what we
see is that the duration of OFDM symbol is 66.66 or 6666 or 67 micro seconds and that
corresponds to the 15 kilohertz sub-carrier bandwidth. What we have given over here is
the cyclic prefix length 4.7 micro seconds for a normal CP, right and so that it fix into
the picture very well and this is the frame structure for mu is equal to 0.

So, when we move further what we find is that on the frequency axis; so, this is the
frequency axis because remember we are talking about time axis horizontally. So, this is
the time axis, this is the time or OFDM symbol index l, time index one can say OFDM
symbol index and this axis is the f axis or one can also think as sub-carrier index k going
in this direction. So, each of the these a different sub-carriers whose detailed picture or
zoomed picture we had seen earlier right.

So, that means, in one sub-frame duration there would be several such OFDM symbols,
right because here we are saying in one numerology there are 14 OFDM symbols there is

443
only one slot present. So, which will be several such OFDM symbols and each OFDM
symbol is consisting of several sub-carriers depending upon the size of the bandwidth
that is available, this is very very important to note.

So, this entire resource grid we called it the resource grid; so, this entire resource grid is
available. So, this also called probably not visible so let me write it here instead of. So,
the entire resource grid is available for allocation or doing modulation and coding
scheme allocation towards having higher and higher throughput. And group of 12 sub-
carriers this is also important to note group of 12 sub-carriers forms a resource block this
is important. So, this is the minimum unit that is addressable. Each of this elements are
called resource elements which we have defined earlier alright.

So, each of these are resource element each resource element is one sub-carrier of one
OFDM symbol for an antenna port. So, if there are multiple layer transmission will be
having them on stacked on top of each other. So, if there is a single antenna system then
you have only one layer and then it is basically the smallest unit which can carry
information. Now, for all reasons we have also discussed this thing that you cannot
address every single resource element. Then the overhead will be so high there is you
will actually the system is going to breakdown it is to going to actually some benefit in
terms of transmission of data. So, they are grouped together, 12 sub-carriers are grouped
together.

And as you can see that the slots keep on varying. So, the total number of OFDM
symbols that are part of or resource element that are part of the resource block keep on
varying because of the numerology right. As we move beyond that to the second
numerology that is mu goes from 0 to 1, we will find that there are 2 slots per OFDM
symbol. So, that is what we get over here from 1 we get 2. So, there was 1 and from this
1 this changes to 2, right and we get 2 such slots and hence in each of the slots we are
going to get 14 OFDM symbols.

So, that means, 28 symbols in all in case of normal cyclic prefix, but if there is extended
cyclic prefix the value would be different and what we have going to find is that since
there are more OFDM symbols in the same duration right; that means, it is now 1
millisecond, but the total number of OFDM symbols has become; total number of
OFDM symbols has now become 28 from 14, right; we had 14 that has become 28. So,

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the symbol duration of each OFDM symbol must decrease right. So, earlier it was 66 it
will become 33 because it has to be half of that and cyclic prefix length also reduces
because that is a combination we have said.

So, now because of which because you have reduce the OFDM symbol duration if you
look at the transition that happens in this the frequency domain effect because of time
domain we know this thing when we shrink the pulse the bandwidth of the system
increases. So, that is what is depicted over here, for ease of understanding the sub-carrier
bandwidth increases. The resource elements which were longer if you look at this
resource element which was longer and narrower in bandwidth will become shorter in
time and wider in bandwidth.

(Refer Slide Time: 23:00)

The resource grid definition remains the same. So, this again and 12 sub-carriers forming
a resource block that remains the same. Only thing that changes in number of elements in
this in a slot remains the same there is not variation, but number of such resource blocks
available changes because, if the total system bandwidth remains the same and one
chooses two different numerologies then the number of sub-carriers supported would
obviously, to be different.

So, number of resource blocks RBs would change as per mu and bandwidth allocation
and these are said by higher layer parameters and they can accordingly be chosen based
on the appropriate operation. So, here again this is the resource element. So, the resource

445
element definition remains the same resource block definition remains the same resource
grid is the total number of resource elements that aware that are available for scheduling
and hence the entire structure keeps on modifying based on the condition.

So, now what we have is that there are more number of symbols in the time domain
which we have already seen and depicted graphically in this picture to give a proper view
of things. So, then we move to the next numerology we find that there are 4 such slots;
that is how the picture is going to happened and hence since there are 4 such slots the
symbol duration OFDM symbol duration which was stretched still here will now reduce
much further right; if the OFDM symbol duration reduces much further then as depicted
in the picture below it the sub-carrier bandwidth increases further right. Resource
elements which were longer will become shorter in duration and they will wider in
bandwidth and they will be more number of resource elements in the time duration to be
allocated.

(Refer Slide Time: 25:23)

So, again depending upon how one wants the use the particular setup one has to one will
set parameters accordingly the structure changes. The definition of resource block
remains the same, 12 sub-carriers. But, now one can have multiple such slots within that
time frame to allocate. So, depending upon the different types of services that are being
addressed by 5G, one can do this different type of service multiplexing or service
multiple access through such a flexible mechanism.

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So, this provides a very beautiful flexible, physical layer which was much needed for a
long time and only now time has come that people have agreed to this common frame
work that this is being allowed. Now, we will discuss in the next lecture that why this
flexible structure is necessary and the how this all started and probably took longer time
to come on to this consensus, but one can easily understand that if one as this flexibility
one can do a lot of things in terms of providing support to various kind of services not
only that there are various different other reasons also to have this basic thing in to the
picture.

So, if one goes to the next higher level that is the third one the fourth one would get 8
slots as we transition from the 4 to 8 we find that the number of OFDM symbols
increase, that is point number – 1. The symbol duration shrinks further. So, to help the
picture being readable we did not reduce the picture over here, but we are changed the
notation or the values of it and one can clearly see that the sub-carrier bandwidth
increases even further, symbol duration becomes shorter, but the sub-carriers become
wider and hence one can support more number of such symbols in the time duration. So,
there are various advantages and disadvantages of each combination one has to
appropriately choose.

Now, one thing I would like to point out at this instant of time is that if we trace back the
sequence of events that we are we have been looking at and so, what we are trying to see
here is the transition and is very important to look at one very important issue, we had
said earlier that the sub-carrier bandwidths indicated over here should be narrow enough,
so that they experience nearly flat fading, right if this is the channel gain, right.

447
(Refer Slide Time: 27:53)

And, then when we transition from one numerology to another numerology, then the sub-
carrier bandwidth increases.

(Refer Slide Time: 28:12)

So, as we transition from one numerology to another numerology and we keep focusing
on this particular section which is about the sub-carrier bandwidth what will find is that
the bandwidth becoming larger and larger.

448
(Refer Slide Time: 28:14)

So, if the bandwidth becomes larger and larger this fluctuation in the channels strength
would appear in some cases such that this sub-carriers are no longer experience in flat
fading. So, this is something one as to understand and carefully choose the numerology
of choice. Further, we will also see later that the cyclic prefix length becoming smaller
and smaller as one changes from one numerology to another.

So, what we have started of discussing is the numerology where the sub-carrier spacing
was 4.7 microsecond in this particular picture, right we had 4.7 microsecond and from
that number this number is changing to the level of 0.57 and even 0.29 even if you go
one level further it will be 0.29 instead of 0.57. So, in that case one will find that the
channel impulse response might be long enough and one is not able to use that particular
numerology. So, one has to see this different effects and choose an appropriate
numerology of choice one actually implement this particular system.

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(Refer Slide Time: 29:27)

So, moving further in this particular slide we have combined the information in a little
bit abstract manner where we you have removed the sub-carrier picture to see only grid
structure. So, this is easier to look at.

So, what we have is, for mu equals to 1, we have the sub-frame structure and what we
have over here is for a mu equals to 0 the sub-frame structure and the total number of
OFDM symbols is on this axis and the total number of sub-carriers is on this axis. So,
over all we see that in both cases number of sub-carriers per resource block number of
sub carriers per resource block is 12 here again we see that number of sub-carriers per
resource block will again remain as 12.

And, here the resource element is 1 sub-carrier here again the resource element is 1 sub-
carrier. Along with this these complex modulations will go in case of mu equals to 0,
your sub-carrier spacing is 15 kilohertz; in case of mu equals to 1 your sub-carrier
spacing is 30 kilohertz. Here what you see is that more number of sub-carrier available,
here lesser number of sub-carriers are available within the same duration of time that
here there are more symbols are available, right whereas, sorry here there are lesser
symbols available, here there are more symbols available because mu equals to 1 thus
symbol duration decreases. So, more number of symbols would fit in.

So, this is how the structure is going to change and this indicates the number of OFDM
symbols that are present in the entire structure.

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(Refer Slide Time: 31:09)

So, here again we simply show what would structure look like in a simplistic picture
when the sub-carriers spacing is a certain value and here the sub-carriers spacing is of
larger value. So, when it is larger value as you can see this width is equal to this width.
Here the sub-carriers spacing is half compare to the sub-carrier spacing over here, but
here the symbol duration is half compare to the symbol duration over here. So, these are
just different pictures to show you the complete story.

(Refer Slide Time: 31:39)

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Further, because this frame structures are flexible it provides as an opportunity to
provide multiple different services within the same frame. They can all be put in
depending upon the requirements. So, one of them what we see is that URLLC which is
the Ultra Reliable Low Latency Communication service. So, when we talk about a low
latency, we note that the symbol durations should be small, so that one can have shorter
duration of transit time. If the shorter duration of transit time is there then the overall
round trip time will be reduced and one can address lower latency applications.

So, we stop this particular lecture here. We will continue on this in the next lecture.

452
 Evolution of Air Interface towards 5G
Prof. Suvra Sekhar Das
G. S. Sanyal School of Telecommunications
Indian Institute of Technology Kharagpur

Lecture – 25
Numerology in 5G and Adaptive Subcarrier Bandwidth

Welcome, to the lectures on evolution of Air Interface towards 5G. So, we have seen the
frame structure for the fifth generation mobile communication system, especially the
series which comes from the house of 3GPP and we were discussing how the slot size
remains constant in terms of number of OFDM symbol, but when it comes to the time
duration for the slot it changes because OFDM symbol changes. So, the entire frame
structure now becomes flexible with different amounts of resources available for
different services.

(Refer Slide Time: 00:52)

And, as a result of which what we see over here is a combination of several different
services which could be multiplexed together to provide various different services over
the same air interface. Now, this is very very important which has happened over the
earlier generation system which did not provide such kind of flexibilities.

And, we have identified that for example; in this case the URLCC which is the Ultra
Reliable Low Latency especially will talk about the low latency part which becomes very
very critical. So, in a typical communication system a slot is the unit which gets

453
addressed. So, in the earlier generation there was a sub-frame which was getting
addressed 1 millisecond duration; now, you can address a slot, that is point number 1.
But, look at the flow of things when it goes from Tx to Rx, an entire transmission unit
has to be decoded at the receiver. So, it has to be generated at the transmitter going from
transmitter to receiver through propagation ok. At the receiver it has to be decoded and
then it has to be sent back to the transmitter, right.

So, the basic unit which constraints this entire flow is this unit which is the slot unit
which is not addressable. Earlier it was the sub-frame unit plus there is this processing
delay at the receiver side as well as at the transmitter side. Now, why we are talking
about this round trip, because there is constraint on latency on the round trip. If this
duration is 1 millisecond then there is by no means by which one should be able to
respond within 1 millisecond from one node to another node with the shortest possible
inter-node connection. However, the only way one can do it is to reduce this duration.

So, first and foremost with mu equals to 0 what we find that this duration becomes 1
millisecond, the duration of a sub-frame which is the one for the fourth generation
system. But, here with different mu configurations one can change the slot duration to a
much smaller value.

(Refer Slide Time: 03:06)

And, you have seen in the previous lecture that the sub-frame size, the sub-frame size
remains constant, but the OFDM symbol duration can become it is very very small. So,

454
there is another mode where it can become even smaller than this. So, when it becomes
even smaller; that means, the symbol duration becomes around 4.5 microsecond
including a cyclic prefix roughly speaking that is the value. So, that means, if we take 14
OFDM symbols in one slot, then the number is not very high right it is it is within around
70 microseconds and so on.

So, that means, you have a huge amount of time. So, if this particular duration is within
100 microseconds let us say so; that means, one should be able to do a round trip
transmission; if this is let us say less than 100 microseconds, so, then you have 10 such
slots available for transmission. So, that means, there is sufficient interval in terms of slot
count that can be used and hence one should be able to transmit the slot the propagation
delay is not much if the distance between the transmitter and receiver is small. If the
packet duration is small then the decoding time would also be small and hence it will it
will help respond to a total of 1 millisecond of response time.

(Refer Slide Time: 04:30)

Further, we will also see that when we go to this new generation system, there is a
provision for mini slot compared to only sub-frame or the slot duration for mu equals to
0 which can also be addressed. And, this slots mini slots can be of 7, 4 or 2 OFDM
symbols, meaning that within a very short burst within a very short burst one can say this
is the entire transmission unit. So, if the burst rate short, decoding time is also short,

455
response time become short because the total response time is counted in terms of
multiples of this transmission time of a slot of a particular slot.

So, this smallest slot duration can provide you a lot of flexibility and capability towards
meeting this URLCC. So, what we see is that because there was a requirement to support
such things, such different services, this particular flexible structure can provide a lot of
support towards meeting the multiple different services within one particular frame
structure.

(Refer Slide Time: 05:39)

Now, we move on to understand the numerology even in a better sense or complete the
understanding one has to go for 38 dot 104 that is the next part which talks about the
base station radio transmission and reception.

So, in that there are two sets of frequency ranges that are defined: frequency range 1 is
from 450 megahertz to 6 gigahertz and the next one is from 24 gigahertz to 52 gigahertz.
So, that means, there is two different ranges over which things are going to happen. So,
usually this is referred to as less than 6 gigahertz and the other set which is greater than 6
gigahertz frequency, ok.

So, we also have 38 dot 101. So, if we take out one particular statement from that what
we find is that the UE channel bandwidth supports a single NR RF carrier; NR is new
radio, radio frequency carrier in the uplink or downlink at the UE that is one part. From

456
the BS perspective, different UE channel bandwidths maybe supported within the same
spectrum for transmission to and receiving from UEs connected to the base station. So,
what it effectively means is the different user equipments will be connected to the base
stations and different UE channel bandwidths should be supported.

So, not only that since each UE can choose a different numerology, the base station may
be simultaneously supporting different numerologies together and one would encounter a
situation where one is going towards a mixed numerology. So, we will see the particular
structure how it fits in.

(Refer Slide Time: 07:31)

The base station should be able to support multiple users within the same spectrum. So,
that is what it means, it also means that each UE with different configuration of
maximum channel bandwidth leading to different subcarrier spacing right. In other
words, within one carrier bandwidth from the base stations perspective, multiple UE
subcarrier spacing is possible. So, what we conclude overall is that UEs can have
different subcarrier spacing and different UEs can have different subcarrier spacing
while the base station must support them even if there within the same spectrum. So, that
is what we get.

457
(Refer Slide Time: 08:10)

So, overall picture that we get is in standard LTE this is the kind of figure which we have
referred to earlier and which we will see where the subcarrier spacing is constant, but
now under mixed numerology situation. So, we have the mixed numerology mentioned
over here different subcarrier spacing should be supportable from the base station. So,
this is a very different thing compared to what has been encountered in the earlier
generation system and this would lead to many different questions and many different
issues many different aspects. So, we will get into the discussion of that particular aspect.
So, let us look into that.

(Refer Slide Time: 08:56)

458
So, we will now discuss about what is the genesis and how things have come. So,
primarily I would like to point out over here that this particular work that we are
referring to is not a very new work it actually started at least 10 years from now. So, in
the year around 2004 to 2005 we will find that there is reference for these works 2004,
2005 we will point out such references and one such reference that will talk about is one
particular material which will actually give the details about it later on. So, let us get into
how things are and why things are in that format.

So, we have seen this particular picture earlier, where we said that between the
transmitter and the receiver there are multiple paths. So, multiple paths would give rise
to a channel impulse response as depicted in this particular picture and we said that they
are needs to be a guard interval or T cp which should be greater than the tau max. So,
this is the tau max of the channel, correct. Along with this there is also mobility which
gives rise to Doppler, ok.

(Refer Slide Time: 10:15)

So, there we will find that in a particular situation you will be having different Doppler
conditions coexisting. If different Doppler conditions coexist then each of the users
would going to experience the different kind of channel. So, mobility gives rise to

459
Doppler, user distance gives rise to path-loss and user equipment capability gives rise to
various ICI problems, various ICI capability.

Further, what we have seen in the earlier discussion is that there are different frequency
ranges of operation. So, if one thinks of below 6 gigahertz and the another set above 6
gigahertz, these different frequencies if you look at and look at the components or
devices that would be useful to making them, as you increase and go towards higher and
higher frequency one of the important factors that comes into play is phase noise.

The effect of phase noise becomes larger. Phase noise effectively means that the
oscillator frequency that is generated is varying about f c; if this is the f c beyond just
being a delta function. So, in the frequency domain it is no longer a delta function, rather
in frequency domain you will find that there is a certain amount of spread in the
frequency and there are certain other spurious frequencies that also coming.

So, as you increase the carrier frequency this particular effect dominates. Further, as you
increase Doppler what we find is that the Doppler frequency f D is proportional to the
velocity of the vehicle multiplied by the carrier frequency. So, simply if the velocity
increases then Doppler frequency increases or if the carrier frequency increases Doppler
frequency also increases further.

So, if we go from the 4G to 5G first and foremost the maximum frequency supported
increases from 350 kilometers per hour to 500 kilometers per hour and the frequency of
operation not only goes up to 6 gigahertz, but it also goes beyond 6 gigahertz. So, over
all these conditions indicate that your Doppler frequency Doppler experienced increases,
also the phase noise increases. But, at the same time you will find that stationary uses
would also be there, that means, pedestrian users would also be there, there would be
indoor conditions, there will be multitude of various outdoor conditions which needs co-
exists at the same time.

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(Refer Slide Time: 12:54)

So, if we look at what is the effect of Doppler so, or let us say phase noise or carrier
frequency offset. So, we said that in OFDM, the sub-carrier spacings are such that they
are orthogonal; that means, the peak of the desired carrier coincides with the null of all
other carriers; that means, there is no interference. But, if there is shift in carrier, the
desired signal strength reduces and there is huge amount of interference that comes into
play.

So, if this interference comes into play there is heavy reduction of signal to interference
ratio, if you have Doppler then the problem is there is no one single frequency shift. So,
if we call it a shift then it can be handled. That means, one can be track the frequency of
set one can do it, but because of multipath the shift does not happen and instead what
you get is basically a Doppler spread condition, right.

So, what is depicted in this picture is this power spectral density verses frequency and we
see one particular spectrum which imitates the Jakes spectrum; that means, there is a
whole bunch of frequencies. What it means that the receiver would perceive that there
are several such multitude of frequencies which is come in and there is a smearing of the
signal in the frequency domain, they just overlapping the multiple values.

So, in that case this CFO tracking algorithm is not going to be much useful under that
situation, if there is only a frequency shift then that kind of algorithm are useful, right.

461
And, if you have complex ICI cancellation algorithms that would also increases the
complexity of the entire system.

(Refer Slide Time: 14:49)

So, if you look at how does the Doppler effects the inter carrier interference we will find
that in the inter carrier interference power term; this is the power for inter carrier
interference there is a ratio of frequency offset with respect to the sub-carrier spacing.
So, this delta f sc is a sub carrier spacing.

So, what do see as this numerator increases the ICI power increases, right as you increase
that the ICI power increases. So, one way which we as designers or transmitters can
reduce the effect of ICI is by changing the denominator term which is in our control and
as you can clearly see this denominator term which is delta f sc indicating sub-carrier
spacing it can be varied. So, this way one can easily implement a method by which one
can take care of such Doppler spreads and this exactly has been adopted in the fifth
generation system. And, originally it was proposed in the by the name of adaptive sub-
carrier bandwidth by us when we were working on this particular issue way back in 2004
– 2005 and as well as we have proposed various mechanisms to handle this in the
subsequent years. So, we will get into all the details of how this kind of thing works.

462
So, going further we just look at this how does this pictorially represent. So, typically
because of frequency offset one gets a reduction in signal strength as well as increase
interference values, but then this particular variation is delta f that is a small delta f and
this is the capital delta f. So, as you increase the sub-carrier spacing simply you can
improve the signal condition at the receiver. So, these indexes indicate the desired and
interference terms and thereby you can improve the overall condition.

So, what you get is that as you keep increasing the subcarriers spacing in this axis and
these different curves are for different mobility conditions that we are tested long time
back, we have we are not introducing a newer set of values because this is an earlier
work that we have done. So, what do you see is that at 10 kilometers per hour, you get a
certain signal to interference ratio. As your Doppler increases at a particular value of sub
carrier spacing, your signal to interference ratio becomes smaller and smaller. This is
something very critical to note simply by virtue of this particular case. As you increase
the sub-carrier spacing the signal to interference ratio increases beautifully especially for
the once where you have higher Doppler condition, right.

So, this clearly indicates that to handle higher Doppler conditions having higher sub-
carrier bandwidth is a much better solution than implementing advanced interference
cancellations techniques which also get limited when you have multiple paths coming to
play and there is a spread.

(Refer Slide Time: 18:28)

463
So, with this we have we have discussed that we have also analyzed the throughput
condition; that means, when you increase the sub-carrier bandwidth what happens for
different throughput conditions. What we find that as you increase the sub-carrier
bandwidth or as you decrease the sub-carrier bandwidth we have discuss this when you
talk about the frame structure, for longer OFDM symbol durations the guard interval
duration is also longer. Sorry, I mean guard interval duration is correspondingly longer.

Now, if you have a certain channel impulse response and you cannot do much with a
guard interval part; that means you are restricted then the overall system efficiency
decreases, right. So, that is what we find that if you are maintaining certain sub-carrier
spacing and you are changing and you are simply studying the effect on different
mobility conditions we will find whether throughput would decrease as one increases a
sub-carrier spacing, but one maintains a certain mobility conditions, ok. Whereas in
another situation it initially increases then more or less it is remains the same up to a
certain point.

(Refer Slide Time: 19:48)

464
So, we go beyond this and we look at the overall structure. So, here what we have plotted
is on the x-axis we have given the velocity, and higher number of sub-carrier or reverse
lower number of sub-carrier indicate higher sub-carrier bandwidth because we have a
bandwidth divided by N. So, as N increases delta f decreases or vice versa.

So, as N decreases delta f increases right. So, 2048 has a certain value of delta f with 20
megahertz bandwidth as we increase to 1024, the delta f increases, as we go to 512, delta
f increases further. So, what we see is being depicted in this particular picture is that if
you are maintaining certain narrow sub-carrier bandwidth, this is very very critical. The
throughput decreases heavily with increase in mobility, right. After a certain point you
simply cannot support the throughput because your interference is very very high. If you
are using a little bit wider then you can support a higher throughput, but there is a
decrease in throughput for low mobility conditions.

Similarly, if we increase the sub-carrier spacing further we find that the throughput as
improved in higher mobility conditions, but it has decreased in the low mobility
condition. As we go on increasing, so, this green set is for 256 which is several times
wider than the 2048, just remember this. So, this directly corresponds to the new name of
numerology that we are using for fifth generation, but the original name that was
proposed was adaptive sub-carrier bandwidth. So, what we have shown is this different
shaded portions indicate the range of mobility which causes a certain Doppler, which can
also be connected with corresponding phase noise in terms of delta f which gives the
highest throughput.

So, if we clear this things up so, will find that is the each particular section represents the
corresponding throughput for that sub-carrier spacing. So, if you have this delta f mu this
delta f mu is much larger than delta f of 2048 and hence it can support a larger
throughput over here, but there is a significant reduction in the throughput in the lower
mobility condition. So, what is suggested or proposed is that one can adaptively change
the bandwidth of the sub-carrier and depending upon the mobility condition or channel

465
condition one can flexibly allocate the sub-carrier spacing. Thereby one can get the best
throughput under all conditions of sub-carrier spacing or phase noise or whatever is the
situation.

(Refer Slide Time: 22:55)

So, if we look at the structure what we had proposed is we had consider that let us say
there would be a much wider bandwidth in that case one would limit a sub part of the
bandwidth to let us say 20 megahertz because as you increase the bandwidth your
processing complexity also increases. So, we had assumed that let there will be smaller
parts and smaller parts can be a various bandwidths depending upon the particular
realization. So, this is in frequency domain you can have several chunks which run in
parallel. One could also think of doing this in TDM fashion depending upon the
implementation technically it is feasible, but this is the approach which is now adopted in
the fifth generation system.

466
(Refer Slide Time: 23:43)

And, the picture that would look like is in a standard LTE is would look like this. In a
variable sub-carrier bandwidth we have certain fractions having narrow bandwidth,
certain fraction having wider bandwidth, this work that we are representing over here is
an extreme case of the picture over here.

In this case, we had a group of sub-carriers which are next to each other whereas in this
case we have allocated, a consecutive group of sub-carriers who have a wider sub-carrier
spacing. Let us say this is 2 and this is delta f sc 1, we have delta f sc 2 greater than delta
f sc 1, right.

467
(Refer Slide Time: 24:32)

Whereas, we can think of an extreme multiplexing of things where we will find that
different bandwidths are multiplexed simultaneously and correspondingly the different
time domain pulsed this would also exists simultaneously. So, what we see is that the
narrow band sub-carriers have a longer pulse duration and the wider band sub-carriers
have a shorter pulse duration.

So, with this also the detailed analysis of signal to interference plus ratio noise ratio and
the throughput calculations have been done and as I had shown earlier this particular
reference which we will give you in details including the cover page which contains this
particular image, one can find all details about the performance analysis that one needs to
do.

468
(Refer Slide Time: 25:21)

So, here we have also proposed the structure in which this can be worked out; that
means, one can think of different FFT sizes; that means, they are all operating on the
same bandwidth, but the sub-carriers spacing is simply different. So, that means, if the
total bandwidth is B, sub-carrier spacing 1 should be equal to B divided by N 1 and this
sub-carrier spacing 2 is the same bandwidth divided by N 2.

So, in this case N 2 is less than N 1 leading to delta f sc greater than delta f sc 1 and here
what we indicate is that in one set of FFT, IFFT operations one would activate few sub-
carriers; that means, send them non zero signals with X k not equal to 0 and it would let
the other sub carriers having X k equal to 0 while in the other FFT, one can have the X
ks not equal to 0 in the portion which is not overlapping in the frequency domain of the
other system. Whereas, here you can have X k equals to 0, X k are the constellation
points.

469
So, by virtue of which if you look at the final frequency domain picture we will find that
these sub-carriers are present because of this. In the next portion we will find wider sub-
carriers present because of this. So, here we will find wider sub-carriers spacing, here we
will find narrower sub-carrier spacing.

(Refer Slide Time: 27:02)

So, implementing this is also not a problem and this particular picture generalizes the
entire thing where we can have different sub-carrier spacing. So, this you can connect to
different numerologies and it can be decoded by different receivers simultaneously. So,
as if this is the base station and these are the different receivers as have been indicated
here receiver 1, receiver 2, receiver 3. They can decode independently. And, one can also
think of a reverse direction transmission; that means, each transmitter these becomes
transmitter would activate only these few sub-carriers out of the entire set of sub-carriers
this receive. This transmitter would activate only this set of sub-carrier.

So, when the signal arise at the base station one would find that corresponding to this
there is some narrow band sub-carriers, then there will be a little bit wider band sub-
carriers and they will be even wider band sub-carriers next to each other. So, then this
way one can have a mixed numerology architecture.

470
(Refer Slide Time: 28:08)

In this figure we have given a detailed block diagram of how the transmitter and receiver
would look like. So, this one is the BS or the downlink transmitter, here we have the
uplink receiver structure. So, all this details have been proposed and you can find them in
the different in the different material.

(Refer Slide Time: 28:24)

In this we have verified that the spectral efficiency improvement from 10 to 30 percent
can be had. It can support different mobility conditions and different phase noise
conditions, as well as low complexity, ICI management can be done we need not cancel

471
the ICI, right. Only thing you need to do is the dynamically adapts this sub-carrier
bandwidth and which you will now term as numerology.

(Refer Slide Time: 28:57)

(Refer Slide Time: 29:01)

The references which we would point out is the first work here which contains all details
of the things that were that are presented in this particular discussion and relevant for the
fifth generation air interface and there are different publications which also point out to
the same. This is the earliest work in this particular direction and there you can also refer
to a patent which can be at easily accessed from this particular website which divide

472
gives all details of the adopting sub-carrier spacing, you call it variable sub-carrier
spacing or whether you call it numerology as per the new statement.

(Refer Slide Time: 29:43)

I would also point out at this point that yeah. So, this particular thesis that you are seeing
in front of you can also refer to this particular work which can describe the hardware
realization of such a thing. So, as you can see from the picture which is depicted on top
of the particular PhD thesis by Christian Blumm which is maximizing OFDM
performance real time adaptivity and you go into the details you will also find that they
have also referred to the work that I just presented to being one of the first kind of work
in this domain.

473
(Refer Slide Time: 30:27)

And we are all really extremely happy that finally, these kind of proposals which we
thought is pertinent is finally, being used in the fifth generation system where the
terminology that is used is numerology and we have the most complicated situation
which is the mixed numerology and if you want detailed analysis of this numerology
please refer to all the details that we have pointed out over here to find detailed analytical
expressions, performance analysis, how to do the simulations and all other details
available.

So, we stop this particular lecture here. We will continue to discuss some more things
related to the choice of cyclic prefix, how does effect and what are the uses, so that it can
also provide you with more tools and methods by which you can improve the systems
even beyond what is available today also give you information about the problem that is
associated with coupling the cyclic prefix along with the sub-carrier spacing. Further we
will go beyond and discuss about the slot aggregation which is also one of the important
characteristics which have been investigated earlier.

Thank you.

474
 Evolution of Air Interface towards 5G
Prof. Suvra Sekhar Das
G.S. Sanyal School of Telecommunications
Indian Institute of Technology Kharagpur

Lecture – 26
Numerology OFDM – Cyclic Prefix & Link Adaptation by Slot & RB Aggregation

Welcome to the lectures on Evolution of Air Interface towards 5G. So, we are discussing
the main unit of waveform in the 5th generation and that is the numerology. We have
explained the frame structure earlier and in the previous lecture we have described how
the numerology subcarrier spacing is to be designed and why it is decided in such a
manner. And, when all did this work start and what is the genesis and the original source
of work which you may find useful towards understanding more details or even coming
up with better designs which can be useful in future generation communication systems.

(Refer Slide Time: 00:57)

(Refer Slide Time: 01:03)

475
So, briefly very very quickly look into the background we simply stated that there is
variability of Doppler conditions and beyond that we also stated that Doppler spread
leads to inter carrier interference. We had explained the orthogonality loss, where signal
power decreases, interference power increases and we said that since the mobility
conditions are different.

And in case of Doppler instead of a single frequency shift there is an entire range of
frequency which comes in. So, even if there is good CFO tracking algorithms its limited
in its effectiveness and ICI cancellation mechanisms are also very very complex and
especially when there is a whole lot of Doppler frequencies the effect of such
mechanisms are no longer useful.

476
(Refer Slide Time: 01:41)

We also identified that the inter carrier interference power which is due to the Doppler
frequency spread or frays noise is affected by parameter which is the ratio of the offset or
maximum offset with respect to the subcarrier spacing. So, if there are situations where
we are unable to reduce this; that means, we are unable to control this because there is a
natural phenomena you are unable to control and one would not like to do ICI
cancellation then the denominator parameter is under your control and becomes a design
parameter.

And we are proposed that this could be used flexibility as per the situation and what we
find happily is that the 5th generation system is actually using such a mechanism which
can provide very simple way of accepting this broad Doppler spread or phase noise
related issues which can give rise to ICI, we have also explained how the system works
visually. So, when there is offset there is reduction in the signal power increase in
interference power, but if we make the denominator larger we find that things can be
improved significantly.

477
(Refer Slide Time: 03:07)

And we have also presented some of the results by which we have shown that as the
subcarrier spacing increases; that means, as the FFT size decrease as the FFT size
decrease as the FFT size decrease and the subcarrier spacing increases, we find that the
wider subcarrier spacing are useful for more velocity or larger velocity. Or in other
words situations where phase noise is larger whereas, they are not good under situations
where Doppler is less or phase noise is less.

So, what we find is that if we have a combination of different subcarrier spacing which
can be brought about by choosing the number of or the size of FFT one can effectively
cover the entire set of Doppler or phase noise or effectively the frequency offset or
frequency spread by adaptively choosing the subcarrier spacing and there you get a huge
amount of benefit up to 30 percent benefit in spectral efficiency can be found based on
the investigation that we have done; based on newer settings even one can find more
precise numbers which are available for the 5th generation.

478
(Refer Slide Time: 04:13)

We also iterated that such systems can be implemented in the frequency division manner
in a way that a large bandwidth can be split into smaller sections each having let us say
20 megahertz or 10 megahertz or 40 megahertz as per availability and they can use
different subcarrier spacing and the detailed ways of how this assignment can be done
are also mentioned in the references which we are pointed out. We also had said that
such mechanism may be implemented in time division manner depending upon the
implementation strategy and similar benefits can also be fetched.

(Refer Slide Time: 04:49)

479
(Refer Slide Time: 04:57)

So, this particular picture we had shown where we said that mixed strategy can be used
and the worse condition or the extreme cases where an absolute mix of different
spectrum, difference subcarrier bandwidth can come into play where this picture
particularly gives the time frequency diagram is the time and this is the frequency axis
how it would look like and what would happen because of the interference? So, some
kind of orthogonality loss is introduced because not all sub-carriers are orthogonal, but
you can choose a set of sub-carriers which will be maintaining some kind of
orthogonality amongst them.

So, when we have a group of sub-carriers they will be orthogonal to each other; however,
one set may be orthogonal to another, but it is not in the reverse direction. So, there is
some kind of orthogonality loss and we have found that the edge sub-carriers which are
at the edge of interference would be suffering the most, but still you can benefit a lot. We
have also shown implementation mechanisms which are also very vital.

480
(Refer Slide Time: 05:55)

And we had also shown how at the base station side the various things can be, various
subcarrier spacing can be introduced while they can be decoded at the user end
independently and the reverse direction they can be generated independently and
combined at the base station receiver side.

(Refer Slide Time: 06:09)

481
(Refer Slide Time: 06:11)

So, we have also presented different architectures and we have provided the benefit. We
have also given you the references which we find are important which you can go
through for finding more details.

(Refer Slide Time: 06:21)

Now, we move on to the other aspect of the numerology that is the guard interval or the
cyclic prefix and we will discuss how this is to be chosen so that together one can find
ways to select both the subcarrier spacing and the guard interval so that one gets where
appropriate combination of choice to in during deployment.

482
(Refer Slide Time: 06:43)

So, in this particular picture although it’s from some papers we have taken it only for
academic reference, you can always find reference to these particular papers. It is shown
that the delay spread has a certain distribution and in this picture which is again from one
of the works by Vinka Erceg we have shown or we have actually taken it from there
which shows that as the distance increases the delay spread also increases following
certain distribution.

(Refer Slide Time: 07:13)

483
So, effectively what we mean is that when you instead of looking at a situation where
delay spread is constant, rather one should take delay spread as the characteristic of a
particular environment. Now when we look at the deployment scenarios what we have
described earlier is that there are various deployment scenarios like indoor scenarios,
urban micro cells, small cells, rural large cells. So, if we look at these different
conditions the amount of echoes and multi-paths and their characteristics will be
different.

So, if they are different then we naturally expect in some environment the delay spread
to be maybe symbolically in this manner, in another situation it might be symbolically
like this and in another situation which is like this. So, it effectively means that there are
larger echoes coming at longer duration of time whereas, in other cases this is smaller
one, so the same air interface has to handle multiple situations.

So, what happens is one would design an air interface so I will redraw it here a small a
medium and a large. So, if one has to define an appropriate air interface then the cyclic
prefix interval should be chosen as large as this because this is tau max over all possible
deployment conditions, but what we find is that if the channel impulse response is small
in certain cases there is a huge loss in spectral efficiency. So, all we have trying to do is
find out mechanisms by which this can be improved.

(Refer Slide Time: 08:45)

484
So, we can actually reduce the cyclic prefix length that is what is the proposal. So, what
we find is that in case you reduce the cyclic prefix where as you encounter a situation
where the channel impulse response is large in that case you would encounter irreducible
inter-symbol interference and there is significant degradation in performance.

So, effectively one has to find an appropriate balance between the two conditions; that
means, neither one can use a very large cyclic prefix that would reduce the spectral
efficiency. And, if one uses a small cyclic prefix then one would end up in a situation
that where cyclic prefix is large there would be ISI and this kind of ISI is irreducible you
cannot reduce it by simply increasing this signal power.

So, this leads to the obvious choice that can one make the cyclic prefix dynamic can this
be made dynamic, the answer naturally is yes one can make it dynamic because the
cyclic prefix is not connected to this subcarrier spacing right cyclic prefix is not
connected to the useful duration of OFDM symbol. It is only connected through the
spectral efficiency because the spectral efficiency would be the ratio of useful symbol
duration divided by total OFDM symbol duration; total OFDM symbol duration is useful
symbol duration plus guard interval.

Now if we find cases where guard interval becomes pretty large then whereas, the useful
symbol duration has not been modified then the OFDM symbol efficiency decreases. So,
one way to improve the OFDM symbol efficiency is to increase the useful symbol
duration part. So, if you increase the useful symbol duration part then the entire fraction
becomes larger and the efficiency increases right. So, if I increase the OFDM symbol
duration then in other words I am affecting the subcarrier spacing.

485
So, the only way it is connected not through the characteristics of the channel, but
because of this efficiency factor one can think of associating T cp with Tu not otherwise.
So, summarizing we find that the frequency spread which is indicated by del f one can
think of putting a sub suffix c indicating with respect to carrier is largely due to Doppler
or phase noise.

And Doppler is largely due to velocity or mobility or due to the carrier frequency
whereas, the tau max is with respect to deployment conditions; that means, it is
dependent upon the multipath scenario; that means, sigma tau or tau max and this affects
your T cp whereas, this affects your capital delta f sc which in turn affects your Tu. So,
there are two different things which affect these two important parameters of
numerology, but if we take OFDM symbol efficiency then we can connect these two.

So, we can connect these two via OFDM symbol efficiency. So, if the OFDM symbol
duration is becoming small because of the because of this Doppler or the phase noise
then one can only reduce the guard interval, but up to that much only where tau max is
still captured within the guard interval. So, we will see further some of the important
outcomes of this.

(Refer Slide Time: 12:59)

So, in this particular picture we had depicted earlier that what are the different
deployment scenarios. So, as we have shown earlier that in the frequency domain one
can divide the entire available bandwidth into smaller chunks and in each chunk one can

486
operate an OFDM system and each can be of different subcarrier spacing and in each one
correspondingly a different amount of cyclic prefix may also be used.

So, this is in frequency division and this is precisely the way the 5th generation NR is
operating and we had also talked about doing it in time domain which is open for
implementation. So, this way one can appropriately handle the different variations and
vagaries of the wireless channel in a very very effective manner and use very low
complexity signal processing at the transmitter maintain the simplicity of OFDM. So, to
do this one has to choose the appropriate value of cyclic prefix.

(Refer Slide Time: 14:03)

487
So, what we had presented over here is that the choice of cyclic prefix or guard interval
can be done in an approximate way in some manner although this is open for
improvements is that this particular guard interval should be greater than in some
complicated function which involves the RMS delay spread of the channel. Now, RMS
delay spread of the channel is something which one can measure or pre-estimate. So, this
is one single parameter which characterizes the delay properties of the channel we will
see it again.

It is also dependent on the signal to noise ratio required or SINR required which is from
the QoS conditions and which decides the modulation code rate and BER. So, it is
interconnected to these parameters which is connected to quality of service. So, or a
particular BLER or BER for a given modulation and code rate is connected to the SINR
requirement. So, it is also a function of SINR required and we had also introduced a delta
SNR indicating some margin which is a bit different from standard thinking; that means,
one can partially trade-off the cyclic prefix with respect to extra amount of signal to
noise ratio because it may be possible that the user end or the base station has some spare
amount of power.

So, we just try to figure out that if that extra amount of power could be utilized was
trading of some amount of ISI that may be present. For example, if one is choosing
QPSK constellation, in that case since there is only phase to be identified and not
amplitude there is certain margin what one can use, but if one extends to 16 QAM then
probably the margin that is available would be less. So, depending upon particular
situations certain amount of extra margin may be available to take care of the extra
benefit by a which can be achieved by using a different or variable amount of guard
interval. So, these are all the parameters that we had identified along with this T f which
is nothing, but our T u it is not the T frame as per the 3GPP descriptions.

And which is equal to one upon delta f subcarrier spacing is also one of the important
parameters while taking a decision of the guard interval. So, if one computes such an
expression and one may scale this RMS delay spread depending upon the particular
power delay profile, one can scale this value instead of using it just like that to find an
exact or more appropriate choice, but; however, this will give you certain numbers and
since the CP is quantized since only fixed values as you have seen 0.29, 0.57, 1.17 and
so on microseconds are there.

488
So, any value in between that this result can throw up one can always go to the next
immediate higher value of cyclic prefix that one is allowed in the standard. So, in this
manner one can also choose an appropriate value of guard interval, one can even
simplify this and what we have also shown over here there is a parameter epsilon which
is again the ratio of delta f c by delta f subcarrier spacing.

So, if one has information or prior information then one can also introduce into this
expression to get an appropriate value of guard interval because this causes certain
amount of interference while the small guard interval if it is used also brings in certain
amount of interference. So, there is a certain trade-off between the interference or
exchange that one can think of how much one wants to distribute here how much one
was distribute there and to find an appropriate size of guard interval.

Although not entire thing can be exchanged, but partially it can be handled because any
ISI that is resulting over here would also result in additional amount of inter carrier
interference. So, there is a complicated relationship amongst these parameters and we
have been able to find one particular expression through which one may be able to
choose the appropriate choice of CP. Using the choice of delta f sc we had earlier
mentioned that the ratio epsilon is usually desired to be kept at more than 0.02 it should
be kept greater than 0.02 to maintain 20 db of SINR accordingly one can fix up all the set
of parameters for an operation.

So, a choice of this together with Tcp and that has to map to an appropriate value of mu
one would get a numerology; that means, to be deployed in the operational conditions.
So, with this we summarize or we conclude the discussion on choice of parameters for
numerology although will present a few results immediately following this.

489
(Refer Slide Time: 19:15)

So, this particular result shows the overhead reduction by changing guard interval by
allowing certain amount of extra SNR. So, what we see is that if a certain amount of
extra SNR is allowed, so, here reference is 15 dB whereas, 0.5 dB if extra SNR is used
or 1 dB or 17 dB then we find that up to 60 percent of reduction in guard interval is
possible. So, these particular set of results are with specific set of conditions which we
have described in the references one is encouraged to going into the references.

(Refer Slide Time: 19:53)

490
And here what we have shown is the distribution of throughput so what we show is that
the variable guard interval or variable CP-OFDM it can enhance the throughput by
twenty percent or so or one can get even better depending upon the operational
conditions. So, by both the mechanisms the cyclic prefix can give you around 20 percent
increase and the sub-carrier spacing can give you around 30 percent increase.

Now together they may not add up to 50 percent they may also depending upon situation,
but that is the different amount of gains that can be benefitted by using variability in
these two parameters ok.

(Refer Slide Time: 20:35)

So, these are the certain set of references which are very very critical in this context. So,
one again can find all details as discussed over here to understand how these different
choices are made.

491
(Refer Slide Time: 20:47)

So, here this particular picture essentially summarizes this can also be found in one
reference from Eriksson also they have given a similar picture. So, we have taken
reference from that and recreated this where we summarized the entire situation where
we say that on one side as the frequency increases, the operation frequency increases,
phase noise increases, so does Doppler spread increases.

So, one can think of this axis as the Doppler spread axis or phase noise axis or delta f c
axis and this one; one can think of as the tau max axis and as we have said from earlier
results because of other measurement campaigns that this happens when the cell size also
increases right. So, when your cell size increases tau max increases and hence the guard
interval required would increase and to maintain the efficiency of the OFDM system the
numerology has to decrease because decreasing numerology means subcarrier spacing
decreasing and T u duration increasing, T u duration increasing means OFDM symbol
efficiency increasing.

Whereas, on this side we find that as the offset increases this subcarrier spacing has to
increase and hence T u has to decrease right. So, this is the reverse trend. So, one has to
choose a combination this is a reflection of different combinations than that one can get
appropriately with methods as has been described in the earlier slides.

492
(Refer Slide Time: 22:31)

Now, we quickly look at another important aspect this link adaptation thing we had
explained in an earlier lecture which we do not want to discuss much now, but we just
have it here. So, that you can take it as a reference and recall the earlier discussions that
we had had and continue on the next part of the discussion that we are going to have
now.

(Refer Slide Time: 22:49)

So, we had said earlier that the OFDM communication system in both the 4G and the 5th
generation they do not allocate one subcarrier so this is the subcarrier unit, this is the

493
resource element any one tiny box is the resource element, this is a subcarrier width, this
is the time width and this forms one OFDM symbol ok.

So, this forms one OFDM symbol all sub-carriers one unit of time and we had also
explained that these different OFDM symbols consecutive symbols and different
subcarriers forms a resource block which we had also described when we talked about
the frame structure. So now, we also mentioned that in this resource block the
modulation coding scheme and the power controls power is kept constant and that is the
unit of allocation of a particular data block or a particular user allocation.

We had also mentioned that in the 5th generation this size remains constant in terms of
number of OFDM symbols which is also same as in the 4th generation that is 12 or 14
depending upon whether extended cyclic prefix or normal cyclic prefix, but because in
5th generation and what we have explained in the just previous slides that the duration of
the OFDM symbol would be different that can become smaller or larger hence the tile
size is going to be different.

Now, what we need to look at is a detailed understanding of the propagation

characteristics. So, we had talked about the propagation characteristics that the signal
strength fluctuates significantly in the time domain as well as it fluctuates in the
frequency domain we can clearly see how the frequents how in the frequency domain the
signal strength fluctuates and how in the time domain the signal strength fluctuates right.

(Refer Slide Time: 24:37)

494
And we had also stated that this was in seconds this is a larger window in frequency
whereas, if we zoom in to that particular picture and see a much smaller window what
we will find? That when time is given in milliseconds that will be zoom into it, there is
much smaller variation in time it is nearly flat you can clearly see there is slight
variation, where indicated colors indicate the signal strength whereas, still in the
frequency domain we have a certain amount of fluctuation.

Now these fluctuations are dependent on two important parameters; one is the coherence
bandwidth and another is the coherence time. Coherence time tells us the time duration
over which the signal strength would remain more or less constant and coherence
bandwidth would give us the bandwidth over which the signal strength would remain
constant in the frequency domain. So, now, if the channel is having very high Doppler
condition then T c is low.

So, if del f D is high then T c is low, similarly if tau max is high then B c is low and vice
versa and reverse. So, if it is low then it is high and if tau max is low then this is high and
there can be other combinations also; that means, there can be cross combination; that
means, this is high and this is low and the other; that means, it is tau max is low and f D
is high. They can also be such conditions because of the propagation scenario.

So, now, when you have this if coherence time is small the signal would fluctuate faster
in time and if coherence bandwidth is small signal would fluctuate faster in frequency.
So, in frequency there will be much faster fluctuations, in time there will be much faster
fluctuations and if the coherence time is large in time domain it will fluctuate slowly, if
coherence bandwidth is large in frequency domain it would fluctuate slowly so that is
what is going to happen.

So, now, what we will discuss is if what is the effect of such a thing on different tile
size? So, one can increase the tile slice or number of slots for allocation in time domain
or one can do the same in frequency domain or one can do the same in both the domains.
So, basically what we are talking about how much of time window and how much of
frequency window are to be grouped together to form a resource block in order to get the
best benefit in terms of spectral efficiency.

495
So, we will see such an effect, we first show the result when if you allocate a larger
window in the frequency domain; that means, more number of resource block and do
modulation coding scheme and power on that window.

(Refer Slide Time: 27:45)

So, here what we say is suppose we group 64 sub carriers together ok, we get a certain
spectral efficiency versus SNR curve. If we reduce the sub-band size to 8; that means,
smaller window then we find that the spectral efficiency increases much beyond that of
64. Now this is the case when there is low diversity condition, low diversity condition
means that the signal strength remains flat over a certain window in frequency and over a
certain window in time; that means, one can do link adaptation over smaller chunks of
our concern and chunks you cannot make lesser than certain numbers.

So, we have said that this number is twelve in case of LTE and in case of 5th generation
we had done the study for the entire range from 8 to 64 we have presenting here only two
extreme results. So, all other results would come in between we are showing only two
results for the sake of ease of seeing these things right. Now if we compare this particular
scenario with another situation, where the diversity is high what we find is that there is
not much effect of changing the block size in the frequency domain.

Now why does it happen in this manner? If we go back and try to discuss and look into
this if there is lot of fluctuation in time domain and lot of fluctuation in frequency
domain in this small size; that means, this window is already getting the effect of

496
averaging the time and frequency fluctuations and one calculates the modulation and
code rate to be used as per this fluctuation. If you increase this size the average over this
entire size has not changed and hence there is not much of a benefit whereas, on the
contrary if one would look at a situation where one would see that over this window.

(Refer Slide Time: 29:53)

There is a certain signal strength and over this window there is a certain signal strength;
that means, a signal is fluctuating slowly in frequency as well as it is fluctuating slowly
in time let us say so; that means, over such a window we find that there is some flatness
a particular modulation coding rate to be chosen.

Whereas the other window one can choose a different modulation and code rate while
satisfying the individual BER constraint, this is very very important. So, this falls
directly in whatever we have discussed when we talked about link adaptation; that
means, each block is to be adapted so that the BER threshold is met you can go back to
the discussion on link adaptation as we had discussed earlier and refer to that particular
discussion for clarity on this particular part.

So, what we find is that when there is high diversity condition there is no benefit. So, if
we understand the channel well then we can adaptively choose the slot that we can
aggregate in time domain and the slot size that we want to put in frequency domain or
number of resource blocks that we want to allocate. So, this the immediate next result in

497
the time domain; that means, if we extend it in time is what we are going to show over
here.

(Refer Slide Time: 31:11)

So, this is link adaptation per 0.5 millisecond and this is link adaptation for 1 millisecond
for 2 millisecond and so on and so forth. So, as you increase the interval over which you
are able to adapt what you find is that the throughput is decreasing or reverse way as I do
it faster I am able to get a much more benefit in spectral efficiency whereas, when we are
doing it in a high diversity condition; that means, within the duration of time for the
smallest unit of block size there is sufficient fluctuation in time domain the averaging
effect is already captured.

So, the gain or change is not significant whereas, the overhead that will come in
signaling the smaller units of tiles will be significantly large. So, here again what we see
is that under low diversity condition smaller chunks of tiles are going to give you benefit
under high diversity condition larger chunks of tiles are give you going to give you the
same benefit without much modification.

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(Refer Slide Time: 32:11)

The last piece of result which we want to show is that one can think of even having very
large code block size and putting different modulations in them.

(Refer Slide Time: 32:17)

So; that means, we are suggesting that one can think of keeping the code rate fixed, but
one can take chunks of data within that code block and vary the modulation index,
instead of choosing coding and modulation scheme for each block which is different
from another block. So, this will save a huge amount of complexity at the transmitter and
receiver side while it is going to give you some benefit the benefit is what we will see.

499
So, this red one is where you adapt the power, the modulation and code rate for each
particular chunk that we are doing the link adaptation, but this result is the case where we
have a certain code rate and you are varying only the modulation. So, what we see is
that, one can get a much more benefit by using even a single code rate without much of
an effect. So, what we see is that if one chooses only a single code rate, but varies the
modulation one can still get sufficient benefit.

(Refer Slide Time: 33:25)

(Refer Slide Time: 33:35)

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So, overall what we see is that there are different combinations of schemes that to be use
and which are also supported in the 5th generation and these are some of the references
which describe all the details of these different mechanisms by which one can actually
get this get all the benefits of get all the benefits of having various adaptation. In terms of
subcarrier spacing, adaptation in terms of cyclic prefix together called the numerology,
as well as one can get all the benefits of link adaptation, by appropriately clubbing a
number of resource block, or by clubbing a number of slots, together to get the most
benefit in order to maximize the spectral efficiency.

In all this context we have identified the resources which are primary in this kind of
work which have been one of the earliest kind of work and which describes all details
that are presented in these different technologies and which are of use in the 5th
generation communication techniques.

Thank you.

501
 Evolution of Air Interface Towards 5G
Prof. Suvra Sekhar Das
G. S. Sanyal School of Telecommunications
Indian Institute of Technology Kharagpur

Lecture – 27
Waveforms Beyond 5G

Welcome to the lectures on Evolution of Air Interface Towards 5G. So, till now we have
been discussing about the various waveforms which have evolved since the second
generation and we have seen a basic structure based on which one can develop all the
different kinds of waveforms that have existed till now. And, in the previous few lectures
we have also seen how the numerology issue has started and how the numerology
solutions have to be picked; that means, the particular solution set in terms of subcarrier
spacing and in terms of guard interval.

We have also seen how if one aggregates the resource block the different kinds of benefit
that one can get. So, today our objective is to briefly go through some of the earlier
things as well as most importantly look into waveforms which have been contending
waveforms for 5G. So, there has been lot of work on different waveforms which have
competed towards the 5th generation, but because of one primary reason that is
backward compatibility.

These waveforms could not find an opportunity, but the flexible numerology which we
discussed earlier fits into the framework very nicely while supporting all the new
requirements. Whereas, given their capabilities it is very very important that we
understand them and with the new flexible framework that has evolved and been
accepted in the 5th generation, we firmly believe that there would be lot of opportunity
for these new waveforms to possibly getting accepted as the next generation waveforms
in the upcoming releases of 3GPP or maybe upcoming version of the mobile radio
communication systems.

So, with this brief we get into the waveforms beyond 5G because as of now they are not
part of 5G although they were designed and people are trying to make them being part of
5G and as we have said earlier that it is possible that in the next few years so that it gets
so it is getting a window before it’s again becomes part of contending technology.

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So, in that period we believe these waveforms will become mature and they would be
able to bring in more capabilities and adjust themselves within the framework. So, that
they provide all the benefits while maintaining backward compatibility.

(Refer Slide Time: 02:39)

So, one of the important requirements of 5G had been low out of band radiation so that
means, within the band of transmission it should be good signal and beyond the out of
band emission should be as low as possible with as narrow transition band as possible.

So, that is one of the key requirements and if we look at what are the problems with
existing systems. So if there is a high out of band, adjacent channel interference would
be high and with the low out of band adjacent channel interference would obviously
below and this is very very important because what we have kind of not discussed in
very great details, but what we have seen is that separate bandwidths can be allocated
and there is very important part which is called carrier aggregation which we are not
discussing.

503
So, in carrier aggregation, suppose there is a certain band of frequencies available and a
particular service is operating in that and another band of frequency and is available and
the service is operating in that, these two bands could be aggregated to provide the same
kind of service this is one thing, but now look at this that the other side of the same
picture is there are some bands which remain in between, this is very very critical.

So, if one has to utilize all the bands in the most efficient manner one should have
spectrum properties of multi-carrier signals which are expected to be as close to Nyquist
filter characteristics as possible that is what is desired, in that case one can utilize things
better. Also if we look at the NR framework we have seen that different numerologies
can coexist simultaneously right so; that means, there could be narrow bands, there could
be mid-band and there could be wider bands, so, they will have different amounts of
interference against each other.

So, again if these bands have narrow transition band or they have a sharp transition band
and there is very less amount of power going into the adjacent channels; obviously, the
performance would be excellent. The second very important property that is desired is
that the peak to average power ratio must be low and we have also discussed the
influence of having low peak to average power ratio.

It helps us getting a better battery life at the user equipment side or providing more
range, so over all there is lot of benefit. And why are these two important considerations
and why have different waveforms being considered? If we look at OFDM the primary
mode with which OFDM is usually discussed in public is that it has a rectangular pulse
ship, which gives rise to a sinc spectrum which we have been drawing also right.

So, in a sinc spectrum the outer band radiation is pretty high it is not desired; however, I
would like to mention an important point which is mostly absent in publications
academic publications is that this we have slightly mentioned earlier that there is a cyclic
prefix in front of the OFDM symbol and when the symbol goes out usually there is pulse
shaping that happens without pulse shaping no signal is going to go out that is for sure.

So, this pulse shaping that happens this is able to reduce this and obviously, it is not a
true rectangular and hence one can expect a lower out of band compared to the idealistic
rectangular pulse that obviously happens but still better performance is desired. The
other aspect which one can think of is the PAPR because we have discussed heavily

504
when we were discussing OFDM that the signal xn is composed of sum over X of k
where k is the subcarrier index s is the OFDM symbol index e to the power of something
something.

So, as many numbers that we add up the peak to average power ratio grows right. So,
peak to average power ratio grows all the disadvantages that we have mentioned comes
in. So, one desires a multi-carrier method, the moment you have multi-carrier you cannot
live without peak to average power ratio by default. So, what it says is that if we can
have no PAPR and yet have multi-carrier then things would be wonderful.

So, this is the kind of requirement and we will see some solutions which do really
provide some great advantage. One of them we have already seen that is SC-FDMA
which is nothing but DFT spread OFDM and hence there is already a mechanism by
which things can be reduced, there could be other mechanisms also, and all these without
any additional information being sent over the channel. So, what is very very critical
without side channel information that is also important. Because if you are sending side
channel information there is a huge increase in extra bandwidth or in other words
reduction in spectral efficiency ok.

Ultra Reliable Low Latency Communication we have seen that URLCC is the
requirement URLLC rather yeah and we have already seen how this is supported and
what we mentioned at that time is also included over here that as your subcarrier
bandwidth increases right initially it was something small, initially subcarrier bandwidth
was small.

So, hence the frequency fluctuation which was restricted to smaller band it is now
desired that the frequency fluctuation is remaining constant over a larger band, but that
may not be true because of the propagation characteristics of the channel. So, non flat
sub-bands may come in so one should find better mechanisms to cope with such a system
any such facility. So, it may not be possible to allow OFDM to do that.

So; that means, this non flat sub-bands is a requirement, so if we have mechanisms
which can handle this at the different that would be wonderful. So, next is enhanced
mobile broadband of course, we require very high data rate, so one of the problems that
OFDM has is the cyclic period now looking at cyclic prefix from the other side. Cyclic

505
prefix has helped us in overcome ISI, but look at this every OFDM symbol there is a
cyclic prefix in front of it which is a necessary evil it is an overhead.

So, now since we are happy with some techniques which can address some of the earlier
problems, next stage would be to go beyond whatever it is already provided and come up
with even better mechanisms. So, as you may know that there are other mechanisms
solutions against CP in OFDM, but we may explore mechanisms which can reduce this
CP overhead.

Along with that there should be MIMO compatibility also so if we come up with
schemes, but they are not compatible with MIMO then again they are pointless. So, these
are some of the important considerations when waveforms are usually design, usually
from the earlier generation to the next generation and this was especially valid for the 5th
generation system and since things have not been in favor of the new waveforms, but
since it is very important to understand them because the next level of activity should be
around these so we should take a look at all these requirements.

(Refer Slide Time: 10:54)

So, we have already established that that low latency is a very important case and we
have also discussed like how things have happened and amongst the various things what
has played a very important role is the short TTI; that means, transition time interval
which is reduced right and then the next question is can it be made even smaller.

506
So, the moment you reduce the transition transmission time interval what we find is that
OFDM symbol duration decreases, as a result of which this subcarrier spacing increases,
if subcarrier spacing increases then what happens is suppose your subcarrier spacing is
like this it’s some imaginary picture, this is delta fsc and the channel fluctuations are like
this is the channel so mod of H f squared let us say all right.

So, under this situation addressing the frequency selective channel within the subcarrier
spacing becomes a problem because originally OFDM was designed to handle flat fading
and there was a single tap equalizer. So, now if one has to get back and use multi-tap
equalizer then all the advantages of OFDM are gone. So, one would like to have some
better mechanisms to address this.

(Refer Slide Time: 12:12)

So, effectively it’s boiled down to earlier more or less all the subcarriers so these were
subcarrier spacing and the fluctuation was more or less flat across each of the subcarriers
whereas, you have a situation like this and hence some solution is required to address
this.

507
(Refer Slide Time: 12:30)

So, the different waveforms that were under consideration or that are still under
consideration for the next generation are some forms of multi-carrier, there are some
form of multi-carrier communication and they could be filtered there could be precoded
so various forms have evolved. So, what we find is that one set is coming under the pulse
shaped OFDM.

So, this is pulse shaped which simply means that earlier we were talking about
rectangular pulse and now probably you can think of some other pulse shape which
could be of value. Now the moment you go for any other pulse shaping in multi-carrier
what happens is that peak to average power ratio increases if nothing else changed
nothing else changes, but only the pulse shaping changes another factor that happens is
the orthogonality also is lost right.

So, these are some important issues that come into play and if one has to allow this to
happen then this has to be done in a very specific way. So, windowed OFDM is one of
the mechanism, filtered OFDM is another mechanism and universal filtered multi carrier
is another mechanism which is very similar to OFDM. Some other forms which are not
just pulse shaped OFDM are new waveforms amongst the new waveforms so this is the
set of new waveforms, one is the Filter Bank Multi Carrier FBMC. Then there is another
one generalized frequency division multiplexing.

508
So, these are the two waveform people have been working upon, so one set of people in
working on FBMC another set of people have been working on GFDM to improve upon
their raw baseline architecture and make them acceptable towards a practical
transmission mechanism. While on the precoded side, this is the new waveforms we find
DFT spread OFDM is already available, this is already present no issues about it and
single carrier FDE is also an extreme case of DFT spread OFDM in that case this is also
available in some sense.

So, we will in this lecture and probably on the next lecture also depending upon how
well we progress. We intend to cut across these different waveforms architectures, we
have already seen this particular waveform we have already seen, this particular
waveform also we have seen a basic OFDM structure we have seen. So, we are
remaining to see the rest of them.

(Refer Slide Time: 15:17)

So, all these waveforms what we consider is they are variants of OFDM one can also
think of them in variants of some basic multi-carrier. So, thinking them as variants of
OFDM may not be very well accepted by everybody, so OFDM as if we call it one of the
critical factors is the orthogonality factor right. So, this orthogonality factor is not carried
across when we go to different waveforms.

So, although we claim that or we say we do not claim we actually say that it can be
viewed as variants of OFDM one may not accept that and one can even go by their own

509
thinking and case a that no let it let there be some multi-carrier structure which is a
fundamental and which can be used, but what we are simply saying is that since OFDM
is very easy to understand and it has very simple architecture one can think that there is a
baseline and there is a variation so there is no conflict in these; in these thoughts as such
ok.

So, directly from OFDM we will find that single carrier FDMA fits in we have already
discussed this through DFT spread, this is also DFT spread OFDM and single carrier
FDE is a direct consequence of making DFT size being equal to the IDFT size. So, there
is not really much difference although SC-FDE is a true single carrier system that is that
is the pure difference.

The next set is the filter bank multi carrier so what we see is there is this multi-carrier
business in it and the difference is that each of the carriers are filtered. So, that is why
you have a filter and you have a bank indicating there is a whole set of filters each one
for each of the carriers so that way it is kind of a variant ok, but this process destroys
some of the properties of OFDM, but brings in certain other advantages.

The next set is the generalized frequency division multiplexing, so the frequency division
multiplexing nature is maintained, this is also a kind of frequency division multiplexing,
but here this is not a frequency division multiplexing this particular method, but one can
handle it in the receiver from frequency domain perspective and then we have filtered
OFDM and windowed OFDM. So, since there is lot of similarity we think OFDM is at
the core of it and one can think of variations about it ok.

510
(Refer Slide Time: 18:00)

So, we have already discussed about the 5th generation waveform structure so we will
not discuss the details of it, these pictures simply explain whatever we have talked
before; that means, different subcarrier spacing can be used and they can coexist there is
no problem in coexistence also.

(Refer Slide Time: 18:08)

(Refer Slide Time: 18:13)

511
And the other important facts that we have also stated is that these are optimized version
of OFDM with scaling, we have already talked about this there is a common flexible
frame structure as indicated by this particular picture as well as one important thing that
has come into play is the use of newer bands and newer techniques amongst which the
millimeter wave and massive MIMO are two very importantly distinct things which have
come in and we will get an opportunity to see them and I would also like to mention
although this has not been explored much.

But the waveform structure for these specific set of things are also very important to be
looked into, very specifically if one things of millimeter wave communication single
carrier till now has very good properties in this particular situation; however, making
multi-carrier work effectively and efficiently needs to be investigated probably better
solutions can be found under these conditions ok.

So, we have already discussed about the various structures in the previous lectures, so we
need not explain them any further it’s just a quick view. So, that you can remember some
of the things and we have also pointed out a whole set of references so will move beyond
that.

512
(Refer Slide Time: 19:34)

So, now, we take a look at the windowed OFDM architecture. So, in windowed OFDM
this is the useful part. So, from here to here is the useful part of OFDM signal and there
is a section which is copied as you can clearly see it is copied into the front. So, when it
is copied into the front it is copied as the cyclic prefix, but then within that one would
designate a guard section ok.

While one would also recognize that this portion is a copy of this portion rather this
entire section is a copy, but what we find is that the useful section is this from here the
useful section starts from here goes up till here right. So, there is a certain extension and
the both front and well as well as at the backside; that means, if this is the original useful
signal part we extend the signal on the front as well as on the back in a circular fashion.

So, what you see is that the circular symmetricity is maintained so if you stretch on this
side you will find that you are back from here you will find that you are back into this
section right that is something which is interesting as well as if you go from the other
direction then you are again back in the front part. So that means, when you are
stretching on that on the on the on this side you will find that you have this section and
this section coming in as we have already discussed in the cyclic prefix part all right.

So, now on top of this there is some kind of windowing is done in time domain. So,
windowing operation means if there is a multiplication of this kind of a window, so when
you have windowing it would result in a change in the spectral occupancy of the signal.

513
So, otherwise if the spectral occupancy of OFDM signal were here right. So, this what I
have drawn is slightly higher let me clean it and trace the exact line.

So, this is the one for OFDM this particular point is minus 30 dB what we find is that the
windowed OFDM as has been depicted and has been calculated falls much faster and in
the in the sideband it can easily obtain a minus 60 dB of adjacent channel interference.
So, by this mechanism one can reduce the adjacent channel interference significantly and
with an appropriate trade-off; that means, one is wasting a certain amount of bandwidth,
but one is obtaining a significant fact significant amount of adjacent channel reduction in
adjacent channel interference.

So, this is a traditional method only thing is that it’s matters whether its being to be used
or not. So, there is I would say there is not a hugely new thing only the structure there is
slight change in OFDM and it can be having a lot of backward compatible compatibility
with other systems. So, at least one of the properties can be improved because of this
mechanism.

(Refer Slide Time: 23:30)

So, in windowed OFDM there is a particular mechanism that is suggested for receiver
operation so that means, and on the receiver side one has to window the received signal
and one has to change over; that means, one has to bring the receiver part, one has to
bring the opposite part; that means, from the front to the back and from the back to the

514
front add these parts in order to reduce the interference between the multiple users and
process the signal.

So, this way one can improve the performance by reducing the adjacent channel
interference with such a windowing mechanism.

(Refer Slide Time: 24:12)

The next particular structure we can look at is a filtered OFDM so since we understand
OFDM this is a this is not a very very huge modification from OFDM. So, in filtered
OFDM instead of windowing one can use a filter impulse response to filter the OFDM.
So, both can be thought of as kind of duels of each other.

So, when we do a windowing in frequency domain one can think of kind of doing a
convolution in the time domain because windowing in frequency domain is
multiplication in frequency domain convolution in time domain is the dual of that. So, if
one does windowing in time it is convolution in frequency, if one does windowing in
frequency it is convolution in time.

So, whenever we are talking about the impulse response in time domain one would
indicate that there is some kind of windowing in the frequency domain. So, the
advantage of windowing in the frequency domain is that you can actually create a
spectrum of the desired characteristics, but of course, with within the limitation of
practical constraints.

515
So, now, if one intends if one is interested to have very very sharp cut-offs then what
happens is that the impulse response becomes long and if the impulse response becomes
long, then it stretches quite a bit into the next OFDM symbol and it can be even larger
than the cyclic prefix of the next OFDM symbol it can result in ISI.

Now if so; that means, if one has to avoid ISI, one has to restrict the channel impulse
response length to a certain maximum value which would be useful because beyond this
channel impulse there is also the channel impulse plus one should also consider the
channel impulse response of the channel of the of the wireless channel. So, together if it
is less than the cyclic prefix one can control ISI otherwise ISI will come into play.

So, one has to decide how which one is more important is out of band more important for
the particular application or ISI is more important, if one is having worse ISI then one
has to put extra length of cyclic prefix or guard interval and has to handle it. In either of
these two cases what we find is there is a trade-off with bandwidth and out of band
radiation and this is again standard methods being applied to OFDM.

(Refer Slide Time: 26:53)

516
The next important class is the filter bank multi carrier. So, we have almost reached the
time line for this particular lecture, but will briefly introduce that before stopping over
and we will continue this in the next lecture. So, in the filter bank multi carrier the first
most important thing I would like to point out is the reference which has been given here.

So, as we have been doing in the earlier case especially for the numerology scenario we
are provided with the earliest reference work which has which we have been doing since
2004, 2005 onwards and we asked you to look at the reference, here also in the same
manner we asked you to look at the genesis or the reference because usually what we
find as researchers in such institutions that there is a general tendency of looking at very
recently literatures and not even going beyond that.

But you will often find that lot of work which we are doing today has its roots back to
much longer time in history. So, this particular work you can find it dating back to 1966
right, so this work is from nineteen sixty six it can be found in bell labs technical journal.
So, so what I am trying to point out is although this is fighting for its place in 5th G and
probably it will keep fighting for its place in the 6th generation hopefully around 2030 or
maybe sooner than that original things had happened around 1960’s.

517
So; that means, the it’s around let us say 70 years from the time that these things have
been investigated thoroughly we are these things are becoming going to be practical. So,
so this has a lot of advantages and disadvantages also the reason things have been
delayed because of the disadvantages and the reason why this has been attractive is
because of its advantage. So, let us look at the basic structure before we close today’s
lecture.

So, there are different filters for the different carriers. So, as you can see first filter
second filter Nth filter. So, as if there are N parallel transmissions which are similar to
the multi-carrier right. So, in each of the multi-carriers what you will find that there is
also e to the power of j alpha 1, e to the power of j alpha 2, e to the power of j alpha N
indicating the change over in the different frequencies and these A 1 and A 2 and A N
indicate the amplitude gain factor of this particular filters right.

And they all add together so overall we do not see any difference with the basic structure
as in OFDM; that means, there are parallel sub-carriers coming in, each subcarrier
choosing a particular constellation point from the constellation which is to be used right
and there is no such restriction that all the constellations have to be the same they can be
different constellations, then there is a channel and finally, there is addition of noise one
can think of at the receiver and the reverse processing has to happen at the receiver.

So, the fundamental difference with OFDM is that there are filters on each of the carriers
and there is a whole bank of filters and hence it is a filter bank and they appear as
multiple carriers operating at different frequencies. So, there is a multi-carrier system
and the advantage is that one can design these filters in such a manner that this transition
band is very sharp and yet one has this multi-carrier structure.

So, although there is multi-carrier structure overall one can be having a very tight
spectral characteristics by virtue of which and highly efficient system can be realized,
not only that one can also shape the characteristics of each of these sub-carriers such that
they can made more resilient to frequency offsets which we find is one of the critical
constraints of orthogonal frequency division multiplexing system. So, with this we bring
this particular lecture to a stop and we will continue on filter bank multi carrier in one of
in the next upcoming lecture.

Thank you.

518
 Evolution of Air Interface towards 5G
Prof. Suvra Sekhar Das
G.S. Sanyal School of Telecommunications
Indian Institute of Technology, Kharagpur

Lecture – 28
Waveforms Beyond 5G ( Filter Bank Multicarrier )

Welcome to the lectures on Evolution of Air Interface towards 5G. So, we have been
discussing several waveform technologies and we have presented the one of the earliest
forms of the 5th generation waveform which is called the 5G NR and we described it in
terms of variable subcarrier bandwidth or adaptive subcarrier bandwidth which we
discussed earlier, as seen in this particular picture.

(Refer Slide Time: 00:40)

We have described various forms of it and then we moved across to the different
architectures of realizations thereafter we would shown the different gains.

519
(Refer Slide Time: 00:54)

And we also started discussing about the various other forms of OFDM which are not
typically yet part of standards, but as the course requires that we also discuss things
which go beyond the existing set of things.

(Refer Slide Time: 01:12)

So, we discussed windowed OFDM as one of them and we described how it is done in
the previous lectures this is just a summary.

520
(Refer Slide Time: 01:17)

We have also talked about filtered OFDM and we have also described the issues and
associated factors with it. And primarily these are all variants of OFDM and these
filtered OFDM if we look at it or the windowed OFDM whatever was there one may
consider the fact that that typically any OFDM system. I mean probably this I had
mentioned earlier also is one where one considers a rectangular pulse shape. But if you
take any commercial OFDM system and you look into the standards you will find that of
course, this is the CP, that there is some kind of a windowing which naturally happens
without which you cannot generally send out the signal.

So, although these have been proposed in literature as separate techniques, but these
those are all pretty similar to OFDM and minor variations or probably more realistic
implementations of things especially the windowed OFDM, but when we talked about
filtered OFDM this is a again a slight variation where you do time domain filtering
which is equivalent to having a window in the in the frequency domain. So, these are
duals of each other in one case you do windowing in time and which appears as filtering
in frequency the other case is filtering in time which appears has windowing in
frequency.

So, then after this we move on to the next set of waveforms as we had said earlier, that
these waveforms as we will be discussing now onwards are future generation waveforms
and that these waveforms have not yet been accepted, but they have a high chance of

521
getting accepted in future generations and one strong reason is that they were contenders
for 5G they many people worked on it and they were discussed heavily. And for some
various reasons it was decided that these waveforms probably require even more
maturity, especially with respect to backward compatibility and hardware complexity
and realization factors.

So, variant of OFDM which is the adaptive subcarrier bandwidth or variable subcarrier
bandwidth is accepted one prime reason was it’s prime resemblance with OFDM and it
could be controlled or realized by simply changing of parameters and hence the new
name was assigned numerology. So, now, we move on to other waveforms which are
important to be learnt to be to be looked at as future generation versions of multi-carrier
systems.

So, what we have here is a multi-carrier structure we described earlier how these
different schemes do come under overall group of multi-carrier combinations for multi-
carrier communications and we are talking about filtering then there is a bank of filters.
So, let us look into the details of it.

(Refer Slide Time: 04:15)

522
So, in case of filter bank multi-carrier what we see is that there are different carriers. So,
this could be first carrier, this is the second carrier rather these are sub-carriers if you put
the name sub-carriers, then it makes more sense and this is the Nth carrier. So, these are
all are typical like the frequency division multiplexing systems and in case of OFDM we
have said that there is a orthogonality factor which comes in, here things are slightly
different.

And in case of OFDM we have also said one of the factors which contribute to
orthogonality is the rectangular pulse shape along with a CP in front of it but here things
are going to be different then what we had discussed earlier. So, amongst several reasons
why these are considered are the OFDM because of it’s rectangular pulse shape in time
domain, in frequency domain generates a sinc which also we had mentioned and sinc as
you know the sinc function has pretty high side lobes. So, there is adjacent channel
interference which is pretty strong, but the good part is there is orthogonality, but again
the reverse side of things is that if you lose orthogonality then there is a big problem.

And that is one reason which gave rise to adaptive subcarrier bandwidth or variable
subcarrier bandwidth and with got the name numerology in or 5G NR right. Now those
are all good, but still they have their own issues with respect to this adjacent channel

523
interference which is still not addressed although the ICI is addressed in this mechanism,
but this still remains to be addressed.

So, one of the competing waveforms the filter bank multi-carrier as it is known what we
see is that, each of these carriers that we have identified carries these complex
constellation points or real constellation points these are basically constellation points or
data right picking from the constellation and each of them are filtered. So, what you see
is that this is the spectral shape of each of the carriers right.

So, each carrier is spectrally shaped and sent out and they are next to each other there is
overlap as you can see there is overlap between the sub-carriers and each carriers’ filter
is designated as A with a sub-index and there is f indicating the frequency domain and
there is a phase component associated with it e to the power of j alpha sub 1 f. So, in
general it is A n you can say it’s the n-th one f e to the power of j alpha n of f right that is
the general form, but this is the amplitude response and this is the phase response and all
of these get added together and they get added together and then they are sent out into
the channel, when it goes into the channel the channel is also represented as a filter.

So, channel can be represented as a filter this is the frequency domain representation of
the channel noise gets added at the receiver end or AWGN is also present with that and
then you have the receiver processing. So, this is a generic structure in case of OFDM
you can think of the filters as the ones which have a kind of sinc structure, but here it’s a
more general one and one needs to find about these things.

So, although these are contending techniques for the 5th generation we have pointed out
or have identified the literature which is the starting point of these things this is the 1966
paper were by Robert Chang and the title is synthesis of band-limited orthogonal signal
for multi-channel data transmission. So, again we are trying to point out the fact that
although they are newly termed as filter banks and their 5G and they will get new names
it’s very very important to go back to the starting point to the genesis of where these
things started. So, that you get a sound foundation of how to build such systems.

So, we have highlighted the earliest paper it is in bell labs technical journal 1966 you can
download the paper and have a look into the details of it we will present a summary of
what is given there. So, in all of these now the question that remains to be addressed is

524
what should be the filter design? So that the received signals remain orthogonal; so now,
the whole problem or the question gets framed.

In OFDM, it is made orthogonal by virtue of rectangular pulse shapes and cyclic prefix
and integer multiple of waveforms. But here the question is in terms of the filter design.
So, that the overall structure remains orthogonal.

(Refer Slide Time: 09:47)

525
So, what we see is that the impulse response is given by a i t for each of the filter and the
channel impulse response is given by h t and real data symbols are indicated by d m k for
the time frequency slot indexed by m comma k right. So, the channel output in time
domain can be given as u i of t that is the i-th sub-carrier here using the i-th filter or the i-
th sub-carrier and that is a convolution of the filter impulse response and the channel
impulse response.

Now the conditions that are thrust into this by virtue of the requirement to find signals
the filter design so that the signals remain orthogonal is translated to expression. So, for
the ISI free transmission we see that the output which is u i of t u i of t what we have
over here and u i of t minus kT. So, remember k indicates the frequency index sorry k
indicate indicates the time shift and i is the subcarrier index.

So, what we find is that this should entire thing should go to 0 for ISI free transmission
right and; that means, two symbols on the same subcarrier both are i i-th subcarrier
shifted in time; that means, two neighboring symbols or any other symbols when it’s
integrated turns out to be 0; that means, no one has a component on the other one and
this is true for every i and for values of k equal to plus minus 1 plus minus 2, k cannot
take a value of 0 because then it would mean this thing and that makes no sense. So, k
takes plus minus 1 on the either side of the signal so there is no inter symbol interference
at all. So, that is one criteria for orthogonality.

The other criteria for orthogonality as we see over here is the one for ISI free
transmission. So, yeah so that is for ISI free transmission just a second, yeah for ICI; that
means, Inter Carrier Interference free transmission, so; that means, you do not want
interference in time domain, you do not want interference in frequency domain and
hence you are you require the whole thing to be orthogonal.

So, here when we translate these requirements of having orthogonal orthogonality, we

have already translated one in the time domain if we look at the frequency domain, we
find we have used over here u i of t right that is the output from the i-th channel that is
over here and u j which is the neighboring or any other value of the sub-carrier index t
minus kT right.

So, this is the setup that we have taken integrate from minus infinity to infinity dt should
be equal to 0 that is what is written over here for all i and j and i not equal to j this is

526
important; that means, i and j should not be equal; that means, you are not taking the
same subcarrier, hence you are talking about inter carrier interference right and for
values of k this includes 0 as well and so for values of k equals to 0 plus minus 1 plus
minus 2 and so on.

So, if you take the value of k equals to 0 you will be getting u i of t and u j of t integrate
minus infinity to infinity dt being equals to 0. So, this is ICI on the same time domain
symbol block, but if you take another value of k plus minus 1 you are taking the i-th sub-
carrier and jth sub-carrier of different symbols. So, u i of t and u j of t minus kT, so that
means, two different symbol.

So, that means, there is one carrier here in this time block another carrier in another time
block, so there is no inter carrier interference between them as well. So, that encapsulates
the overall orthogonality requirement criteria for this particular system. So, now, we
have stated the problem the rest of the part is to find out these filters.

So, once these filters have been identified which meet this criteria then you have actually
solved this particular problem. So, this is the overall structure for filter bank multi carrier
communication system, it’s a more generic than OFDM and that would also satisfy the
requirements as it’s given over here.

(Refer Slide Time: 15:07)

527
So, what we find is we are not solving it we are just simply taking it from that particular
paper and for the sake of description and understanding the things. So, Ai of f which is
the amplitude response of the filter, so what we see here is that A i of f is the amplitude
response right this A n indicating the n-th filter.

So, the solution that has been brought out in that particular paper is that A i f squared
times H f squared and H f is the channel transfer function should be equal to C i which is
some arbitrary constant and plus Q i of f which is greater than greater than 0 because
these are all squared terms right, for a range of f which lies between f i plus minus f s as
indicated over here and it is 0 otherwise; that means, outside this range it should be equal
to 0.

Now C i is an arbitrary constant, but what defines this particular product is Q i of f which
is the shaping function and it is said that it should have odd symmetries about f i plus f s
by 2 and f i minus f s by 2, it’s an outcome and we are going to use the outcome and we
are going to see how does it look like.

So, if we look at the amplitude, so the amplitude versus frequency plot this is the
frequency plot this is the amplitude plot. So, at f s plus f by 2 and f s minus f s by 2, we
find that Q of f has odd symmetry right. So, this is what is the requirement and
accordingly A i H f A i squared H f squared, where A i is the filter transfer function of
the transmitter for the i-th subcarrier and H f is the transfer function from the channel.

So, the product squared would have to look like the shape as given in this particular
picture right, so it has to take the shape and then you get the orthogonality criteria. From
this if you take the square root of this then you are going to get the product A i of f H f A

528
i times H f; H f would be translating to the expression or to the to the filter whose
amplitude versus frequency response would look like this right.

So, this overall summarizes the characteristics that are required, so if you design your
filters with such characteristics then one can get orthogonality. Now one should keep in
mind that this requires the knowledge of H; that means, the channel ok. So, if we go back
and look at this whole setup we want the received signals to be orthogonal this is a
criteria which one has to pay attention whereas, we are not restricting ourselves to
orthogonality criteria over here. If we had restricted ourselves to orthogonality criteria
over here, then we would not have taken the channel into account and we could not have
commented on what would happen when the signal would go through such a channel.

So, this is a more generic one which says that given a particular channel now can you
design the signal such that they are orthogonal at the receiver end. Now if one wants to
get back to the situation where wants to find the orthogonality over here, then one can
simply set the channel to be an ideal filter and one would get the criteria required at the
transmitting end right that is that simple. So, this is more general and it is useful if I
know the channel characteristics and it is especially useful, if the channel is going to
remain constant over a certain duration of time.

(Refer Slide Time: 19:06)

529
So, there are some more criteria that that comes up it also says that C i plus Q i of f
which is basically here as you can see over here C i plus Q i of f which defines the
amplitude function, amplitude squared of the filter as well as of that of the channel and
the product of that multiplied by C i plus 1. So, this is C i plus 1 and Q i plus 1; that
means, the neighboring one is an even function about f i plus f s by 2 right.

So, what we see over here is the response of Q C i plus Q i of f; that means, it is given
over here it’s written over here the product function is described above has to be a even
function around f i plus f s by 2. So, around this it is an even function so that is another
condition.

(Refer Slide Time: 20:02)

And finally, we get to see that the phase should be shaped such that alpha i which is the
phase of the i-th filter minus alpha i plus 1 that is the phase of the neighboring one is plus
minus pi by 2 plus gamma i of f where gamma i is an arbitrary phase with odd symmetry
about f i plus f s by 2 right. So, now, if you look at the phase then the phase will have a
structure which is represented by this picture graphically it would look something similar

530
to this and you can have other phases also depending upon the values of gamma i and
over all these criteria or these conditions if they are met successfully then one can satisfy
the ICI free and ISI free transmission schemes.

Such that, the received signal at the receiver remains orthogonal for a particular given
channel transfer function right. So, now this clearly means that if we have a wire-line
channel the channel remains constant for the entire duration of the communication link
provided we are having a circuit switch connection or if we think of point-to-point
connection one point to another point for the entire duration of the communication this
channel transfer function should remain typically constant, in that case this is easily
realized.

In case of wireless links there is a problem because this H of f should ideally be written
as H of f comma t which indicates that the channel transfer function fluctuates with time
and hence these schemes to be realized in it’s exactness as described just now is valid as
long as we maintain the coherence time constraint we had seen such a constraint earlier,
when we talked about the link adaptation mechanisms that are typically used.

So, now if we add this kind of adaptivity into the system this can also be considered as
one more dimension of link adaptation, whereby you would like to get a signals which
are orthogonal at the receiver for a given communication channel. So, which satisfies
both ISI free as well as ICI free communication, ICI and ISI free transmission
requirements.

531
(Refer Slide Time: 22:42)

So, now typically if we put everything together the amplitude response would look like
as we have given over here and the phase response would look like this for the difference
of carriers, what we see is that although we described initially it is a frequency division
multiplexing mechanism typically in a frequency division multiplexing mechanism we
had said quite some time back that one would have to put some kind of a guard interval
between them a guard band which is a wastage which is not used for anything other than
reduction of inter channel or adjacent channel interference.

Here we find that there is overlap which is allowed between the neighboring channels,
but the filter coefficients are designed in such a manner that there is ICI orthogonality
ensured as well as ISI both go to 0, if we use appropriately designed filter coefficients.
Of course, points to remember that H f is supposed to be known, if H f is not known and
one is using ideal then the transmitted signal would be orthogonal, but once it passes
through an unknown channel there is no guarantee of such orthogonality criteria and
results could be quite away from expected values.

532
(Refer Slide Time: 24:08)

So, then we move on to see certain transfer functions of the filters or the gain versus
frequency plot for different pulse shapes or different filter structures and what we have
seen, what we are seeing over here are the root raised cosine which is a standard thing
which we all know pretty well sorry this yeah this is a root raised cosine which is pinkish
color, which is slightly difficult over here to distinguish, but we will trace that.

Then we have the square root raised cosine right which is again common thing which we
get. Then we also have the Gaussian which is dashed line and we also have another one
which is known as the PhyDyas filter. So, this PhyDyas filter is an outcome of one of the
European funded research projects and they have come up with filter characteristics
which are very much likely to be used in such systems which have a lot of good
properties.

So, we briefly discuss this what we find is that the root raised cosine which is a little bit
pinkish as we can see over here, the out of band I mean if we look focus in this picture
the inset picture if you look at the inset picture and let us take the appropriate color to
help us yeah let us let us take this red color instead and we trace it. So, this is this
particular one is the one for the raised cosine, this is for the raised cosine right and what
we can also see is that the raised cosine envelope for out of band is as per this right, so
which is significantly high or the highest amongst the related ones that we have
considered.

533
Then as we move to the root raised cosine, I will use the brownish dark red color and
what we see over here is the root raised cosine is there as we follow with the marker
right which is very much close with the raised cosine for the main lobe part, but we can
identify the distinction, so here is the root raised cosine and here is the raised cosine. So,
there is a gap in that and if you look at the adjacent channel or out of band the envelope
would be here which is better than that of the raised cosine as we can see over here.

Then we go to the Gaussian so for the Gaussian we again see that the out of band is the
best and in fact, it is the best filter that one can think of with a pretty narrow the main
band, as you can see the main band is here right the main band is here. So, it is one of the
best possible filters, but it’s one of the ones which is pretty large time domain impulse
response, so it’s usually not preferred from that perspective.

Whereas, if you look at PhyDyas it is a tradeoff between all of these and again if we try
to trace it, what we will find is that the PhyDyas which is a black one is here which is
lying in between them the PhyDyas filter characteristics is lying between them and here
the envelope goes there the out of band. So, which is worse than Gaussian, but it is better
than the raised cosine and root raised cosine as we can clearly see right. So, this is this is
how you can pick the filters design your filters if they satisfy the previous criteria you
are done.

(Refer Slide Time: 27:55)

534
So, what we see over here or what we summarized is that it is shown that for known
channel; that means, if the channel is known, transmitting filters can be designed such
that the received signal is free of ISI and ICI while attaining maximum possible baud rate
signaling rate; however, the system is designed for real data symbols only right of
course, you can change it for complex data symbols and what is one of the things that we
are going to see next, in the next lecture.

So, what we summarized is that if we want mechanisms which are multi-carrier

mechanisms, but they are not OFDM, but they have there some other ones and the
special properties that we want in them or the ones where we have good out of band
signals; that means, less adjacent channel interference then we have to go for structures
which is usually termed as the filter bank multi carrier, the genesis is given in this
particular reference where each subcarrier is filtered and there is criteria for designing
the filter coefficient which provides no ISI no ICI given a channel, such that there is odd
symmetry about a certain frequency position f i plus f s by 2 minus f s by 2 with the
product of the channel transfer function included with that of the filter.

And there is even symmetricity again with the product of the channel and the filter and
as well as there is criteria on the phase which completely defines the filter and hence one
can attain structures which look like this, so, as to attain orthogonality even under
transmission through a channel provided the channel coefficients are known. So, this
technique one of the problems of this technique is the receivers are pretty complex
people have been working on low complexity receivers, enough techniques have to be
developed on low complexity MIMO mechanisms which can comfortably work with
them.

But the biggest advantage is that you can really shape the filters such a way that you can
use really narrow bands of available channel spectrum. So, that the desired signal can be
sent through such narrow bands of channel, you can also group larger sub-carriers
together and they can be sent through and under all conditions you can maintain
orthogonality at the receiver. So, we bring this discussion to an end over here in the next
lecture we will start talking about another transmission mechanism which was also a
contender to 5G and the remains enough work to be done in order to make it mature and
potentially a candidate technology for the next generation.

535
Thank you.

536
 Evolution of Air Interface Towards 5G
Prof. Suvra Sekhar Das
G. S. Sanyal School of Telecommunications
Indian Institute of Technology, Kharagpur

Lecture – 29
Waveforms Beyond 5G (OF set QAM DFDM & UFMC)

Welcome to the lectures on Evolution of Air Interface Towards 5G. So, we have been
discussing the waveforms which goes beyond 5G which are expected to be in the next
generation standards.

(Refer Slide Time: 00:34)

537
So, we have discussed filter bank multi-carrier air in the previous lecture, briefly
speaking we talked about filtering each of the sub-carriers.

(Refer Slide Time: 00:40)

538
And we discussed the conditions under which one could design the filters and there were
two conditions which were identified ISI free and ICI free.

(Refer Slide Time: 00:48)

539
And it was also shown about the different conditions that come up to meet these two
different requirements.

(Refer Slide Time: 00:59)

And there was some kind of symmetry which was brought out as the necessary
properties of the filters.

540
(Refer Slide Time: 01:02)

As well as there was some kind of shape structure for the phase difference between the
neighbouring sub-carriers is also pointed out.

(Refer Slide Time: 01:09)

And typically what would be the amplitude and phase response would look like for a
filter bank multi-carrier was discussed.

541
(Refer Slide Time: 01:17)

And finally, the different pulse shape or the filter characteristics that are to be used were
also described and how they compare against each other was discussed.

(Refer Slide Time: 01:27)

And in the conclusion, it was shown that by means of the different methods it is possible
to have ICI free and ISI free communication system if one appropriately designs the
filter based on the conditions which have been arrived in this particular section.

So, then we said that we move beyond the FBMC and see some of the other structures
which exist.

542
(Refer Slide Time: 01:56)

So, one of them what we look at is OFDM with offset QAM. So, for OFDM with offset
QAM we would start off with the paper or we would mainly look at the work which was
due to Saltzberg and that was again from 1967 and again we are pointing out that these
may be very old classics, but they contain the foundation for the work that is being still
done or that invokes interest in the new generation communication system. So, in this
setup what was proposed is that the channel transmission signalling rate if it is defined as
b and the channels are spaced at b by 2 apart. So, that is what you can see that b by 2
apart ok. So, that is what is pointed out and all channels have the same spectral shaping.
So, this was variant and symmetric about its center frequency.

So, variant in the sense that we will see certain structures where one could go beyond
this and we will see what are the outcomes, but as of now this remains with the structure
that they all have the same shaping that is not a problem that is kind of pretty fine and the
role of about the frequency displaced b by 2 from the center frequency is square root
Nyquist’s roll-off right. So, this is these are some of the conditions and these give rise to
eliminate ISI in each channel; that means, each subcarrier and inter carrier interference is
also removed when the channels when the channels are in phase quadrature. So, this is
another part which is critical for us to review. So, this gives us a different structure and
finally, this also satisfies the earlier criteria and let us see what do they mean finally.

543
(Refer Slide Time: 03:48)

So, what we see over here is that there would be two adjacent carriers which are in
quadrature right, so we have a sine and we have a cosine. So, these are the two adjacent
carriers in quadrature and they are staggered oppositely in time with 1 by b. So, what you
see over here is clock 1 in the crimson or reddish colour that is given over there and
clock 2 is driving the other line and the first line is going to one of the carriers which is
at which is in sinusoid and the other one is triggering the quadrature carrier. So, basically
they are staggered oppositely with 1 by b difference. So, what you see is that one of them
is sine, the other is cosine which are quadrature, but they are staggered and the difference
is 1 by b and the sampling rate of each of the data stream is b by 2 because it is similar to
offset QPSK if you have studied offset QPSK only thing is that it is extended to
multicarrier right.

So, what we also find is that there is an oppositeness in it; so; that means, in one series
you will find the sine being triggered by clock 1 as over there, but in the next one you
will find that the carrier with sinusoid is being triggered with clock 2 as you can see over
here. So, this line is triggering this one right with sinusoid and hence the corresponding
cosine will be triggered by clock 1 right. So, this is kind of alternate whatever happens
over here alters over here, and the sine and cosine are at offset with each other and the
neighbouring carriers are with sine and cosine.

544
So, then the gating pulse is of course, used as typical gating pulse. So, this way one
would be able to realize the offset QAM and all the advantages of offset transmission
techniques we have discussed quite earlier would apply to this. So, this only helps us in
extending the offset QAM transmission methods to OFDM and hence one can try to get
the benefits of offset coming offset QAM communication on multi carrier systems.

The receiver as we can see is the exact opposite of it. So, what whatever is happening at
the transmitter it has to follow in the same structure, but in the reverse order. So,
basically sine goes with clock 1 in the first channel and cosine goes with the clock 2 and
in the next one it is the reverse; that means, sine goes with clock 1 and the cosine goes
with clock 2, right. So, that is the standard processing that has to happen at the receiver
and one would be able to decode the signals.

(Refer Slide Time: 06:44)

Full Cosine

545
Half cosine

So, to observe the effect of amplitude distortion, delay distortion and phase distortion on
or phase offset two kinds of transmit filters were conceived in the work; one is the full
cosine as described over here. So, this is the full cosine curve that is the green in colour
and the other one is the half cosine which is described over here in the frequency domain
and that is as per the red coloured curve in this picture which describes the frequency
characteristics of the two filters.

So, let us study or see the impact which has already been analyzed and accordingly one
can choose, the different filter structures or the filter shapes as per the need.

(Refer Slide Time: 07:29)

So, what we find over here is there is a comparison which is made between a single-
carrier and a multi-carrier system and in this it is the phase error and this side it is the
distortion and two curves have the same x-axis and y-axis as you can see, but on the right
hand side it is the half cosine and the left hand side it is the full cosine. So, if we try to
compare the effect on the single-carrier system what we find is that this point which is

546
corresponding to this point over here, the half cosine has a worse distortion for the effect
of carriers phase offset on single carrier system.

Now if you look at the multi-carrier system there is a slight better performance in the full
cosine, because full cosine would be somewhere here right. So, the full cosine curve
would follow this line somewhere like this if we compare against each other right. So,
that is a somewhat better in that sense right. So, full cosine is going like this for single
carrier this is for multi-carrier right as given in the index.

(Refer Slide Time: 08:43)

So, now if we move ahead further and see the effect of delay distortion again we will
compare the full cosine and half cosine. Filter characteristics, what we find is that the
half cosine has a better performance on the single carrier system right. So, we have the
single carrier performance over here. So, if we bring the full cosine performance, the full
cosine performance would be somewhere there. Now if we compared the multi-carrier,
the best carrier case, so, the full cosine is somewhere there; that means, it would be
somewhere around this point ok.

So, here what we see is that the full cosine is better for multi-carrier and half cosine is
better for single carrier under the delay distortion case. So, depending upon the
application one has to choose the appropriate one and this is of course, for the best
carrier. For the zero degree carrier again the performance there is a performance

547
difference. So, one has to see what criteria one chooses and accordingly one has to
choose the pulse shape for this system.

(Refer Slide Time: 09:51)

Finally what we see over here is the amplitude distortion. In the amplitude distortion we
have the single carrier full cosine which is given by this and the single carrier half cosine
is given by this. So, up to a certain amount of attenuation there is not much difference,
but beyond that what we find is that for single carrier system the full cosine performs
better. Now if we compare the multi-carrier systems what we will find is that the half
carrier has a distinct advantage over the full carrier in terms of distortion this is the half
cosine and this is the full cosine. So, the full cosine has more distortions. So, depending
upon what is important one has to choose the appropriate filter shape in order to get the
right performance ok.

548
(Refer Slide Time: 10:49)

So, what we find in this particular study is that OFDM with offset QAM transmissions
provide a method of transmitting digital data at speeds very close to Nyquist data rate of
band-limited channels without using sharp cut-off filters. So, we find another method of
doing the same and in addition the use of large number of narrowband channels is
effective in combating delay and amplitude distortion of the transmission medium.

So, these are some of the requirements and they also meet the criteria provided by the
other work that we are studied before. So, we have at least two different ways of
realizing a multi-carrier system which has good characteristics in terms of out of band
and most of the works beyond this build on the platform which have been developed a
with these particular works.

549
(Refer Slide Time: 11:35)

So, with this we move on to the next important architecture that was also studied as a
contending waveform in fifth generation system and they were being selected and they
also have very good characteristics and as said we do expect that they would still carry
on to evolve or mature and they may be replacing the existing numerology or the
adaptive subcarrier bandwidth based OFDM system which is currently accepted as the
standard for 5th generation.

So, what we see in the universal filtered multi-carrier structure it is a compromise

between OFDM and FBMC. So, that is one of the things. Now if you look at OFDM and
FBMC, FBMC essentially has a large number of carriers and each carrier has a filter
associated with it and this operation is to be done at the transmitter as well as at the
receiver, whereas, OFDM replaces the entire set of operations with FFT structure with
IFFT at the receiver and IFFT at the transmitter and FFT at the receiver.

So, the order of complexity of OFDM is significantly lower than that of FBMC although
both can maintain orthogonality criteria. The advantage of OFDM sorry, the advantage
of FBMC is that it maintains a pretty narrow out of band or low out of band signal
leakage compared to OFDM. So, this unified universal filtered multi-carrier is an attempt
which reduces complexity to some extent and brings in performance of out of band
which is better than that of OFDM system. So, it is somewhere between OFDM and
FBMC both in terms of complexity as well as in terms of performance.

550
So, the characteristics are the pulse shaping is done over a group of sub-carriers.
Remember here in FBMC we talked about each sub-carrier undergoing pulse shaping
here it is reduced unlike OFDM-CP is not there because FBMC-CP is not there and
typically when you do filtering your length of the signal increases. So, whatever is the
length of your original signal it would increase by the length of the filter and hence, one
has to accommodate this extra length. So, this can be comparable to the extra length of
CP as is used in OFDM and hence no additional CP are usually encouraged, but if one
wants one can do it, but that will obviously, reduce the spectral efficiency.

Now, the filter length usually selected is usually lower compared to FBMC because in
FBMC you have per sub-carrier and you have really narrow band filters whereas, here
you have a compromise. So, essentially the filter length is smaller and hence you would
also expect naturally that the out of band radiation or out of band leakage would not be
as good as in FBMC. It will be a little bit worse, but maybe better than OFDM because
you are pulse shaping over a group of subcarriers. Now in OFDM, you essentially do
pulse shaping, but that is over the entire set of sub-carriers. So, it is again coming in
between.

So, let us see what do we have over here. So, there is IDFT operation which is
corresponding to the IFFT operation right. So, that is like the OFDM system and then
there is a filtering. So, this filtering operation is the one which actually does this pulse
shaping over a group of sub-carriers right. And you do them over multiple such bands or
blocks and the entire thing add up together and send for transmission. The receiver side
is of course, the reverse operation, but there is slight change because there is a speciality
processing which reduces the signal processing complexity and we will see that in the
lecture now.

So, moving further we need to remember this architecture that we have drawn over here
there is IDFT or IFFT followed by filtering and then there is addition.

551
(Refer Slide Time: 16:19)

And what we see is that the output of the transmitter can be written as X of length N plus
L minus 1. N is the size of number of subcarriers, L is the filter length and minus 1
because after convolution you have one unit less and Fi is the filtering matrix. So, you
can operate it as a matrix and Si is the set of sub-carriers that are to be used in the blocks
and then we have the data part. So, we have together the entire set of signals that needs
to be processed and B is the number of resource blocks ok. So, F is the linear
convolution matrix as we can clearly see. S i is the input frequency domain data and n i
is the number of subcarriers for the i-th resource block.

So, that is how this whole thing is structured that you can clearly see as compared to this
particular picture all right. So, then the different filter coefficients can be chosen
independently for every resource block. So, this is different compared to what we have in
the previous structure.

552
(Refer Slide Time: 17:40)

So, now moving further what we see is that the UFMC received signal without noise is
basically f i convolved with the signal x i and x i is the time domain filter for the i-th
resource block and x i is the IDFT of the data in the i-th resource block. So, this is the
time domain representation in a linear convolution form whereas, previous it was in the
matrix notation form all right. So, what we have x i is given as since it is the IDFT you
can clearly see the IDFT expression that is over here and S i is the set of subcarriers,
subcarrier indices belonging to the i-th resource block.

553
So, each block has a certain set of subcarriers and if we consider the output of the i-th
resource block then the element of the output would be f i x i and this is this convolution
operation that you are seeing. This convolution operation is simply expanded over here,
nothing else that same operation and at the output. So, now, this is at the receiver
noiseless receiver. So, we are talking about the noiseless receiver structure. So, forget
noise because we want to establish the receiver structure and once we establish it
whatever noise would come in has to be accepted.

So, what we see is at the output you take a 2N point DFT instead of taking a standard N
point DFT. One way to look at this is that instead of having N point you now have N
plus L minus 1, so many points. Since we have N plus L minus 1, we need to have 2 N
which is greater than N to take care of all the points that is one of the ways of looking at
it. So, if you take a 2N point DFT and then the k prime-th element because we need to
look at how this is helping us ok would be Y i whatever signal you are getting and e to
the power of minus j 2 pi m k prime because we are talking about the k prime-th element
and you are seeing the 2N in the denominator indicating a 2N point DFT and of course,
you have a 2N in the summation also indicating a 2N point DFT operation right.

(Refer Slide Time: 20:17)

554
So, then as we as we see this expression Y i, so, you can expand Y i in terms of the
equation here ok. So, you are going to replace Y i which is here in terms of f i and x i
and then you have this summation of g equals to 0 to L minus 1 which comes in
additionally in this particular expression right. So, whatever is here is now included in
this particular equation and then what we have over here is x i is getting replaced by the
IDFT of capital X i that is also available over here. See whatever is x i present in this
particular expression you are using that expression over here and you are having this
summation over the particular set of sub-carriers which are of your interest, and
summation over m is continuing. So, this summation over m is here this summation over
m is here and this is the summation over g. So, all the components are now in place.

So, now you could also replace this f i of g with this particular operation that you are
seeing here along with g over here that you are seeing by its corresponding Fourier
transform or DFT operation which indicates capital F i of k right. So, basically you have
a X i F i and then you have rest of the terms m k term over here and m prime m k prime
term over here and this particular operation leading to the DFT of F i which is the filter
transfer function. And then by manipulating this or working on with the terms what you

555
find is that what you get over here is X i F i and all the terms accumulated here, you can
bring it over here and instead of putting k prime you are using the variable p over here to
make the terms appear better. So, we will see what do we get for p.

So, what we have over here is k prime is equal to 2p. So, if k prime is equal to 2p then
you get it if you put 2p over here 2 and 2 cancels. So, you have the denominator as N
which is matching over here as the denominator of N and then k comes over here and p
comes over here right. So, that is how we get the expression. So, for, so, our k prime is
even for p belonging to this sub-carrier set. So, this is to be remembered.

So, if k is equal to p; that means, if you have k is equal to p in that case Y i 2 p k prime is
equal to 2p ok, that is what is there. So, if k is equal to p Y i 2p that is Y i 2p that is what
we have over here, what we get is if you put over here k is equal to p these whole terms
cancel out because just let us look at this remove these terms and you take the pen. So, if
k is equal to p you are going to get X i F i e to the power of k is equal to p this is 0 ok,
and the summation. So, when you have the summation you see the summation is over 2N
right.

So, basically you are going to get 2N terms denominator there is 1 N term. So, basically
you get this 2 term. So, that is why you have this 2 factor and k is equal to p, k is equal to
p. So, k is equal to p k is equal to p; so, X i p and F i p right. So, that is what you get.

So, what we see is that in the even indices you get X i p times F i p; F i p is known. So
therefore, we can easily decode X i p which is the transmitted data and for all other k, Y i
2p should be equal to 0. So that means, in order to decode we must do a 2N point DFT at
the receiver that is what you see 2N point DFT at the receiver and one must decode at the
even subcarriers. See if one decodes that even subcarrier then one gets the desired signal
with the corresponding filter coefficient since the filter coefficient is known one would
be able to recover the data signal as it is.

556
(Refer Slide Time: 25:05)

So, for k prime equals to 2p plus 1 or k prime equals to odd for p being element of these
sub-carriers what we see is that Y i 2p plus 1 is has an expression where you would put
over here 2p plus 1, earlier we had put 2p and that 2 and these 2 had cancelled, but now
that is not going to happen right. So, that is not going to happen now and you are going
to evaluate these terms. If you evaluate these terms and get into some things what we
will find is that it becomes a weighted combination, the weighted combination of all data
in all the sub-carriers of the particular resource blocks. So, there is ICI at odd indices
right. So, since there is ICI at odd indices this is of not much use for us and we are only
concerned with Yi 2p and we will decode our data.

So, what we see is that for all other resource block j not equal to i, the output index will
never match to any of the subcarrier index and thus the output of the even sub-carriers is
0 for j not equal to i. So, this way one can decode the UFMC signal and at the output of
the odd sub-carriers one finds the ICI terms as obtained above right. So, if one follows
through the step 1 would be able to regenerate all the things.

557
(Refer Slide Time: 26:28)

And then what we find is that the spectrum, one could be able to generate the spectrum
with out of band characteristics as shown in this figure. So, once again what we find is
that there could be overlap that is possible; so that means, efficient spectrum usage is
possible and in this line and in this figure this black one is for OFDM and the slightly
greenish bluish colour this one is for UFMC is for UFMC. So, what we find is that
because we are kind of filtering and filtering a group of subcarriers, therefore, we are
able to reduce the out of band leakage by a significant margin when compared with
OFDM.

The complexity is also not very high as compared to OFDM and the performance is
going closer towards FBMC and this is somewhat realizable in all terms and hence this
makes a good candidate. The only problem that we have over here is there is no CP. So,
managing the inter symbol interference is one of the factors and that needs to be
addressed appropriately ok.

So, with this we bring this particular lecture to an end where we have come considered at
least two signalling mechanisms. One is UFMC which is a universal filtered multi-carrier
and we have also seen offset QAM OFDM which is an extension of the earlier version of
filter bank multi-carrier and essentially what we are focusing on is waveforms which
have characteristics especially in terms of out of band leakage we are much superior to
OFDM, but the constraint that we found in FBMC is that the complexity is becomes very

558
high because you have to have N number of filters and N number of paths at the
transmitters, similarly N number of paths at the receiver and trade-off between these two
would be UFMC which has complexity somewhere between OFDM and FBMC and out
of band leakage performance again between OFDM and FBMC to a desired performance
limit.

In the next lecture we will discuss the generalized frequency division multiplexing which
is again another contending waveform for the 5th generation as well as we hope it
continues to remain and become mature even better because lot of work is still going on
with GFDM. So, that it is able to provide all the facilities and bring in all the features
which are required in the next generation system. So, in the next lecture we will talk in
more details about the GFDM or generalized frequency division multiplexing.

Thank you.

559
 Evolution of Air Interface Towards 5G
Prof. Suvra Sekhar Das
G. S. Sanyal School of Telecommunications
Indian Institute Technology, Kharagpur

Lecture – 30
Waveforms Beyond 5G (GFDM)

Welcome to the course on Evolution of Air Interface Towards 5G. So far we have been
discussing about the various waveforms, which are potentially future generation
waveforms, and we have seen various structures namely FBMC and UFMC. So, will
briefly revisit UFMC in a few minutes, and then will proceed on to seeing the next
important structure, which is the generalized frequency division multiplexing as we had
said in the previous lecture.

(Refer Slide Time: 00:47)

So, in the last discussion we had presented the generalized structure for UFMC, where
we had said that there is initial DFT block and group of subcarriers are filtered right that
is what we had mentioned.

560
(Refer Slide Time: 01:09)

And if we look at the notations which have been carried forward, we do it over here that
means there is the filtering which is reflected over here. The IDFT operation which is
over here; and S are the data vectors which are here right, so that is how these equations
frame up. And B is the block is the number of resource blocks that are to be used. And
then we had also identified that for each of the resource block there is a certain size of
the resource block, which we had also indicated here.

561
(Refer Slide Time: 01:35)

I mean in this case the S i indicates the size of the resource block, whereas in the
previous case it was indicating the data, but rest of it is fine. And we also summarily said
that the output is usually done in a manner that there is 2N-point FFT, and the reason is
that the output is longer than N, there is N plus L additional things because of the
filtering operation that happens. So, one has to take a 2N-point to FFT.

562
(Refer Slide Time: 02:09)

And when one takes a 2N-point of FFT, if one takes the even subcarriers right; so, when
one takes the even subcarriers for k prime equals to 2p, then one finds the desired signal
along with the filter coefficients. Now, since the filter coefficients are known, one can
easily recover the desired signals; for all other values of k, it was shown to be 0.

563
(Refer Slide Time: 02:30)

And for any other block, where the resource block is not the desired block, the index are
not going to match and therefore, there is no issue about it, so that is how the UFMC is
done. And we also said that it is somewhere between FBMC and OFDM it is between
them, because like FBMC there is filtering operation, but unlike FBMC it operates on a
group of sub-carriers, because in FBMC it operates on every sub-carrier so, this a more
generalized form you can think of it that way.

And it is more towards OFDM because of the complexity, one can use FFT architectures
in this processing and the complexity is lower, where is an FBMC it is per subcarrier
filtering, so such facilities are not directly available. And hence complexity wise, it is
between them; performance wise also, it is between them; especially, in terms of out of
band leakage, that is one of the main reasons why we are going for this.

And we have said earlier that given a spectrum band this is f, one would like to use
narrow bands, wherever their gap exists. So, if there is a certain gap exist, one would like
to fit in a waveform within this structure as efficiently as possible and if rather possible
one would like to have a multi-carrier structure also within that, so that is the

564
requirement. And these different waveforms have the capability to do it, complexity is an
issue. So, UFMC what we said earlier is one which compromises between them,
provides the facility to sneak in small section of bandwidth, yet have low out of band
leakage and have comparable complexity in with OFDM and much lower than that of
FBMC.

But when things come out to be very very narrow bands available and very sharp
transition bands required then, FBMC is more suitable. FBMC’s also has the feature of
orthogonality by which it has been designed, which we have discussed in the lecture
before that.

(Refer Slide Time: 04:31)

So, moving further lastly we had actually compared the out of band radiation leakage for
OFDM and UFM UFMC where we find that significant reduction in out of band leakage
is possible.

565
(Refer Slide Time: 04:42)

Then we move on to the desired discussion, which is due for today that is the generalized
frequency division multiplexing. And this will be the last waveform that we considered
in this particular series of lectures, where we are looking at future potential waveform
structures, especially multi-carrier structures. And we had said initially that all these
waveform structures, they are some variant of OFDM in some sense. Now, we also
would have said at that point that you may not agree with this, but these are all
generalized multi-carrier techniques.

OFDM is more popular. So, one can view them as variants of OFDM, but rather if one
sees them as a generic multi-carrier and these are variants of multi-carrier techniques,
then it is rather better. The previous class of waveforms that we have studied, they are
mostly orthogonal, there is not much of a problem, there is no inter carrier interference
which is available, but then when we go to this generalized frequency division
multiplexing; this does not come under the category of orthogonal waveforms, it has
some kind of non-orthogonality present in it.

And let us see, now why we should look into it and what are the advantages, what are the
disadvantages, what are the structures and what are the gains and benefits finally, it
provides.

566
(Refer Slide Time: 06:04)

So, to look at that we must briefly look at some of the statements from Gabor theory,
which helps us to understand the system in an easier manner. So, according to Gabor’s
proposal a function can be expanded into a series of elementary functions, which are
constructed from a single building block by translation and modulation that means, in
this particular expression we are looking at f of t, it can be expanded using g m, n of t
which are the elementary functions. So, what it says, is that it can be expanded into a
series of elementary functions right. So, these are the elementary functions ok, it is
expanded into a series.

And of course, you need coefficients we will talk about each, but each of these
elementary functions are given by a structure which is this. So, this is more or less self

567
explanatory for people who work in the domain of signals and systems. So, what we see
is that there is a translation in time that is what we you see over here, what we also see is
that there is a modulation in frequency ok. You can also say, there is a translation in
frequency and translation in time, so that is what is happening over here. So, there is a
translation in time and frequency domain that is what is happening over here, which can
be also seen by translation and modulation terms ok.

So, here g t appears to be the base elementary function, which is translated in time and in
frequency which is represented as modulation. Here m and n are integers. So, there is a
lattice structure over which this is translated so that means, given a function, so this
function could be our arbitrary waveform. And this waveform would exist over a certain
duration in time and it would also occupy a certain bandwidth, now what it says is that
this waveform can be expanded into a series of certain elementary functions. So,
elementary function can take a certain shape, you can translate, you can shift in time and
frequency and you can make a combination to represent this waveform. These
coefficients in that case would represent the information bearing signals or values, which
are used along with these basic elementary coefficients.

(Refer Slide Time: 08:45)

568
Let us look at this, so what we have over here is the Gabor’s elementary function g mn of
t, which is basically g t minus n a what we saw over here right and e to the power of j 2
pi m b t are shifted and modulated copies of the single building block g, in this what we
said, and a and b denote the time and frequency shift respectively. Each g mn has the
envelope of the shape of g and only the real part is shown in this particular picture. So,
this is your g of t, this when shifted in time is g of t minus a and g of t minus n a right.

And each of them can be shifted in frequency or modulated in frequency in a manner g t

e to the power of j 2 pi b t of course is there. And here g t e to the power of j 2 pi m b t
right. So, this can also be shifted in frequency, so that means by using this base
elementary function, this is the base elementary function one can actually cover the
entire space all right.

(Refer Slide Time: 10:03)

And one represents such a thing pictorially in this manner. So, if g is localized in the
origin, so if this is your g which is localized in the origin in the time frequency plane.
Then g mn that is this one, which is of our concern is localized at the point coordinate
system point na, mb. So, basically you have divided it into such lattice structure and a is
the basic unit of shift. So, this is the na unit of shift on this side and if this is the b unit of
shift, then you have nb unit of shift.

So, basically this entire Gabor atom if you call it, gets translated in time, then in
frequency to be given as g mn which are basically indexes of m and n over here

569
respectively, so that is how you can span a time frequency grid and any particular signal
can be represented in this manner. So, just for example if you look at OFDM, then sorry,
one of the carrier signal is like this, the next carrier signal would be a higher frequency
carrier signal, and then another one which would be here would be basically even higher
frequency signal.

So, so basically it covers a certain space in frequency and a certain space in time. So,
what this particular thing tells us that this Gabor atom can be used to cover the entire
time frequency grid. In case of OFDM, there is only one time slot; so there is only
shifting in frequency that keeps on happening. Now, if you think in terms of block
OFDM, then one can think of also translating in time as well.

(Refer Slide Time: 11:54)

So, moving further digital communication system transmits a sequence of binary data
over a continuous physical channel that is of course, what we see. So, this is the
transmitter side of things and this is the receiver side of things. And the transmitter sends
a signal formed by linear combination of g mn weighted by binary coefficients d. So, this
d m, n written over here is the can be thought of as the same thing as c that we had
described over here and that time we had said this is the coefficients which carry
information right.

So, they are the Gabor synthesis coefficient you can say that through this you are
synthesizing the function that you are sending over the channel. And then the receiver

570
recovers these coefficients by taking a inner product with the analysis function gamma
mn. So, what we have is g m, n on this side and we have gamma mn on this side and
there are different combinations different ways you can create them. So, it is not
necessary that they are the same, but you can also get sets which would also which
would be the same, but you can also go beyond them, which are different set of functions
which can create, help you recover the original coefficients that one sends the signal
with.

So, this a overall framework on which the system is built and then we move on to the
generalized frequency division multiplexing architecture.

(Refer Slide Time: 13:19)

So, before we proceed there a few more things we need to look at is if g is the pulse
shape, then for the product ab equals to 1; a and b we had said are the tiles basic
coefficients for ab equals to 1, which is the scenario for OFDM. We find that the Balian-
low theorem states that the signal cannot be well contained in time and frequency, what
it effectively means that time frequency localization is not possible, if you have the
coefficient set as ab equals to 1; that means, your lattice if it is structured in this manner,
then it is not possible to have well localized time frequency signals.

571
Now, we have been saying that OFDM has the problem that since it is rectangular in
time, it is absolutely well localized in time, but if you look at in frequency it is a sync
structure. So, a sync structure means it is actually spans to infinity and there is a huge
amount of signal in the out of band region, which we would like to reduce. And what we
find is that by a fundamental theorem, OFDM does not allow you to do that and hence
you must come up with different mechanisms.

So, within the Gabor framework, it is said that if you let ab product of ab to be less than
1, in that case it is an over-sampling systems and they come under the category of
frames, we will not discuss it here. You can actually localize the waveform in time and
frequency, you can form well-localized pulses that means, which would be localized in
time, as well as it will be well localized in frequency.

So, if this is your time axis and this is your frequency axis so, overall you will find that
the signal is well contained in time and frequency grid, it does not spread beyond a
certain small region and time and frequency. For critical sampling, which we have
already said that frames and orthonormal basis are possible. So, like OFDM you have
orthonormal basis, but time frequency localization is not possible, if ab equals to 1. And
the under-sampling system that means ab greater than 1, in this case the family will be
incomplete at however it was shown that by Mazo, which we are going to shortly see that
communication under in under-sampling system is possible, where sampling can be
decreased until the Mazo limit.

So, essentially we would primarily like to be in this region in order to get well localized
time frequency pulses, but the problem is in that case your spectral efficiency would be
reduced. So, again you pay something and you get something whereas, here your spectral
efficiency in terms of number of bits that you are sending is good, but there is significant
amount of adjacent channel interference, which would like to reduce. So, one would like
to come up with systems which are close to critical sampling in some manner and has
good out of band emissions, so that one can squeeze in wherever you find empty spaces.

572
(Refer Slide Time: 16:31)

So, as we said earlier about this under-sampling system. So, will just put one slide on
this, will not spend more time on this. There is something known as the faster than
Nyquist system, which is introduced by Mazo in 1975, where the signal is modulated
faster than the usual rate which introduces inter symbol interference. Naturally, we know
that if you are using sync pulses and you have a bandwidth of W, then you can send the
highest rate of signaling as 2 W symbols per second without inter symbol interference
that is what is the primary statement.

So, here what a Mazo had actually shown that you can actually go beyond that and yet
you can recover the signals up to a certain limit. So, the limit till which you can increase
the signaling rate is known as the Mazo limit and for sinc pulses it is shown that up to 25
percent faster does not decrease the minimum Euclidean distance between the symbols
right, so that means using a binary modulation of course.

So, when you go with higher modulation then things would be different as it is expected.
So, this is another domain which is to be investigated further in quite great details and
whether this actually brings us the desired benefit in the overall complicated framework,
which we already have needs to be explored further. But for us it is important to know
that there exists something, which is beyond the ISI free signaling that we have been
discussing.

573
(Refer Slide Time: 18:01)

So, now we go on to the generalized frequency division multiplexing structures. So, why
is GFDM the primary reason is that it is flexible in terms of time and frequency
resources, which we will see. And it is resilient to synchronization requirements we will
also see that, it is good spectral efficiency as it uses circular pulse shaping like the one
which OFDM uses similar, but it is different which reduces cyclic prefix length in
frequency selective fading channel. So, these are some of the benefits of GFDM.

(Refer Slide Time: 18:33)

574
But on the other hand, GFDM has high complexity we will see there. It also has out of
band leakage, which is high, one of the reason for it being high is that it is a uses circular
pulse shape amongst other things ok. So, one has to find methods to take advantage of
these particular things and see if something can be done in order to reduce, in order to
reduce the out of band.

It also has high peak to average power ratio, because when you are shifting away from
the rectangular pulse shape your PAPR is going to increase. So, again these are some of
the areas, where GFDM needs to be improved whereas, these are some of the areas
which are its advantage.

(Refer Slide Time: 19:22)

So, let us look into the generalized frequency division multiplexing framework. So, what
we see is that it is a multi-carrier framework that means, it has spectral efficiency
advantage. It is also a block based system that means, that one can actually transmit in
blocks of data. For example, if one would have OFDM all go in parallel in frequency,
this is well understood by all of us ok.

And all of them happen in one symbol duration ok, if it is single carrier frequency
domain equalization, single carrier means there is only one carrier, but one would send
multiple time slots ok. So, this is f frequency division multiplexing, this is time division
multiplexing equivalent one can think in those notions, but here we have both time and
frequency at the same time, meaning one can equate one time block to that of an OFDM

575
symbol. So, as if there are multiple OFDM symbols like not OFDM, but if one
understands OFDM which can be grouped together and it forms one block.

So, I would erase all of these things, so instead of seeing it as like OFDM as we just said,
OFDM would be thought of as one block in comparison to this. Whereas, this has
multiple such blocks together and one can actually choose the different block
combinations, one can choose to use this block, one can choose to use this block, one
might choose to use this block or one might choose to use this block. So, this is a flexible
structure that is has, it can have various combinations of parameters which is given by m
parameter on this side and n parameter on the other side. So, there are two parameters m
and n parameters. So, names can be different m means the number of time slots and the
number of sub-carriers. So, one can flexibly choose it and can make various
combinations.

Now, in OFDM what you would find is that generally for OFDM there is a symbol
duration there is a CP, the symbol duration there is a CP, symbol duration in CP, whereas
in GFDM it is suggested that you have a block of symbols and a common CP for it, so
that effectively means that you process the entire block simultaneously that is another
feature. And you can also see directly that because there is a cyclic prefix for every
OFDM symbol, the amount of overhead that is present in such a system is much more
than in GFDM system.

So, in GFDM system what we find is there is only one cyclic prefix and we have
described earlier that the cyclic prefix length is dependent upon the channel constraint.
And hence the cyclic prefix length in this case and this case would be the same. So, the
percentage overhead is less in GFDM system as compared to OFDM system.

576
(Refer Slide Time: 22:35)

Moving down further, now in GFDM system what is done is there is a pulse shape for
every symbol duration. So, for example, we can clear of all of these what happens is that
yeah. So, what happens is this symbol duration there is a certain pulse shape ok, the next
symbol duration there is another pulse shape and in this symbol duration there is another
pulse shape. So, this is one way of visualizing the entire thing.

And all of these subcarriers are having the same pulse shape. All of the next set of
subcarriers, I mean usually all of them have the same pulse shape. This is one way of
viewing it, the but more accurate picture would be that this every every symbol there is
there is a pulse shape and the pulse shape is not exactly restricted to this time duration
and that is that can be understood from the way we have drawn this thing. So, this
indicates that the pulse shape is a long pulse shape right. This is the ideal pulse shape for
the center one, because it is symmetric.

For the other cases, it has to wrap around right, for the other cases it has to wrap around.
So, this wrap around thing is this circular shift that is present in GFDM system, because
if one would not wrap it around in that case the if we think of this pulse shape, this is the

577
central pulse shape. So, when we use it over here, then it will be extending on the left
hand side; if we use it here, it will extend on the right hand side.

So, effectively the signal the symbol is stretching over a much longer duration and hence
the efficiency would be less. To improve the efficiency, you actually wrap it around you
wrap it around on both the ends, and hence you are able to create a much higher spectral
efficiency. And the flip side of it is that because you are wrapping it around, you are not
able to get a smooth start at the beginning. So, if you are not able to get a smooth start
this beginning, abrupt start, in that case it is obviously, going to give you a high spectral
leakage.

The other thing is that it has overlapping subcarriers like we had seen others so hence
spectral efficiency is high, so that is that is not much of a problem. So, let us look deeper
into the thing. So, what we have over here is one of the pulse shapes ok, then it is shifted,
then it is shifted, then it is shifted and you can clearly see that if you wrap it around that
means, when I move it here part of it is here and part of it is here. So, because of this
when the signal suddenly starts, then you are going to get a sudden burst of increase in
the signal level which causes out of band leakage. So, this needs to be controlled in a
generalized frequency division multiplexing system.

(Refer Slide Time: 25:35)

578
So, let us look deeper into the structure. So, what we have is there is this data symbols
and these are the pulse shapes which are of critical nature. So, let us see how these are
addressed. So, in the first time slot the g 0 to g MN minus 1 are the samples of the pulse
shape of the first time slot.

The second set of signals indicate the frequencies shifted version of the pulse shape, so
that means, if there is a certain pulse shape. So, let this be a pulse shape in the first time
slot ok, in the first sub-carrier. The second sub-carrier is going to get the same pulse
shape, but it will be frequency shifted by e to the power of j phi 0 times k indicating that
it is a frequency shift from the first sub-carrier to the next sub-carrier ok.

The next column would be the same pulse shape with additional frequency shift, like that
you are going to have N such sub-carriers, all of them are going to have the same time
domain pulse shape, but they will each of them will be frequency shifted. The next set of
pulse shapes, would be the pulse shape for the second time slot and that is a time shifted.

So, when we are talking about the Gabor version, so this is what we have in the Gabor
version. This is the basic Gabor atom, these are frequency modulated Gabor of the of the
primary atom and from here that is the first column over here to the first column of the
second slot, it is the time shifted version. And from the first column to this column over
here, it is the time shifted and frequency shifted.

Now, if we compare the second frequency over here with this one, these two have the
same frequency shift, but there is one unit of time shift difference between them. So,
between this and this as has been pointed out there is no difference in the frequency shift
that means they are the same sub-carriers.

579
So, in the time frequency diagram when we had if these indicate the first block, if these
indicate the second block, these indicate the third block and so on. So, basically this one
and this one they have the same frequency shift, but they have two different time shifts.
So, this is the time axis this is the frequency axis whereas, this and this they have a
frequency shift with respect to each other, but there is no time shift between them, but if
I take this one and compare with this one, so there is a time shift as well as frequency
shift. So, there is a time shift as well as there is a frequency shift between these two right.
So, this is what we should keep in mind. So, this is the primary Gabor atom and then we
are shifting it and creating it right.

So, if you look into the equation carefully, you will be able to get how the signal is
generated. So, every data symbol is multiplied with a pulse shape and there are M times
N number of such pulse shape right. So, if we revisit back to the structure that we have
over here; so, this is the basic Gabor structure and if there are M, N which is small m
small n in this particular thing and capital M capital N over there. So, you have M.N
number of Gabor atoms right, each Gabor atom is multiplied by a coefficient that is what
we said, each Gabor atom is multiplied by a coefficient and it is sent out.

So, here correspondingly what we have over here is that each of them are multiplied by a
coefficient and they are added together to produce the final signal form. So, because of
the time and frequency block domain representation, you have M times N number of
such Gabor atoms, and each must get a corresponding coefficient which is indicated by d
in this case and the cumulative is the x in this particular slide, which is f in the original
slide, where we had discussed about the Gabor structure.

580
(Refer Slide Time: 30:02)

Like that this entire time frequency grid is filled out. So, this particular diagram helps us
understand the basic layout that is what we have is on one side if we look at it carefully,
so here the first few set of columns this picture is a scaled down version of what we
should have. So, this entire equation that you see it is summation over l equals to 0 to
MN can be constructed into a matrix equation ok. And it is a matrix multiplication, this
is a vector and this is a matrix of size M N cross M N. So, this is a matrix of size M N
cross M N and hence you can create this entire operation ok right.

So, what you see is that the first few columns they have the same time domain pulse, but
each of them are frequency shifted version right, so that is what you see that varying
frequency, but constant time shift ok, they have the same time domain. Now, what you
see in the next set of columns corresponding to what we have here, the next set of
columns. So, there there is time shift, so from here you can clearly identify, you can
clearly identify the time shift in the pulse.

The next set of columns, you can again identify the time shift right. So, we take a
different colour yeah, you can identify the time shift, the next set of columns you can
identify the time shift and then this one right. So, there are different time shifts for a
particular time shift, these are the subcarriers different subcarriers. So, these are the
frequency shift. So, now if you as has been pointed over here this one and this one, these
are two different time shift pulses, but within this structure they have frequency shifts,

581
within this structure these are frequency shift. So, this one and this one they have the
same frequency shift and this one has the same frequency shift, but between them there
is a time shift. So, this is a pictorial representation of this column structure of what is
actually represented in the analytical expression over here right.

So, we stop this particular lecture over here. And in the next lecture we will discuss
about, the ways the receiver can operate there are different receiver structures and what
is the performance comparison of all the different waveforms, that we have seen till now.

Thank you.

582
 Evolution of Air Interface Towards 5G
Prof. Suvra Sekhar Das
G. S. Sanyal School of Telecommunications
Indian Institute of Technology Kharagpur

Lecture - 31
Waveforms Beyond 5G (Pre - coded GFDM)

Welcome to the lectures on Evolution of Wireless Communication towards 5G. So, what
we have discussed still now is the different waveforms which are futuristic which have
been investigated and which require even more attention for them to be made mature
towards acceptance in the next generation communication systems. And, we have seen a
variety of waveforms namely the filter bank multicarrier then unified universal filter
multicarrier waveform, we have seen Faster than Nyquist we have, we have also started
seeing generalized frequency division multiplexing.

(Refer Slide Time: 00:51)

So, we will start looking at GFDM and we will complete the discussion on such different
waveforms. So, we have said earlier in the previous class that GFDM is the generalized
frequency division multiplexing.

And hence, it is, because of the generalized form it is flexible in the time and frequency
resources which we have been seeing will again see today it is also resilient to
synchronization compared to OFDM, because in OFDM we have seen that, because they
are a sinc in nature in the frequency domain. So, although the others are orthogonal that

583
is the peak occurs at the 0 of the neighboring sub-carriers, but a slight offset causes a
huge penalty, because of inter carrier interference.

And we have also seen that, because there is a guard interval or a cyclic prefix. So, if the
guard interval is small then and the channel impulse response extends beyond the CP
then there is ICI; ISI and ICI which causes for the degradation in the performance. So,
GFDM has a better resilience and it has good spectral efficiency, because it uses circular
pulse shape which we have seen in the previous lecture.

(Refer Slide Time: 02:01)

The problems are it has high complexity out of band leakage is still present, but there
mechanisms to reduce it, PAPR is high, but again there are mechanisms which have been
proposed to reduce the PAPR as well as out of band leakage, so, as well as reduction of
complexity.

So, with these additional features which have been introduced into this GFDM, it is now
in better shape and is a good contender for the next generation waveforms. So, as you are
seeing that we are looking at waveforms trying to build waveforms with certain good
characteristics, but once you try to build one good characteristics the other one falls
down. So, the, the engineering part of it is to improve overall characteristics of the
waveform and provided with better features than what existed in the previous generation
systems.

584
(Refer Slide Time: 02:49)

So, GFDM as we had seen in the previous lecture is that we compared with OFDM; that
means, with OFDM, we had separate subcarriers. So, these were different, different
subcarriers that were present, right and the subcarriers existed for a time duration, right.
And each of the subcarriers, who are having different carrier frequencies, right and so on
right that is how these were present.

In the single carrier FD, we have also discussed single carrier FDE. since, it is a single
carrier it covers the entire band and it is kind of small duration of symbols, because the
bandwidth is large.

So, in one case, it is FDM that is what we had written in this case, it is more of a TDM
architecture in GFDM, you have both FDM combined with TDM, because it is a block
based OFDM, it is a block based system.

So, there are M blocks in time domain and there are N subcarriers in the frequency
domain. So, that is how the whole system is and we have compared with OFDM like this
is one OFDM symbol duration, this is the second OFDM symbol duration, this is the
third OFDM symbol duration. So, here you have blocks of GFDM. And there is one
cyclic prefix in front of it thereby helping it to have a better spectral efficiency even than
OFDM. The subcarriers overlap and hence there is no loss of spectral efficiency.

585
(Refer Slide Time: 04:26)

So, these are something we have seen and this picture also we had explained in the
previous lecture where we said that one can think of the pulse shape. So, if we think of
this pulse shape which is a spanning over longer duration of time. So, once you have a
long duration pulse shape then you naturally can make the spectral occupancy of that
particular symbol to be pretty sharp; that means, it is not spreading across in the
neighboring sub-bands, but now in GFDM what we have seen is it has circular pulse
shape.

So, what does that mean is that this pulse shape is, is if you look at the whole thing there
is one time block second time block, third time block and the fourth time block, all right.

These are the four time blocks so, there are M is equal to 4. In this system, in this
particular diagram and in one time sample in one time block the pulse shape would be
this. So, it is basically the pulse shape, it is expanding beyond one time block or one
symbol duration. And that one can compare with the partial response signaling where as
in OFDM, it finishes within one time block N, N samples. So, as you shift the symbol
pulse shape to the left and the right what effectively happen?

586
Now this is the more simplified diagram, but if you take a extreme shift; that means, for
the first symbol. So, if it is the first sample here instead of shifting, it just linearly you do
a wrap around or you do a circular shift. If you do a circular shift then what happens is as
you get over here pulse shape which looks like this for the first symbol.

For the second symbol, it is this one for the third- third time block, it is this one and the
fourth time block it is this one so; that means, if we try to draw it a fresh.

(Refer Slide Time: 06:27)

So what we have is in the, in the first time block the pulse shape is something like this.
And all the subcarriers are carrying this same pulse shape, subcarrier 1 to subcarrier N,
ok. In the next symbol duration the pulse shape I should chose the different color would
be for the first subcarrier, it would be something like this for the last subcarrier, it would
be like this, ok.

For the next time block, we can change the color to may be black we will have the pulse
shape which is going like this. And for the Nth the pulse shape would go like this, right.
And then for the last one, we can again change the color to given indication for the first
subcarrier it would look like this. For the last subcarrier, it would look like this, right. So,
this is how they will be and you can complete the notation, this is the first subcarrier, this
is the second subcarrier, the third subcarrier and so on, right and if we chose the different
colors to indicate.

587
So, again you are going to have on the first subcarrier and you will also have in the in
the last subcarrier, you will also have this color in the last subcarrier, you will also have
the same color the bluish color in the first subcarrier and so on and also for the black,
right.

So, that is how the whole structure looks like now if you on would compare this with
OFDM, one could say that if we roughly partition this, ok. So, roughly if you think if in,
in, in, in, in this manner. So, then in OFDM case you are going to have one symbol, two
symbol, three symbol and four symbol and each of them are going to have their own CP,
right. So, this is for OFDM, right. So, this is how they would contrast against each other
time domain although all the frequency components would be present. So, here all the
frequency components would still be present 1 to N.

So; that means, in each symbol duration you are processing N samples whereas, in case
of GFDM, what you are doing is you are taking this whole block together. And then if
there are N number of such time blocks and if there are N subcarriers. So, you are getting
M times N samples to be processed in one go.

So, this is one of the major differences between OFDM and GFDM to look at it generic
way. One can also think of putting different pulse shapes. So, basically this is your gt,
ok. And this one, if you write this g t is your g of t minus let say 1 T and then we can
have the black one as g of t minus 2 T and then the green one, we can have g of t minus 3
T and so on and so forth, right. And all of them are having the same on the same
subcarriers. So, if you look at this is g t e to the power of j 2 pi k by N and k is equal to N
in this case, all right and that is how you are translating. So, the g t is translated in time
as well as it is translated in frequency as in the Gabor framework what we have defined
earlier.

So, this picture might be able to help us to understand the overall picture or overall
explanation of a typical GFDM system, ok. So, now, we get back and the, this particular
picture is also relevant for us in our discussion. So, if we take this particular pulse shape
which is for the first set we will find in frequency. So, these are the corresponding
frequencies spectrum occupancy of the different carriers, right.

So, what we have is that here as you as you observe we have the first column then the
Nth column. So, first to N minus 1 1 to N minus 1 column of the GFDM modulation

588
matrix would indicate the N subcarriers, ok. The N-th to 2 N minus 1 would indicate the
same subcarrier. So, 2 N subcarrier is basically the first subcarrier and, and sorry the 2 N
subcarrier is the first subcarrier and 2 N, sorry the N-th subcarrier is the same as first
subcarrier and 2 N minus 1 is the same as N minus 1 subcarrier, right like that.

So, similarly over here in this set what you will also find that 2 N to 3 N minus 1 and
here you are going to find 3 N to 4 N minus 1. So, overall so, again what you will find is
that 3 N is the same as the first subcarrier and 4 N minus 1 is the same as the N minus 1
th subcarrier. So, like that they are arranged. So, again first subcarrier first symbol first
subcarrier, second symbol, first subcarrier, third symbol first subcarrier fourth symbol
like that they are arranged first subcarrier second subcarrier first symbol third subcarrier
first symbol fourth subcarrier first symbol and like that. So, this is how you have to
visualize the entire picture, ok. So, for these set of columns we have the spectrum
occupancy given in this particular picture.

So, what do you find is again g n and g n shifted in frequency by the exponential S
function? And here we are what you find is g n and then it is shifted in time by this
frequencies by, by this time samples and by mod modulo MN, it means there is a circular
shift by means of circular shift. You reduce the spreading in time and thereby you have a
more compact single in time, but the flip side of it is the out of band naturally becomes,
more than if you would let it grow in a linear fashion. So, this is the overall framework
for GFDM that we are looking at, ok.

589
(Refer Slide Time: 13:46)

So, this is how these entire set of equations that we have described can be visualized in a
graphical manner. And this whole equation that we have over here can be represented in
a matrix notation and the A matrix which is the modulation matrix is contained of
elements where this g is the first column is the g t, you can think of it as the g t. And then
all the columns up to the N minus 1 column or the N-th column are basically the
frequency is translated 1 then the first column over here is the time translated version of
this.

And the second column over here is the time translated and first frequency translated
version of the original Gabor atom, ok. That is how one can think of the entire structure
and can understand the whole picture, ok.

590
(Refer Slide Time: 14:36)

So, this picture we had explained and now you can naturally follow through all the
descriptions that we had given earlier.

(Refer Slide Time: 14:42)

591
So, if we look at the, the situation now. So, what we see is that x is equal to A d where d
is the vector of constellation points A is the modulation matrix and x again is the vector
of GFDM modulated symbols. So, here this is MN cross 1. And this again would be MN
cross 1 and this would be MN cross MN, right this modulation this GFDM modulation
matrix, all right. So, that is how the whole thing. So, MN number of samples are
available and so, we have the entire equation now.

So, A d represents the x GFDM modulated signal H represents the channel which is the
convolution channel matrix, right. And h is the channel impulse response and we can get
the received signal in z and, and this is how we can write the entire set of equations. So,
if H is the circulant channel matrix which represents the convolution operation. And so,
basically you have X times H is equal to z and of course, there is noise term which gets
added. So, instead of X, we are writing that matrix equation A d, ok. So, now, if you look
at z, we can expand H because it is a circulant matrix in this form, where WMN is a M
times N order IDFT matrix, right. This is a this is a natural way of factorization and these
are the Eigen values or this in order words, you can think of it as the Fourier transform of
these coefficients, ok.

So, this is the diagonal or the channel frequency matrix, right. So, this is how you can
expand the whole thing. So, this is what is the received signal. So, what we are now
going towards is how do we recover d from this z that we have received.

592
(Refer Slide Time: 16:54)

So for receiving there are two ways of doing it one is known as the two stage receiver in
the two stage receiver the channel is equalized first, ok. First you equalize for the
channel and then you followed by G module GFDM demodulation, ok. We have written
GFDM self interference the reason is if you look at this A d, A d is such that everything
is mixed up it is, it is not necessarily a orthogonal matrix, it is generally a non orthogonal
matrix. And hence there is a lot of self interference due to operation at the receiver. If I
do A Hermitian A then it is a matched filter operation and we are going to get a huge
amount of self interference, but at the cost of certain other advantages with GFDM
provides.

593
So, when we are equalizing at the receiver what one needs to do is if you look at the
previous expression we have A w lambda W Hermitian. So, we have W lambda W
Hermitian, right. And A d, right this is your equal to z. So, now, what is being done is
this is being multiplied, right. So, if you multiply that what will you get is W Hermitian
W is identity and then in case of Aeq.

So, this is basically the channel equalization part, ok. So, this is zero forcing frequency
domain equalization. So, in case of zero forcing frequency domain equalization instead
of Aeq the, the lambda equalization eq indicates equalization, you can take it as lambda
inverse. So, the moment you multiply W with W Hermitian with W, you are going to get.
So, basically you replace this z with W lambda W Hermitian A d, right. So, this will
produce an identity and then you have a product of lambda AQ with lambda.

So, this is your choice of equalization matrix at the receiver and you can choose it to be
lambda inverse. In that case, this product will again produce an identity matrix then
again W W Hermitian will again be identity. And then you are left with A d so; that
means, if you are using the lambda inverse of A Q then you are received signal can be
written in this manner and then you can recover the whole thing. So, whereas, instead of
doing zero forcing, you can also do a MMSE equalization. So, in case of MMSE
equalization your MMSE equalizer A lambda eq would look in this manner and instead
of. So, once you have done this equalization. So, you will be left with so, once you are
done with that you will be left with lambda AQ, lambda AQ times A and W Hermitian,
sorry lambda eq lambda this is not a lambda eq lambda A d and here you have a W, ok.

So, this whole thing now needs to be equalized. So, generally you would have it in a way
that this cancels out the interference either by MMSE procedure or by zero forcing
equalizer. And then whatever is remaining you would have to equalize that with Aeq as
the equalizer coefficient for A and then you need to recover the whole signal. So, for
matched filter operation your Aeq would be equal to A Hermitian and for zero forcing it
will be a inverse, ok. For MMSE, it will be which looks like this where this is the
covariance matrix of noise and for unbiased, you have to modify this expression with a
factor extra factor which is described in this particular equation.

594
So, again these works can be these details can be found in some of the references which
we will provide in the in the material then you can easily go through the derivations and
find out how these kind of things work out.

So, you have to equalize the channel and then you have to equalize for the GFDM
modulation matrix. Now, if you compare this with OFDM you will remember that A
matrix which is the GFDM modulation matrix is comparable or it is equivalent to IDFT
matrix at the transmitter for OFDM. So, if you write W with the IDFT matrix then this
will be the IDFT matrix for case of OFDM and the sizes of course, will be different this
is the MN cross MN and this is usually N cross N matrix. So, you can also compare with
the MN block size of OFDM to take MN size of samples simultaneously and when you
have to equalize both the channel and the GFDM modulation simultaneously. So, what
we have is Z is equal to HAd, right that is what you get.

(Refer Slide Time: 21:49)

595
So, Z is equal to HAd, right. So, now, you have to recover d. So, HA together you can
assign it to be equal to B. So, you can write whatever you have received as Bd plus noise
and then you have to find a B equalizer matrix which can cancel or normalize the
problems that has been introduced by the B matrix.

So, here again the MMSE equalization would be in this manner and the unbiased
MMSE would be again a modification with this scaling factor which is also described
over here and details of this are available again the papers that we can provide to you ok.

All right, so, now, d is receiver operations although they appear straight forward in the
mathematical notation, but implementation of MMSE is not a very- very simple job, it is
very- very complicated, you can see lot of matrix multiplications that happen over here
and there is matrix inversion. So, the order of complexity is very high without doing any
reduction of complexity any matrix inversion or multiplication is typically around order
of N cube although you can bring it down to N to the power of 2.7 or something like that
very still very close to order of N cube let’s say. So, you can easily imagine the amount
of complexity that is involved and then there is a set of low complexity transceiver
architectures which again we can provide as reference, but we will not discuss in this
particular lecture, because those are special aspects only for those who might be
interested in the very great details of such receiver architectures.

So, we will skip few set of things, but it will be made available for those who are
interested. So, you move forward and look at another modification of GFDM which is
called the pre coded GFDM and will briefly tell you about this.

596
(Refer Slide Time: 23:50)

So, in the receiver you basically have A Hermitian A as the operation when you are
doing matched filter. So, if you study these characteristics of such matrices, these
matrices turned out to be block circulant with circulant blocks. Again details of these are
available in reference papers which will provide to you so; that means, there are block
structures there are block structures which appear in a circular fashion and within the
blocks also you will find that there is a circular symmetricity that is present in it.

(Refer Slide Time: 24:25)

597
So, that is exploited in factorization. So, A Hermitian A can be factorized in this manner
where FbM is the block IDFT matrix and if you are doing H A; that means, channel
together with the modulation matrix then you will be again having another similar
factorization, but this is of size N and in this case this will be of size M, ok. So, now, if
you look at the way this receive this signals are, ok. And this can be factorized with
block IDFT matrices, right. So, the good part of all of this is whenever we talk of IDFT,
we get low complexity implementation, right. So, once we can realize this in terms of
IDFT operations, we will get a great advantage in reducing the complexity.

So, all that we are seeing over here is that in this processing, if we could somehow use
this factorization and spilt the processing complexity between the transmitter and the
receiver then we can reduce the complexity of operation at the receiver quite a bit, all
right. So, in this manner, if you look at the whole factorization matrix, right. So, we
should be able to do a lot so that means, HA Hermitian HA operates. So, if you are at the
receiver you would be able to get this whole factorization and then you can do some

598
IDFT operation on this side, IDFT operation on the other side and you would be able to
manage the the operation.

(Refer Slide Time: 26:10)

However, from this we have this motivates us to precode the GFDM modulator with
FbM, right. If you are, if you are going to operate on a A Hermitian A matrix and if you
are going to operate on this joint processing; that means, if you are going to take H A
together then you can do a precoding with Fb. So, if you are doing precoding with FbM
then your FbM on data, you write FbM on data and then you get this particular part. So,
what you see over here is that A Hermitian operation should be done at the receiver. So,
if this operation has to be done at the receiver then the receiver sees A Hermitian A,
right. So, if the receiver sees A Hermitian A. So, A Hermitian A can be factorized in this
form, right and where D is a matrix which, which is of this structure, which is of this
structure.

So, if we can get this D matrix, we can demodulate our signal finally, we have to
equalize for this D to reduce the complexity you can preprocess at the transmitter with
this. And then you only have to process it with the block DFT matrix at the receiver side
right the same thing applies in case of the HA based operation. So, what we do is we do a
preprocessing with either Fb that is block IDFT matrix of size M or Fb of size N
depending upon whether we are going for two stage processing or we are going for a
joint processing, right.

599
So, at the transmitter you choose one of the options depending upon a pre-agreed a
condition and then the signal goes to the channel when it comes to the receiver, if
depending upon the mode of operation it would either go via this path or it will go via
this path, right.

So, in the two stage receiver case there is a frequency domain channel equalization
which happens first and then at the receiver you are doing a DFT based operation. And
then D blocks equalization happens at the receiver in the other case as you can see over
here in the matched filter reception you are doing a F b H A multiplication at the, at the
receiver side followed by this a D block, this D matrix based inversion in order to get the
particular detection symbol out. So, what are the benefits of doing this precoding is what
we are going to briefly discuss and again all these details are available in this particular
paper which is again easily available, ok.

(Refer Slide Time: 28:54)

600
So, with this, with this we also move to another form of precoding which is called the
DFT precoding, and this is also available in this particular paper. So, one should feel free
to download and get into the details.

So, here the idea is relatively simple here we do a precoding with DFT spreading matrix.
In a similar fashion that DFT spread OFDM or kind of systems or SC-FDMA kind of
systems are handled. So, with this DFT precoding then there will be a subcarrier
mapping matrix followed by the GFDM operation. So, there is this is the precoding that
happens in case of DFT precoding and here these are the possible precoding options that
happen in case of GFDM.

So, here on you are seeing that the GFDM operation is happening. So, here also you are
seeing that GFDM operation is happening. So, these things are happening before at the
transmitter and at the receiver accordingly you have to do the reverse processing and
then you get back your data.

601
(Refer Slide Time: 29:58)

Similar, manner in a similar manner, because you have HA, H is a matrix A is a matrix
you would be able to also decompose into a singular value decomposition based
structure. And in that case, you would be able to a preprocess at the receiver like at the
transmitter side you could pre-coded with a V and at the receiver side you would
multiply with the U Hermitian. And then you can get back your original data and this
kind of a system you would call a S V D based pre-coded GFDM system.

602
So, here you have a S V D based pre-coded GFDM system, but this depends upon the
channel matrix, right. Here also this one there is no dependence on the channel. In this
case, there is dependence on the channel only when you are doing the channel joint, joint
processing if you are not doing the joint processing then there is no dependence on the
channel over here. In this case, there is no dependence on the channel in F, in SVD there
is some more dependence on the channel, right.

(Refer Slide Time: 30:56)

So, what we see over here is the frequency domain view of the signals. So, in case of
GFDM, we see that these signals are concentrated around one frequency band. In case of
the BIDFT-N based pre-coding. Again we see a similar structure, it is concentrated in
one frequency band and hence it is spread in time, right, where as in BIDFT-M mode, we
are seeing that the signal structure is having spreading coefficients across the entire set of
signal bands, right. We also have seen some more variants one is the LFDMA LFDMA;
that means, when we do the DFT, we do the DFT over a set of subcarriers which are next
to each other collocated, ok. Whereas, we can do IFDMA; that means, interleaved
frequency division multiple access.

In that case this frequency distributed all over, they are instead of having localized
frequencies one can have one frequency component here, here, here. And there and the
next frequency component would go there, there, there and so on and so forth.

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(Refer Slide Time: 32:09)

So, what we find? That is interesting results over here. In case of AWGN channel when
we look at the BER there is no difference in performance. So, that clearly indicates that
these methods does not degrade the performance of a typical GFDM systems these the
non-degrading pre-coding techniques. Now when we go to frequency selecting fading
channel frequency selective fading channel what we find is that when you are doing this
BIDFTM; that means, block inverse discrete fourier transform of size M; that means, of
the two stage receiver case you find that we are getting a huge amount of performance
benefit, right. The, the bit error rate is becoming better and what we also see is that the
IFDMA with zero forcing also has some good performance and. So, is LFDMA, but in
the reverse order.

So, this is the best then this then this compared to other typical GFDM systems. So, so
why does it happen one can understand, because there is a frequency domain diversity
gain that one that one gets in this scheme, in this scheme and in this scheme the more the
order of diversity the more is the gain and that is what is reflected over here, right in this
particular picture. So, what we gain is that by precoding there is no loss in BER in case
of GFDM. So, these are non distortion techniques; however, when we look at frequency
selective fading channel this is; obviously, provides a much better improved performance
than other known GFDM techniques.

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(Refer Slide Time: 33:42)

Interestingly, there is also very important performance metric which is the peak to
average power ratio. So, in peak to average power ratio what we find is that OFDM
which is here has a standard peak to average power ratio.

A standard form of GFDM has increased peak to average power ratio whereas, if we are
doing a let us say SVD based GFDM, there is a reduction if you are doing block DFT-N
there is a similar reduction, ok. So, this is for SVD based this is for block DFT based and
if you are doing BIDFT-M, sorry if you are doing LFDMA, right. So, we get a reduction
over here and if we are doing BIDFT-M. So, we see a huge reduction in the peak to
average for ratio and which is also the same as in IFDMA.

So, what we find is that this IFDM and BIDFT-M they provide a similar gain in
performance. Although BIDFT-M produces a better BER performance than other
systems, right. So, what we conclude is that pre-coded GFDM system provides a very
low PAPR which is a very very big advantage for providing for low complexity devices
for uplink procedures and all other things. And they also improve the BER performance
in a frequency selective fading channel.

So, finally, will conclude this particular lecture over here and what we will do is because
of time constraint we could not add it in this particular lecture we will briefly look at the
performance comparison of this different waveforms in the next lecture and then we will

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move on to newer things different techniques of fifth generation communication system
from the next generation from the next lecture onwards.

Thank you.

606
 Evolution of Air Interface Towards 5G
Prof. Suvra Sekhar Das
G. S. Sanyal School of Telecommunications
Indian Institute of Technology, Kharagpur

Lecture - 32
Comparison of Waveforms

Welcome to the course on Evolution of Air Interface Towards 5G. So, till now we have
seen the different waveforms and it is high time that we compare their performance
against each other. So, that we get a picture of how things would work out and what is
the right solution to be picked up. So, till now we have seen various different waveforms
like OFDM of course, we have seen its variant then SCFDMA SCFDE then FBMC,
UFMC, GFDM and all these different forms that we have seen. We have also seen pre-
coded GFDM where there was some modification before sending the waveform which
give us performance in terms of lower out of band as well as low PAPR as well as
improve BER performance.

What remains was low complexity performance; we did not show you the low
complexity results, but they are very details and they are available in different papers.
So, it is recommended that you can follow those papers to look at the different
architectures, we can reduce the complexities especially of GFDM transceiver systems;
for other systems there are other papers which one can easily find out. So now, we get
into the discussion on comparison of the different waveforms that we have been talking
about.

607
(Refer Slide Time: 01:32)

So, we have the three different waveforms which are kind of important. So, the first one
is Filter Bank Multi Carrier on the left, then we have Generalized Frequency Division
Multiplexing and we have unified filtered multi carrier Unified Filter Bank Multi Carrier
system. So, FBMC as we have said it has very good pulse shaping where each subcarrier
is linearly pulse shaped. So, you can see the first point of difference or its characteristics
right and in case of GFDM each subcarrier is circularly pulse shaped. So, that is where
one would compare against each other right.

So, that is the difference and we had also shown the diagram how things would transit
from one to another and here what we find is that each sub groups are OFDM modulated
and then filtered ok. So, what we see in the first two it is per subcarrier based whereas, in
the last one its group based and in OFDM it is for the entire set there is one filtering. So,
this is kind of tradeoff between the extremities which are shown in the left and OFDM.
And, what we find for GFDM is that it is a block based transmission scheme, this is also
that what we have identified that it is a block based mechanism. A block based
mechanism in the sense that not just one symbol, but multiple symbols are grouped
together and a block is formed and a CP is added in front of the block.

So, its entire block which is processed whereas, this is symbol by symbol processing and
this is also symbol by symbol processing on the other hand. It is a generalized
framework for waveform, this can be used for translating to other things and then GFDM

608
can be converted to other forms. The problem here is that the sub-carriers become non-
orthogonal owing to the different pulse shapes; in a manner that if we take the
modulating matrix A A Hermitian that is not equal to identity right that is what happens.
So, there is the matched filtered receiver that when implemented will not give I mean
interference free signals. So, there is lot of interference amongst the modulating signals,
but it has several other advantages which we have discussed.

When we look at FBMC the orthogonality among sub-carriers is forced for AWGN and
flat fading channel that is the advantage. And, in this case what we find is that it may
converge to FBMC as well as filtered OFDM depending upon how you configure the
entire system right. So, this is again slightly different compared to the other two. In
FBMC there is no cyclic prefix, in GFDM there is a cyclic prefix for the entire block,
here again there is no CP ok. So, there is no CP for this, in case of FBMC, ISI is present
in frequency selective channel and it is not suitable for tactile internet, it is flexible in
terms of pulse shape. So, one can choose different pulse shapes and get different
characteristics. This is flexible in terms of the time frequency resource grid because we
said it is a block based.

So, one can reduce the number of blocks, one can increase the number of sub-bands in
the frequency domain. So, basically a tile can be made in frequency and time as one
desires in depending upon the application scenario right one can also think of structures
like this. So, it is very flexible waveform. If you look at today’s 5G NR it is also flexible,
but does not use GFDM it uses a variant of OFDM. So, potentially the framework is now
laid whereby, in the next generation GFDM can easily fit into the framework. This is
suitable for tactile internet because you can make it small duration signal as well and
short response time is also feasible, you can make wider subcarrier bandwidth short
symbol duration. So, things are feasible in this, this is also suitable for tactile internet.
So, these are overall characteristics and then we will get into the relative performance of
each other.

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(Refer Slide Time: 06:27)

So, to look at the relative performance we take a set of sub a set of simulation
parameters. So, where we have taken a 64 subcarriers for simulations its it is just for a
primary evaluation and number of time slots is 5, that is a block based system 16 QAM
modulation is used; we did not go for QPSK because QPSK detection can be done by
means of only phase differentiation. So, amplitude distortion is not going to affect the
system much whereas, if you take a 16 QAM system. So, in a 16 QAM system your
amplitude distortion is going to influence significantly. So, we need not go to higher
order systems we could have gone to 64 QAM, but it is not necessary because all the
different effects are already captured in the 16 QAM we found a mid-path.

In the pulse shaping that is used for GFDM system it is RRC with different roll-off
factors, but we will be looking at this roll-off factors primarily. And, for OFDM also the
roll-off factor is kept the same with RRC, for FBMC it is PhyDyas filter and there are
different filters equilibrium filter for UFMC and so on and so forth. CP length channel
length is made same as that exponential power delay profile just for the sake of
simulations and evaluation performance. And, these are the other two important
parameters of subcarrier bandwidth and coherence bandwidth of the system that is used
for evaluation.

610
(Refer Slide Time: 08:10)

So, this is the first result that we see that is the BER performance with ideal receiver. So,
this is something; that means, when you take the BER performance with the ideal
receiver; that means, you assume perfect synchronization and all alright. So, with ideal
channel information available everything available how do they perform? So, what we
find is that in these systems the SCFDMA sorry the SCFDMA system which is sorry the
BIDFTM BIDFT GFDM is here; basically this is the set of curves which identify that
performance. So, it is basically this set of curves ok.

So, we see that it is the best performance in BER terms because, there is spreading gain
advantage and we have discussed this earlier.

611
(Refer Slide Time: 09:11)

A quick step back you will find that BIDFTM provides this one which we had described
earlier provides significant diversity gain.

(Refer Slide Time: 09:19)

And here is the frequency domain spreading of the signal that helps us understand that
across frequency the signal is spreaded. So, when it combined at the receiver it takes
advantage of the compare of the combining. And, hence it provides the significant
advantage relative to all other waveforms ok. So, then we look at the next waveform
which is SCFDE. So, SCFDE is this waveform as you can see which is so single carrier

612
frequency domain equalization. Again this also is pretty good in terms of the fact that
you can have the DFT spreading, if you would remember there is a DFT spreading
followed by OFDM which is IFFT.

So, if it is of the same size then they cancel out each other and you result in single
carrier. If you add a cyclic prefix you can do frequency domain equalization and it
retains the characteristics of single carrier. The extra advantage of SNR is because there
is cyclic prefix per symbol whereas, here there is per cyclic prefix per block. So, there is
some reduction of loss in SNR otherwise they would have the similar characteristics of
performance ok. So, moving further we see the next one which is IFDMA there is
Interleaved Frequency Division Multiple Access GFDM.

(Refer Slide Time: 11:01)

This is this one which we have also described earlier and then we have this one which is
localized allocation for GFDM. And, followed by this we have SCFDMA with IFDMA
that is a DFT spread OFDM ok with interleaving and then we have DFT spread OFDM
with localized. So that means, you have this DFT spreading blocks, if you allocate them
on the same sub-carriers on the corresponding sub-carriers it is localized. Whereas, if
you if you would allocate one of them there, one of them there, one of them there that is
kind of interleaved division. So, there we see the performance that interleaving improves
the performance right. So, again this is the interleaved which is the performance here, is
the localized which is the performance.

613
And then we move further we see the GFDM system which is the cross, if we follow this
that is here with zero forcing receiver which is matching with OFDM right. So, there is
no loss of performance in that sense and then what we have is UFMC over here which is
relatively worse compared to these performances. And finally, we have FBMC up there
which loses its orthogonality that is what we had pointed out; FBMC has the worst
performance due to ISI induced in the wireless channel. Whereas, others can take care of
it and in fact, BIDFDM can provide you the highest amount of diversity as well as SNR
advantage compared to the other systems.

(Refer Slide Time: 12:46)

Moving ahead we take a look at the result where we have 5 percent carrier frequency
offset. So, that is kind of small carrier frequency offset that is present in the system. So,
again what we see is that in this case also because, it has already degraded here things
are only worse in case of FBMC. I mean this is not better anymore, but if you just take
CFO things would be different, but we have frequency selective fading channel. So,
performance is obviously different and then what we see is that GFDM with a zero
forcing is most resilient compared to others.

So, this filtering and pulse shaping is helping it to counter some of the carrier frequency
offsets and as we go higher up what we see is that interleaved frequency division that is
also GFDM. This is also GFDM which is here that is localized allocation and then we
find OFDM over here. So, these are close to OFDM, but only slightly better and then we

614
see SCFDMA which is affected by carrier frequency offset and both of the versions
SCFDE. So, all of these are worse in performance relative to OFDM which is worse
relative to the various forms of GFDM and then we see that UFMC is again up higher up
which is already there. So, kind of worse performance is already carried forward so it is
already degraded by the channel conditions.

(Refer Slide Time: 14:22)

In terms of capacity evaluation again what we what we compare against is the Rayleigh
fading channel capacity and then what we find is GFDM is again providing the highest
capacity followed by OFDM. And, this gap can be due to the CP loss, then we have
SCFDMA, I mean these all are pointed out over here and finally, at the bottom we have
SCFDE. So, what we see that GFDM is performing better in the frequency selective
fading channel as well as under CFO as well as it has the highest capacity capability that
is spectral efficiency in bits per second per hertz compared to the all other schemes.

615
(Refer Slide Time: 15:13)

Then we move forward to the other important performance metrics which is the PAPR
and we have described the PAPR earlier. And, we have stated that PAPR is important
issue because when we are especially talking about the uplink, that means, when we are
talking about sending signals from user equipment to the base station let us say right. So,
you would you have a small power amplifier here relative to the one at the base station
and you would like your signal to be as much compact in the amplitude form as possible.
So, that you can operate near the saturation region and you would be able to maximize
the utilization of the power available at the user end.

So, that is why we would like to have waveforms which have low PAPR, high PAPR is
not desired because you will have to have a back-off; back-off means lower transmit
power, lower transmit power means poor coverage and more wastage of battery
especially of the hand-held devices. So now, if we compare all the schemes what we find
is that again FBMC is the one with the highest peak to average power ratio compared to
all other waveforms. So, one may find some relevant papers which talks about pulse
shaping only worsens the PAPR. So, if you take a rectangular pulse shape and do pulse
shaping on top of that especially for multi-carrier systems things only become worse and
that is what is reflected in FBMC system.

We also see that GFDM by itself has worse performance because it also has pulse
shaping on sub-carriers. So, one is actually not doing much in case of which is followed

616
by OFDM. So, one can think of OFDM as the reference point because, this is kind of
acceptable is used and remember this fact that in 5G they are allowing OFDM to be used
in the uplink direction also while, the SC-FDMA is still allowed. Although it is still
allowed they are going for OFDMA an uplink and there used to be a very popular
standard known as WiMAX which was competing with LTE at some point and WiMAX
had OFDMA in uplink as well as in downlink. So, OFDM in uplink and downlink
whereas, in LTE there was SCFDMA SCFDMA at lower PAPR that was the primary
reason.

So, anyway OFDM can act as the benchmark in this in this system right. So, we can take
this as the benchmark point and compare others. What we find is UFMC is only slightly
better you know, one reason that when you are grouping subcarriers together then
effective number of subcarriers could become less or you are kind of playing around
with the phase factors with them. However, these three or these few set of results only
show us that things are only as good as OFDM or worse right. Things max can be as
good as OFDM, if you use the schemes by itself and then we look at some of the
variants, that we have analyzed in our work and we will present it here. One of the first
things that you will see is that the single carrier or the SCFDMA right.

SCFDMA with localized allocation is significantly lower than OFDM around 2 dB

benefit, you can get in terms of PAPR and then with interleaved allocation you get it
even better that is here so, this is the first, this is the second. So, this is the first, this is
the second that we have just discussed and SCFDE is similar to the second scheme so,
this is the third scheme that we have discussed. So, more or less SCFDE gives you a
better performance than OFDM systems that is quite expected because, you are having
single carrier like performance, but it is derived from OFDM. So, some of the
reminiscent things would be providing you a higher peak to average power ratio ok. So,
then we take a look at the next thing that is some variant of GFDM that is localized
FDMA GFDM; that means, you are doing some kind of an allocation which we have
described earlier. So, that performance is coming over here which is again similar to
number 1.

So, this is 4 right this is 4 which is similar to number 1 and then we take a look at some
of the other GFDM based schemes which is IFDMA. So, IFDMA is interleaved
allocation. So, this one which is you can put it as number 5 and then you have the sixth-

617
one sorry this is this is number 5 and then you have the BIDFTM which is number 6. So,
once again we find that BIDFTM provides a huge reduction in peak to average power
ratio and in fact, it is the best performance. So, it is a pre-coded version of OFDM which
can reduce the PAPR by a significant margin which can only provide better uplink
capabilities. So, with this we can compare the different waveforms with important
performance metrics.

(Refer Slide Time: 20:53)

But then we move on to another very important characteristics which is the out of band
spectrum leakage right and that is one reason why the filtering has been done on these
different waveforms. So, what we see is while FBMC has been relatively weak compared
to all other waveforms and the different metrics that we have been comparing, we find
that it is the best scheme as far as out of band spectrum leakage is considered. So, you
can clearly see from the picture that FBMC is basically this one with the brown color.
So, that is the FBMC spectrum and FBMC spectrum is having the very very narrow
transition region and beyond that the out of band is at the level of nearly minus 85 dB
with respect to the peak performance. So, which is very very good. So, it is the best in
fact, and no other scheme can achieve an out of band performance which is as good as
FBMC.

So, if out of band leakage is the most important criteria then of course, FBMC is the one
of choice, but of course, one has to remember the other losses that one has to bear with

618
under different conditions. So, if conditions are favorable in terms of flat-fading I mean
ISI is not affecting the performance then FBMC can be chosen to work in within very
narrow bands and signal has to be fitted into such available gaps. In this context what we
see is that these two groups of GFDM are relatively worse compared to FBMC ok. So,
they are not really as good as FBMC in that sense whereas, again FBMC is coming
somewhere in between and this was expected while, OFDM is somewhere up there ok.
And, then we also have DFT spread OFDM also along with it.

So, what we find is that in this case FBMC has the best spectral characteristics and we
can rank FBMC as number 1 and we can rank UFMC as number 2. And, then you can
rank GFDM as number 3 and then we have OFDM. So, in that order I would put it like
that right and of course, if you are able to do some filtering on these then the
performance would be somewhat better than what we are seeing in this particular picture.
So, overall what we see is that FBMC is very strong spectral characteristics, but worse in
other terms whereas GFDM is better than OFDM in terms of spectral characteristics, but
much worse than FBMC. But, on the other counts it has a much better performance than
the different waveforms.

(Refer Slide Time: 24:02)

So, now when we look at this particular result we have windowing is what we were just
mentioning in the previous one. So, W stands for Windowed GFDM. So now, what we
see that the outlook that was presented earlier has changed significantly. So, this result is

619
the one for Windowed GFDM and what we have here the next one is this one is for
windowed OFDM ok and then we would also identify this one as UFMC ok. So, that it is
easier to read and then we have here this one as GFDM in its original form and finally,
we write this one as OFDM right.

So, we have of course, not mentioned the best scheme which is FBMC which stands its
ground so FBMC has not lost its position. So, again in order of ranking what we see
now, is that FBMC would be ranked number 1 in terms of out of band spectral
performance ok. And then of course, we have windowed GFDM as number 2 and then
there is a question on UFMC and windowed OFDM because, depending upon what we
are looking at. So, while transition is faster for windowed OFDM, but finally, it settles
down at a higher level its, but still it is less than minus 70 dB ok. So, if 60 dB is
acceptable then this is not a problem. So, otherwise we would put them at UFMC has a
better performance over here, but transition band is a little bit wider.

So, we can still put UFMC as number 3, OFDM as number 4 or these can be swapped
and then GFDM and finally, ranks exposed to OFDM. So, this is one reason why all
these waveforms people started investigating. So, what we see is OFDM clearly had very
poor out of band leakage performance while, FBMC has the best. And, OF and
windowed GFDM is the second best and pretty close to FBMC and if we compare the
other performance some variant of GFDM is always having a better performance than all
other schemes. So, what we can summarily conclude is that the different waveforms that
were investigated, they have improved upon the out of band, they have improved upon
the PAPR.

These two are very very critical reasons why the different waveforms were analyzed,
most fundamental reasons. Along with them there were two more reasons: one was the
carrier frequency offset resilience and then there was symbol timing offset resilience.
And, these performance are partially reflected only in CFO, we are we have not
represented the STO performance, but these are available in different papers and one can
look at them. These performances are important because, that would characterize the
capabilities of these different waveforms in terms of high Doppler tolerance as well as
asynchronous operation tolerance. So, we can compare we can take up the different
scenarios and see how they perform against each other and choose the appropriate
solution.

620
So, if a flexible structure is available or if a flexible structure is feasible then one can
switch between the different waveforms or they might be able to intermingle or they may
be going to stay with each other with a certain amount of performance capabilities.

(Refer Slide Time: 28:37)

We see chart of different requirements kind of here we have out of band emission, we
have BER performance, we have PAPR, we have resilience to carrier frequency offset.
And, then we have spectral efficiency as the different KPIs and we have the whole
different set of waveforms in this axis right, the names are there. What we find is that
FBMC has very low out of band which is desired and BER performance is very good for
BIDFT GFDM, PAPR wise also this is very good right.

Resilience to carrier frequency offset it is not that strong, but GFDM is stronger and
spectral efficiency wise what we find is that GFDM is kind of very good in that sense.
So, what we conclude is that there are various conditions under which different
waveforms are performing better and there is no one single waveform which outperforms
all others in all quarters. So, this is something to be remembered and hence there is still
some miles to be covered before there is a clear winner which can be identified.

621
(Refer Slide Time: 29:51)

So, in this particular thing we have identified with the with the marks like HR indicating
Highly Recommended and NR is Not Recommended indicating the different waveforms
and the different performance different evaluation or different performance metrics
which would be working out. So, what we conclude is stated just now that different
waveforms has different capabilities and with some more additional work we think that
we might be able to come up with waveforms which would satisfy the different
conditions in very good manner.

So, that you have a newer version which provides much better benefit than OFDM had
been providing. And, we would expect such waveforms to be part of the sixth generation
communication system over here. And, in the next lecture we will start discussing about
the propagation conditions which will create us which will provide us with sufficient
platform to discuss the different MIMO schemes and understand their performance
before talking about a few more issues related to the fifth generation communication
system.

Thank you.

622
 Evolution of Air Interface towards 5G
Prof. Suvra Sekhar Das
G. S. Sanyal School of Telecommunications
Indian Institute of Technology, Kharagpur

Lecture - 33
Channel models for Performance Evaluation -Part – 1
(Large Scale Fading)

Welcome to the course on Evolution of Air Interface towards 5G. So, till now we have
been discussing various methods for generating waveforms, which would be essential for
taking care of new requirements and advanced new methods, which would take care of
several additional capabilities of the waveforms that may be desired in future. So, once
we have done that, it is now high time that we start taking look at other important
aspects, especially multiple antenna based signal processing.

So, let me first tell you that there are NPTEL course; there is an NPTEL course which is
now available in archive which talks about MIMO communications which deals in
details. So, we do not make a point over here to go into the details, but only give you the
summary of the results, all details can be found in such an NPTEL course.

However, to make this particular course complete, we need to overview some of the
methods over there. But, before we study such issues, it is important that we understand
the propagation effects, and there will again be a short review of the entire thing we will
do it pretty fast with an assumption that people either know it, it is just a revision or for
others to make up for the material based on what we just show to read up additional
things.

So, what we will do is our plan is to discuss the propagation which will basically be large
scale effects, then small scale effects, then will go into the MIMO effects; MIMO
propagation effects the issues that will lay the foundation of the various things that are
needed to understand the MIMO methods, why do they work and what are the issues.
And we will also highlight, some of the aspects where MIMO is restricted. So, once we
are aware of these things, then we will be able to appreciate the different MIMO
techniques, thereafter, the entire course will proceed towards it showing the different
applications and system level concepts which are useful for the fifth-generation.

623
(Refer Slide Time: 02:24)

So, let us begin with our study on the propagation effects. And so, we will study the
large scale, and small scale and as quickly as possible.

(Refer Slide Time: 02:30)

So, we begin with our study of the large scale. Now, it is very important to study
wireless for various reasons which we have already highlighted. Amongst then the other
important aspects are it provides a fundamental limit to the performance of
communication systems. And as we said we also wanted to review the various

624
performance evaluation methods. So, therefore we need to understand the system or the
propagation characteristics through which these things get evaluated.

The second important thing is the wireless channel is random and that is why, it is given
the term fading right. So, again although things are random, but still you can understand
some of the properties by modeling the entire thing as a random process and hence, if we
can characterize the random process, then we have characterized the system in a
statistical manner. And hence that will be useful for us in evaluating the statistical
performance of any communication system.

So, what we have is we will study the time frequency and which will help us to study the
space characteristics. And typically, there are various kinds of links between the
transmitter and receiver one of them is the line of sight, the other is non-line of sight
which is mainly due to obstruction. So, these things have to be we have to be aware of.

And therefore, we need to study the signal propagation, because whatever signal we said,
whatever we have discussed earlier goes through the wireless channel. And when the
signal is received, after it has gone through the channel, we need to reconstruct the
original transmitted signal. So, if we know the kind of distortions and the effects that the
channel brings in, we will be able to only recover the effects in a nice manner.
Otherwise, without knowing what has happened to the signal will not be able to recover
the signal just blindly.

Again to study all of these things, models are very very crucial, because if there are no
models, then one would have to resort to only experimentation. So, if there is only
experimentation, then we one has to go out with transmitter boxes, receiver boxes and
which will contain entire circuitry of the signal generation, entire receiver signal
processing do experiments and then get the results and then evaluate, whether the design
has been proper or not.

So, this is not only cumbersome, it is time taking and it only delays the entire execution.
So, it is better that if we have models, we can do lot of evaluation in the lab, in our rooms
and we can come up with designs which are pretty good working versions. And then one
can go up and create prototypes, go for testing, field trials, and finally design the actual
system of operation.

625
So, therefore models play a very very vital role. So, if the models are very accurate; if
they are accurate, then you design needs minimum modification, when it goes for actual
implementation. And if they are inaccurate, there will be a lot of discrepancy between
the result that we observe in our studies, in our experimentation in the lab, compared to
when we go to field trials and further when we go for the actual system design, and
hence it increases the time of implementation.

So, the entire process of standards, which you have discussed earlier is dependent
heavily on lot of simulation results, which in turn depend on the models. And ITU does
provide a lot of models for evaluation, 3GP provides a lot of models, IEEE provides a lot
of models. So, what will do here is we will look at the fundamental aspects the main
issues. And once you are equipped with this, then you can easily understand the various
parameters the model structures, which are described by different standards and
organizations. So, they also depend on models and systems which are more fundamental.

(Refer Slide Time: 06:23)

So, you know wireless propagation, the different things that happen to the signal or
reflection, diffraction and scattering. And there are large-scale fading effects due to
shadowing and we will discuss more of them. As well as there is multi-path phenomena
that means, the signal which goes from the base station to the receiver, it propagates
through multiple paths, there could be line of sight path, there could be non-line of sight
path right, there could be obstruction which is not shown over here as well as there

626
would be mobility in the picture right in the scenario. So, all of these contribute to
various effects.

And again we would like to iterate that we are not going to study the physical
phenomena of these things, but we are going to study the effect of these things on the
signal. So, if we have sent x t, it has gone through various effects. And then finally, we
received the signal y t which is an accumulation of the signals along with that there will
be some multiplicative coefficient right.

So, we want to study, what happens to this and what characteristics of these coefficients,
do capture the various effects that are over here. We do not want to get into the details of
how these coefficients will be decided or how these will be designed or parameters
chosen to capture these different effects. We will accept certain models and will go by
using them.

(Refer Slide Time: 07:55)

So, when we study the wireless propagation effects on the received signal due to the
signal propagation over the wireless path. We categorized the study into various smaller
components, so that the study becomes easier, it is more meaningful than to study the
entire thing simultaneously.

So, what we see is that the wireless channel fading phenomena will describe what is
phenomena can be broadly separated into small scale fading and large scale fading ok.

627
So, large scale fading, essentially talks about models or gives us models which helps us
in predicting the signal strength over large separation distance between transmitter and
receiver. And that we study again in two parts the path loss and shadowing which will
discuss in this lecture.

The small scale fading talks about the fluctuations of receive signal strength. So, it
predicts the fluctuation in a statistical manner, when the separation between the
transmitter and receiver changes by orders of wavelengths comparable to the
wavelengths. When we study this, we discuss it in three different parts; one is time
selectivity, frequency selectivity and finally space selectivity.

In time selectivity, we classify the channel as fast fading or slow fading. Frequency
selectivity, we classify it as frequency selective or frequency flat, in the space selectivity
either as rich scattering or poor scattering. One fundamental issue, why we study it in
this manner is the reason that had we taken everything together. Then we would have
reached a situation, where the received signal would be non-stationary.

So, when we study small scale fading, we take away the mean, you take away the mean
or the average. So, this is without the average, it is a constant average signal and this
average is studied in the large scale propagation effects. So, we studied separately, when
we do the analysis we again do it separately, otherwise analysis would become very very
difficult.

So, when we study the average, again we distinguish the average into two parts; one is
the area average or the area mean, and the other is the local mean, and that helps us study
again in further details. So, when we go and study small scale, we consider usually a
given average, which is predicted by the large scale fading, so that is how the overall
study is distributed. However, when the signal is received, it contains everything. So,
once we go through it, things will be clear.

628
(Refer Slide Time: 10:49)

So, this picture one can find a similar picture in the wireless communication book by T-S
Rappaport, which describes the signal fluctuation over small separation distance. And
here by the green color, we have identified the signal which is fluctuating over small
separation distance as you can see and the large scale fading is nothing but the averaging
of the signal, which is indicated by the red color.

And one can clearly see that the average decreases slowly as separation distance
increases, while the small scale fading fluctuates or the small over small distances the
signal fluctuate significantly spanning a range of around 30 to 40 dB. And whereas in
large scale fading, it required to move across few hundreds of meters to kilometers in
order to get a similar fluctuations.

So, this gives us an indication of the range of fluctuation of the received signal, which is
much more than 40 dB, 50 to 60 dB easily and even more. And accordingly, raises the
imagination to the level, where one needs to question about how to design the receiver
ADC and things like that. So, there are ways to go around that, and there is lot of
adaptation in the signal transmission usually through power control and AGC which
ensures that you do not have a huge constraint or a big challenge on the receiver
component design. So, again if we understand these things will be able to appreciate,
how things have to be taken care of.

629
(Refer Slide Time: 12:15)

So, a large-scale fading phenomenon which is mainly caused by power dissipation

because, generally when we see radiate the signal from a location, the signal usually
propagates. And when we capture it, usually we capture a small area of the signal which
has radiated across. So, when the signal radiates is a huge cloud kind of thing with how
the signal expands and we capture only a small portion using antenna at the receiver.

And hence, we captured in a small portion of the signal energy and therefore there is and
as you increase the distance. The fraction of the energy, which is captured by the antenna
keeps on decreasing, because this sphere over which the signal expands becomes larger
and larger the surface area becomes larger and larger, whereas this remains the constant.
So that is what we study under large scale fading effects, it is the effects of the
propagation channel.

And when we study this we study about the path loss, where we do not consider any
shadowing will discuss what is shadowing. And as said the signal strength fluctuation
occurs across hundreds of meters. There are various ways of the models that people work
on, there are ray tracing models, but what we look at is statistical models as we have
been saying, since the beginning of the lecture.

630
(Refer Slide Time: 13:31)

So, if we combine everything together and as we increase the separation distance from
transmitter to receiver, one would find with the received signal strength decreases. The
monotonic decrease is usually studied under the path loss phenomena, which talks about
decrease in signal strength as a function of Tx-Rx separation distance only ok.

Now, around this there is the effect of shadowing will not call the phenomena
shadowing, but the effect which we observe is basically fluctuation of the local mean,
which will explain at an appropriate point of time. And that adds on top of it in the dB
scale or gets multiplied in the linear scale, so that gives rise to local fluctuations and
which is again a variation of the mean in a local region. On top of it there is small scale
fast fading, where there is a huge fluctuation of the signal strength ok. So, everything is
cumulative.

So, in the linear scale these gets multiplied, and we get the signal. In the dB scale,
obviously they will get added, dB scale is the logarithmic scale. So, as the as the
separation distance in the transmitter and receiver increases, the fluctuation continues,
but the average keeps on changing with distance. And if we study the average over the
area, there is a continuous decrease of the average; as we can see there is a continuous
decrease of the average, there will be local fluctuation of the average and there is
instantaneous fluctuation. This is a gross picture, and you study each of the things
separately.

631
(Refer Slide Time: 15:17)

So, in free space propagation there is unobstructed line of sight between transmitter and
receiver. Some of the examples are satellite and microwave links and Tx-Rx the received
power at the transmitter decreases proportional to Tx-Rx separation raised to a certain
power. And it follows the power law function is a Friis free space the space equation,
which gives the details.

(Refer Slide Time: 15:48)

632
So, the Friis free space equation tells us that the received power r indicates received, P
indicates power, at a separation distance d, is equal to the transmit power divided by d
squared and this whole thing is multiplied by transmitter antenna gain indicated by t,
receiver antenna gain r lambda squared and lambda is the wavelength of the frequency
under use and L are the system losses ok. So, usually you can consider these to be omni
directional and then these gains will turn out to be unity and then you can get a simpler
models so, all these what we have just described are given in the few bullets later on ok.

(Refer Slide Time: 16:46)

633
(Refer Slide Time: 16:49)

So, what we find, we will go further and what we usually measure the received signal
strength rather we describe the path loss, because the received signal strength is a
function of the transmit power. And transmit power can be depend; is usually dependent
on whatever settings we do, but this the loss is independent of the transmit power.

So, the model should capture a ratio of P t is to P r or P r is to P t. If it is P t is to P r, then

you will get negative or positive sign according to the choice of the ratio, whatever its
the loss? So, if we consider P r by P t as the ratio which identifies the loss and then
given, so this is basically captured by this expression it is in the log scale, in the linear
scale, you are going to get the appropriate expression which we saw before.

So, given a transmit power, you just multiply it in the linear scale or add it in the dB
domain and you are going to get the received signal strength that is how we usually
discuss these things. Usually, antenna gains are omitted to keep things simple and this is
the expression that you get. And here what we see is that d is raised to the power of 2, so

634
that is the path loss exponent all right. And this is pretty good in the far field of the
antenna.

(Refer Slide Time: 18:30)

Now, what we see is that if you let d tend to 0 right, then received signal strength tends
towards infinity. And hence this model is not a very very correct model, so what we do is
we define these things in the far field region, which is the region beyond the Fraunhofer
distance, which is defined by 2 D squared upon lambda, d is the largest dimension of the
antenna, linear dimension lambda is the wavelength. So, this Fraunhofer distance should
be greater than the largest linear dimension of the antenna as well as should be greater
than the wavelength.

635
And then the for path loss models, d cannot be 0. So, we use a close in distance d 0 and
that is a reference point. So, usually the received signal strength for some distance d 0 is
measured and you are given this particular value. So, if you are given P r d 0, then you
simply multiply this by d 0 squared and divide by d for d greater than d f and this entire
thing works out.

So, since we put this constraint, we do not have any further issue of d being going to 0,
so that is what is what we explained is simply given in these few expressions here in. So,
this P r d 0 is usually mentioned, where d 0 is also mentioned and P r is also mentioned
at d 0, which is used to translate the received signal strength at a particular distance d.

(Refer Slide Time: 19:50)

636
In the same thing, hence can usually easily be translated for path loss as well path loss at
distance d can be referred to the path loss at reference d 0, so that is what the received
signal strength in dBm would mean dBm is milliwatts, we will always refer to signal
power in milliwatts in most of the things that we do. So, d 0 has various ranges which is
usually used this is thing, something one can know and then we move ahead further.

(Refer Slide Time: 20:12)

So, there is a very important model, which is known as the two ray propagation model.
So, in the two ray propagation model, what we see is from the free space model, there is
usually non-usually line of sight. But, in most of the communication systems that we are
going to encounter would be non-line of sight right.

So, when you have non-line of sight, what you have is, there is one line of sight path and
one path which is reflected from the ground and goes to the receiver end. So, under
various set of assumptions, for example this incidence angle is almost 0 and that happens

637
when the separation distance is very very large compared to the heights of the transmitter
and receiver. So, when d is much much larger than let us say h t plus h r under those
conditions, you can get this angle which is almost equal to the raising angles. And then
there is a certain condition on the reflection coefficient, which gives us the value of
minus 1 right, which will we use in this particular model.

So, what we aim to do over here is we know the received signal and the direct line of
sight, the received signal along the reflected path, you add them together vectorially and
then you receive the signal. You can do it in various ways, we will follow the method
which is described in Rappaport, but you can also follow the classical method that you
consider the baseband signal as e to the power of j 2 pi f c t. And the other signal is e to
the power of course t minus the propagation distance divided by c and the other part is e
to the power of j 2 pi f c t, so t minus one of the distance is d and d 1 let us say, the other
distance is d 2 upon c, add these two signals and then take the amplitude of the signal,
and you are going to see what is the effect right.

So, so here effectively what we are studying is the path loss difference between the line
of sight, and the non-line of sight. So, effectively one of the paths is a direct path and the
other path is one with a path separation of delta x upon lambda. So, lambda is the
wavelength which will give us, so basically what you have is f c divided by c, which
leads to delta which leads to lambda in the denominator. So, if we take the amplitude of
this, we get the amplitude of the received signal strength. Take the square of this, you are
going to get the received signal power. So, with all the steps that are followed we skip it
here for brevity, which you can follow through in any of the courses or the books which
are given in details.

638
(Refer Slide Time: 23:06)

We will finally go into what we end up with; of course there is a few set of assumptions,
one of the assumptions we have already stated over here, d is greater than the h t plus h r,
and for very very small angles which are used in the derivation our objective is not to
derive over here, our objective is to mainly look at the end result.

What we find is that the received signal strength, which is a function of separation
distance d is proportional to P t naturally G t antenna gain at transmitter, G r antenna
gain at the receiver, h t squared is the transmit height and then we have h r squared,

639
which is the received height. And what we see most important in the denominator, we
find d raised to the power of 4, this is a huge distinction from the model of the Friis free
pace equation, this is to be noted.

So, what we find is that when we have one line of sight and one reflected path right, then
compared to Friis free space equation which says the path loss is proportional to d
squared. Here we find the path loss is proportional to d to the power of 4, which makes it
significantly different compared to line of sight. So, this is a very very simplistic
analytical model which only helps us in understanding how things happen, but in reality
there is a huge amount of measurement which goes through in deciding this value. And
usually, this value 4 that is over here is known as the path loss exponent, and which is a
very very critical factor for characterizing the channel.

(Refer Slide Time: 24:33)

So, when we take in the dB scale, we write it as if you take the dB value of this 10 log
base 10 of this, this is what you get, and what we see? There is a 4 multiplied by 10 log
base of t and this is what you characterize as n p known as the path loss exponent right,
so that is what is given over here as n p and everything is referred with respect to the
close in distance d 0.

640
(Refer Slide Time: 24:49)

What we see is that this path loss exponent n p varies over different environment. In free
space, it has a value of 2 which you have already seen. In urban cellular, it has a value in
the range of 2.7 to 3.5. In shadowed urban area, it has range of 3 to 5 and in building line
of sight it is less than 2, where there is this waveguide effect due to corridors right long
corridors and so on, so that is kind of a situation which you can encounter.

In obstruction, what you will find, it is going to 4 to 6 that is one of the highest values. In
factories, it is 2 to 3 because of a lot of reflections on metallic parts. So, what we see is
that the path loss exponent can vary from 1.6 to 6 depending upon the situation case to
case basis. And this would significantly influence the received signal strength prediction
model. So, as per this model, if we know this path loss exponent, then we can predict the
received signal strength given a particular transmit power.

641
(Refer Slide Time: 26:04)

Along with this, there is also something called shadowing effect, which we bring in as
the next parameter, and which is added to the path loss model, which would otherwise
predict only the average as a function of only transmitter-receiver separation distance.
However, if you look into practical systems, you will find or any realistic situation if you
would like to imagine.

The path loss tells us that if you go to a separation distance d, there is a certain received
power which is predicted by the separation distance d given a particular transmit power P
t. If you would go to any other direction on with the same distance d, the received signal
strength predicted by the path loss model would remain the same.

However, we know from real conditions that in one direction there might be a lot of
foliage, whereas in other directions there might be line of sight or there might be other
kinds of obstructions which is very different from the kind of obstruction that we receive

642
in one direction. So, hence this path loss model, which is only dependent on the
separation distance is not a correct or completely accurate way of capturing the
propagation conditions and hence you add the shadowing phenomena.

The shadowing phenomena is one which is modeled with lot of details will briefly talk
about it here again, because to only make us aware of the situation. So, what we know is
that this shadowing phenomena has been modeled based on various observations and
there has been huge detailed amount of papers which talk about talks about the
correlation, these fluctuations. And since, there is randomness that means, we do not
know, where we are going to do the measurement.

And since our evaluation should capture all possible scenarios, therefore one should be
able to capture the various the fluctuations. And hence, we get into a stochastic process
or a random variable is introduced into the model. So, once we talk about the random
variable, we need to talk about its distribution. It has been observed from various
measurement campaigns that this log-normal distribution describes this in the best
possible way compared to all other models.

So, log-normal means that if we take the dB value of it or we take it in the log domain,
then it is normally distributed, so that makes things simple. So, when we record or when
we talk about path loss in the dB domain, we have a Gaussian distributed random
variable which is added to the mean. So, simply taken things if one would take the
average over here at a separation distance d, one would take an average over here, one
would take an average over here, one would take an average over here, one would find
that the averages are different.

However, if one would take average across all points which are separated at a distance d,
one would average out these fluctuations and one would get received signal strength at a
separation distance d. And hence which results in the path-loss model, and hence it is the
area mean. Whereas, when we are talking about the average in the local region, we
talking about the local mean which is a fluctuation about this thing. And hence this is
added on to this expression which only predicts the average receive signal strength is a
separation of transmitter-receiver distance. So, when we talk about log-normal fading or
the average local fluctuations this S as a zero mean and variance which is denoted by
sigma x in dB, and there are various ranges of the values of x dB.

643
(Refer Slide Time: 29:42)

(Refer Slide Time: 29:42)

So, there are different models which capture, we will look into one particular model
which is from the 3GPP. So, here what we see that the loss expression is given by this
equation by L, I is a constant which captures several losses corresponding to systems.

644
And it is defined for 2 gigahertz as one particular value this I and it is given as another
particular value at 900 megahertz. So, this is what the model tells and the separation
distance R is in kilometers, if one is to use this particular model. And if one reads off,
this particular coefficient one would find that it is 3.76 multiplied by 10 and hence 3.76
is the path loss exponent for this particular model. What we find here, another important
thing is that the shadowing standard deviation is mentioned as 8 dB.

(Refer Slide Time: 30:38)

So, we will discuss all the various expressions, here we have it over here in this
particular slide; that this particular slide actually captures is from the document M.2135,
which we have described in our early lectures. So, one can refer to M.2135 which is a
document which tells us about how to use different models in the performance evaluation
of the communication systems, especially with respect to IMT-Advanced. So, this is
primarily with IMT-Advanced, but then you go to IMT-2020, and there is not much a
significant change in the models there are some new additional things that have been
brought into.

645
So, we will just see a glimpse of what happens? So, in one scenario which is indoor hot
spot scenario, in the line of sight condition, what we see is that the path loss exponent
can be thought of as 1.69 as the coefficient. And remember we had said that in indoor
conditions, they can be situations in path loss experiment is less than 2.

Here we see a non-line of sight condition indoor and then it is can be read off as 4.3. We
will see another case, so in urban micro, we again see that as 3.76 as the path loss
exponent. In all these things, we will find that the sigma values are also mentioned that is
3 in one case, 4 in another case and in different cases, it has been specified accordingly.
So, once we use these models in order to predict the signal strength to calculate the
coverage due to the signal and one can proceed to plan the whole network.

(Refer Slide Time: 32:16)

So, we stop our particular discussion over here. We will continue on to with this in one
more lecture, we will talk about the effect of this shadowing on coverage and how to
calculate the coverage area and the boundary coverage probability which is essential for
evaluating the performance of various schemes that are there existing today and are
going to come in future.

Thank you.

646
 Evolution of Air Interface towards 5G
Prof. Suvra Sekhar Das
G. S. Sanyal School of Telecommunications
Indian Institute of Technology, Kharagpur

Lecture - 34
Channel Models for Performance Evaluation - Part - 2
( Small Scale Fading )

Welcome to the lectures on Evolution of Air Interface Towards 5G. So, we are
discussing propagation model. In the previous lecture we have discussed the large scale
propagation model where, we have primarily seen the path loss as well as the shadow
fading parameter.

(Refer Slide Time: 00:33)

And we have also given you expressions or some samples of the path loss including
shadowing expressions which are typically used for evaluation. So, briefly we have

647
discussed about the average received signal strength in the area which is predicted as a
function of separation distance between transmitter and receiver d which is predicted
only by path loss is enhanced with a shadow fading parameter s. In the dB scale we have
declared that it is this Gaussian distributed and with a zero mean and a standard deviation
sigma sub chi or x dB; it is given in dB because this entire equation is in dB. So, that is
also given in dB and then we have expanded this thing and we have said that one can
look at the typical profiles that are mentioned; as example in this particular one which is
about IMT-Advanced where it talks about the path-loss exponent and as well as sigma
parameters.

(Refer Slide Time: 01:26)

So, that is what we have identified in the previous lecture.

648
(Refer Slide Time: 01:41)

So, using these models one can find coverage probability which will shortly see and we
have also been talking about this IMT-2020 which is nothing but the 5G.

(Refer Slide Time: 01:48)

649
So, there also we have been looking at the different path loss exponent and they have not
changed over significantly for the fourth generation evaluation models to the ones used
in the fifth generation model and those are path loss exponent these are the sigma dB that
is what we were talking about. So, using these one can generate various realizations of
the channels and one can find various performance aspects of it. So, that is something
which one should be aware and we will briefly talk about one particular way of
calculating the coverage probability so, let us look at that.

(Refer Slide Time: 02:28)

So, what we are interested using these models because these are talking about large scale
propagation models about the coverage probability in a particular area. So, again we will
talk about the methods that are used. There are various methods we will just talk about
by the first principle beyond this there are several advanced techniques which have been
developed, but it is probably difficult to put everything into one platform. But, of course
there are relevant papers which one can follow using whatever we are discussing here.

650
So, the received signal strength in the log domain at a distance d from the base station is
given by this particular expression which we have explained so long and where x dB
represents the shadow fading parameter; it is a random variable with Gaussian
probability function because, it is in dB and with a mean of P r d. So, this received signal
power in log domain has a mean value of this which is nothing but this part and a
standard deviation of sigma which is for this particular thing ok. And therefore, it is
represented as; that means, this is distributed you will find that this is distributed as
normal in the dB because, everything is in dB with a mean and the corresponding sigma
that is how this is represented alright.

So, the probability now since this is a random variable so, this is a random variable. So,
the probability that is the received signal strength, the received signal strength that is
how we would call it crosses a particular sensitivity level gamma right. So, this is in dB
m right. So, this is the received signal strength is in dB m crosses a certain sensitivity
level which can also be given in dB m is given by the probability that the received signal
strength is above that threshold that is it, that is what we want to calculate.

So, that is simply integrate from gamma to infinity the PDF; Probability Density
Function now with the variable x yeah that is where we are back ok. So, this can be
expanded as 1 minus integrate minus infinity to gamma and you can clearly recognize
this is the CDF. So, which is 1 minus it is less than the threshold gamma which can be
expressed as 1 minus the CDF and since it is Gaussian distributed we now know what is
it is going to be half complementary error function gamma minus the mean value divided
by root 2 sigma.

So, we see that we can calculate the probability of coverage at a particular distance given
the description of the path loss model and as one increases the difference one can find
the coverage probability at that particular distance. So, this of course can be translated to
Q function where you can see that half and root 2 has been absorbed that is the standard
translation.

651
(Refer Slide Time: 05:25)

So, what we are interested in calculating is the circular coverage area which is
determined by the radius R sub gamma, that is R sub gamma is the radius at which the
signal level crosses the threshold gamma right and what is the probability of doing that.
So, you define a coverage area as a coverage area is maybe a circular coverage area with
a particular radius wherein, the at the boundary the signal crosses the threshold of
gamma with a probability that P probability that received signal strength is greater than
gamma which is defined as prob R gamma right that is it that is the probability value.

So, that is how you define the coverage probability that at the boundary with this radius
what percentage of time one is covered. So, which is the likelihood of coverage at the
cell boundary; let me clear of all the ink on this particular page yeah.

652
(Refer Slide Time: 06:27)

So, the likelihood of coverage at the cell boundary with d will now be set equal to R
gamma; that means, coverage at the cell edge. So, the way to do it is whatever
probability of coverage we have been discussing can be associated with an infinite small
area at a particular distance d from the center. And, then we can simply integrate or
average out this probability over the whole area that is the whole idea, that is what we
want to do in order to find the coverage probability alright.

653
(Refer Slide Time: 07:04)

654
So, moving ahead now; so, the percentage useful area is simply the area averaged
probability of coverage right that one can calculate. And, to do that it is sometimes
essential to translate the expressions in terms of received signal strength at the cell
boundary or the cell edge, then things becomes easier. Because, through path loss model
one can easily calculate the average received signal strength at the cell edge and from
that one can do all the calculations so, things are better. So, we know that the average
received signal strength at a distance d is by this expression. We have been talking about
this and now you have to translate this expression to the one in terms of R gamma.

So, if we look at the expression between this and this there is no such big change because
this d is now replaced by R gamma and it is again cancelled by R gamma. So, the
equation remains the same, only thing is that we have introduced the parameter R
gamma. The advantage is when we look at the entire expression; that means, if we look
at this particular block then one will easily recognize this is P r at R gamma bar; that
means, the average received signal strength at cell edge. So, we can now reference things
with respect to this and P r d 0 bar is nothing but the average received signal strength at d
0 we have defined what is d 0.

In the next few steps you replace d with r because, that is the cell radius or the radial
distance and therefore, you can use the probability of coverage at a distance r from the
center is the same expression where, the d is replaced by r and the same expression; it
was complementary error function which have expanded in terms of error function. And,
then this P gamma that is what you have over here P average received signal strength;
you have expanded over here which is again not new. And, then what you can find is
again this at the denominator and at the numerator cancels out. So, it is the whole
expression is nothing but the received signal strength at the distance right alright.

So, we will erase some of the ink to reduce the clutter ok; proceeding further what we
now do is we club these two terms over here and the rest of the terms in the next step and
we have a meaning associated with it. So, we say that let a denote this thing so, this is a
and we also have this thing denoted as b right that is what is given below. So, if you have
these two replacements you can have probability of coverage in terms of error function
as written in the expression above. So, now one can use the different path loss models
that have been described in order to calculate the coverage probability at the cell edge.

655
Once you calculate coverage probability at any distance or at cell edge then you can go
back in calculating the percentage useful area of the cell that is possible. Now, one quick
interpretation on this is that, if you concentrate on the term a what we have I mean, if we
look at this a multiplied by root 2 multiplied by sigma x dB is equal to gamma minus P r
R gamma bar; indicating that this term is capturing the difference between the sensitivity
level and the received signal strength right. So, let us say sensitivity level is minus 75 dB
m and the received signal strength is minus 70 dB m.

So, this term is able to capture the margin that is present between the sensitivity level and
the average received signal strength and that influences the coverage probability. So, you
can now see in terms of margin and that is because you have over here the average
received signal strength at this cell edge. And, that is why the earlier introduced concept
of translating things to cell radius and received signals power at cell edge is very very
important right.

(Refer Slide Time: 11:41)

656
Moving ahead then as we said one can calculate a few and there are different ways of
doing it, you get certain expressions. Well, this is for available for reference, but that is
it.

(Refer Slide Time: 11:53)

So, we have discussed about the margin and that is a graphical representation of what we
have just discussed. So, there is a threshold and this is basically P r received it is P r of R
gamma bar. So, that is and this particular thing is the margin right. So, if we are actually
calculating we are actually calculating this particular area which is kind of outage

657
probability. So, clearly if this is fixed and we want a higher or higher coverage or lower
outage probability then we should shift this entire thing upwards.

In order to shift the entire thing upwards, all you can do is to increase the margin, if you
increase the margin your average received signal strength will now shift there and, hence
your mean point is supposed to shift over there. So, you are going to get your curve
which will look like this right and hence, your area under coverage will be this. So
therefore, which is a much smaller area and you have reduced the outage probability or
you have increase the coverage probability. So, to shift this upwards you can do two
possibilities, if you look back. So, what you have is a P t term over here. So, basically
you have to increase this term, to increase this term either I can increase this P t term that
is increase the transmit power or I can decrease this term.

So; that means, the path loss value would be smaller and hence this overall expression
has to increase which is nothing, but this expression correct. So, two ways to do it and
that is very logical if you reduce the cell coverage, if you reduce the cell radius then you
have increase the coverage probability. Or, if you increase the transmit power you have
increase the coverage probability, but the problem is interference comes in two play you
have to handle it in a different manner.

(Refer Slide Time: 13:58)

658
So, there are certain examples assignments which will be made available which you can
take advantage of and work on using these things. So, with this we move on to the next
set of discussions especially on the channel structures which is primarily about the small-
scale fluctuations. So, that is very very critical.

(Refer Slide Time: 14:28)

So, we have talked about the large scale fluctuations and so, we are done with the large
scale fluctuations. We will take an overview of small scale fluctuation so, that we
understand what happens so, that we can quickly look into the effects of MIMO how
does MIMO work and what is the advantage and you can probably these devise better
schemes even beyond what exists today.

659
(Refer Slide Time: 14:44)

So, in the in the small scale fading we have actually described the small scale fading. So,
we will briefly take a look at some of the fundamental models. So, here what we assume
that you are taking a top view of this plane. So, basically you are looking from top and
there is this floor area or there is a road on which the vehicles are moving. So, you are
seeing basically from top that is what is happening. So, the vehicle is moving along the
positive x axis with a velocity v and there is a incoming a plane wave from a particular
direction indicating that your mobility is in this side. And, some base station is here and
the signal is coming there or it might come by a reflection also from that particular
direction ok.

So, E field is along the z axis; that means, it is kind of in this direction and theta n is the
angle at the MS. So, certain assumptions are that transmitter-receiver separation distance
is very large and one can use 2D model for a wave propagation. So, that is what we have
already discussed.

660
(Refer Slide Time: 15:39)

So, it is the same same issue now that what we are talking about. So, the Doppler due to
mobility is given as f D n is equal to f m cos theta n, where you have the where you have
f m denoted as v c; v by c times f c which is the maximum Doppler shift. So, you can
clearly see that if cos theta equals to 0; that means, if it is coming from this direction then
the Doppler shift is maximum. If theta is from the opposite direction; that means, if it is
in the reverse direction it is negative of that value. So, the least possible value in that
case or the negative of the amplitude or the maximum value.

And any other direction you can replace with the cos theta, there is a component of
Doppler along the direction of mobility and the rest of the terms are defined over here.
So, the transmitted band pass signal one would usually write as the real part of the
baseband complex envelope s tilde t e to the power of j 2 pi f c t, that is that is a standard

661
model. And, s tilde t is the complex envelope of the signal, there are N propagation paths
and therefore, the received signal r t. So that means, if you recall the diagram there is this
base station, there is this user device. If the signal comes via multiple paths forming
different angles and each of these angles are theta n.

So, the received signal is a summation of the signals that has come via the different paths
with coefficients C n indicating the attenuation or amplitude factor of the signal coming
along the n th path. And, each of the path has an associated Doppler frequency with it so,
f c plus f D n and what we will see is that the signal, that is received at time instant t.
Signal that is received at time instant t is the original source symbol, but it must have
started at a time tau units before the present time. If it starts at time tau tau n units before;
that means, it has taken a propagation time of tau n corresponding to the delay associated
with that particular path. And, hence we have t minus tau n replacing t in all the
equations.

(Refer Slide Time: 18:08)

662
So, we proceed with this so, that is that is basically the signal structure. So, this is the
received signal which we had seen in the previous page. And, if we expand the equation
what we will do is we will just see e to the power of j 2 pi f c t is the term which we have
collected over here and rest of the terms we have kept together. And, that is there is a
specific reason for this because, e to the power of j 2 pi f c t is the situation what we
would like to handle separately because, this is the pass band signal and with the with the
real part of it.

So, what we can clearly realize is that this is the equivalent received baseband signal
when this has been transmitted and that is what exactly is written over here. So, this
entire thing is equal to r t tilde t right. So, that is that is what has been explained. And,
then in the next expression what we have is this entire term is we are collecting together
into the term phi n of t indicating that each path C n each n th path is having an
associated amplitude and an associated phase with it. This is very very important and the

663
signals by each path are coming with a delay; that means, different signals are coming by
a different paths right.

So, the signals which have been generated at different instants of time corresponding to
the path delays are coming and getting added together at the receiver. So, this is causing
ISI and this is well known. So, what we look at is the phase component associated with
each of the paths and one can easily calculate the phase difference because, of path
difference. And so, if you are taking the delta at the same instant of time; that means, if
two paths differed by delta tau n, two different paths then we can compute the resultant
difference in phase.

So, simply since let us take f c is almost equal to 1 gigahertz, let us neglect f D with
respect to 1 gigahertz. So, what we have essentially is the path difference between let us
say 2 is 2 pi times f c times delta tau n. Now, if you let delta tau n is approximately equal
to 1 nanosecond which means that two path lengths are different from each other by 1
nanosecond. What you will find is that the phase difference is 2 pi times 10 to the power
of 9 1 gigahertz multiplied by 10 to the power of minus 9 that is ; 1 nanosecond. So,
together it is giving you around 2 pi phase rotation; so, if two paths are different by 1
nanosecond.

So, if you take the speed of light it will approximately turn out to be 0.3 metres; that
means, 30 centimeters. If two paths are different by the 30 centimeters there will be a 2
pi phase difference and you are adding up several of them. So, even if paths are different
even less than 30 centimeters difference; so, you are going to get the phases which are
spanning 0 to 2 pi. And, many of them are coming together and we are adding them
together. So, what you can see is that there is a mixture of different phases along with
different amplitude factors associated with the coefficients of reflection.

664
(Refer Slide Time: 21:32)

So, this particular channel representation of the received signal that we see over here can
be modeled as a linear time variant filter having a complex low pass impulse response
given by g t t comma tau as given in this particular expression. So, if you compare these
two you will easily figure out that these are coefficients of the channel impulse response,
where the channel impulse response is given by this particular expression. So, where
each tap has a gain factor and a corresponding phase factor. So, then we are interested to
look at the channel impulse response characteristics at any instant of time. So, what we
will find is we have actually discussed that part.

665
(Refer Slide Time: 22:17)

So, what we will now make is a very very important assumption is that the let the delays,
the relative delays be very very small relative to the symbol duration. So that means, if
we assume that the symbol duration is really large; that means, T s is the duration is
much greater than delta tau n, I mean for all n let us say right. That means, this is not the
exact notation because we are talking about difference between two delays.

Then we can approximate all the different delays to one particular delay that is tau cap
that is an; that is a kind of situation. So, what is that? So, this is the situation when all the
path lengths are almost same right. So, if they are on an ellipse, if all the scatterers
reflectors are on an ellipse whose two focal points are the transmitter and receiver. So, in
that case the trans; the length would be the same and that is a kind of approximation or a
scenario that we are looking at.

666
(Refer Slide Time: 23:39)

So, under that condition we will find that the impulse response which we had drawn
which we had written can be written in this form; that means, you are going to get delta
tau minus tau cap instead of tau n. So, you are removing this tau n and hence this is out
of the summation, it goes beyond the summation. So, this entire set can be written as g t
with the single delay factor right. So, that is what is the channel impulse response and
you are interested in the in the Fourier transform of it.

So, if you take the Fourier transform of the channel impulse response. So, you get it as
capital T f and you just look at it. There is a delta function, you take a Fourier transform;

667
if g t with e to the power of j 2 pi f tau cap right and then what we are interested in is the
amplitude response. So, if you take the amplitude of g t what you will find is that the
modulus of g t modulus of T f would be left with modulus of g t. So that means, it is not
a function of frequency anymore and this is primarily because of this assumption set that
we have made.

So, under these conditions the amplitude response is not dependent on the frequency;
that means, if we have a frequency f and if we write T of t comma f at a particular
instant, it will be a constant value across all frequencies. And, if we have time in this
axis, then at every instant of time we can imagine that this bar to be at different values
right, that is what this bar is going to fluctuate like ok. So, that is what gives rise to flat
fading; what we have been talking about for a long time and that is one of the
components of the study that is what we have been looking at right.

Quickly we can even say that, if that condition is not true anymore; that means, if this
condition is not true. If this condition is not true, if this condition is not true, if this
condition is not true; that means, we are left with a situation like this then what is going
to happen.

(Refer Slide Time: 26:12)

668
That means we do not have a situation where, the transmitter and receiver are at the focal
points of an ellipse and all reflectors and scatterers are coming from the same ellipse, this
is the right path I mean like this. What if there is they are the focal points of other ellipse
also and the signals keep coming like this. So that means, there are resolvable delays
right. So, let us take a quick look at what happens when they are resolvable delays right.

(Refer Slide Time: 26:55)

So, that is the kind of picture that we get when they are resolvable delays and there are
groups of reflected waves which come at a certain delay, which we have just finished
studying. Another group would come at another delay and we have also studied the
effects of that, another group would come at another delay which we have also studied.
So, what is happening is if you would launch an impulse, an echo is going to come at a
certain delay which is let us say tau 1 and here all rays from different directions are
going to come and, they are within the same delay unit that is tau 1. The next group of

669
echoes are going to come together and they will add up and will not be able to recognize
them separately.

So, this one would be g of t comma tau 1, this would be g of t comma tau 2 in
correspondence to what we have just discussed. So, in this situation what we have is all
the properties that we have discussed in the previous set, same and valid for any one
particular delay at any particular delay. But, we have this entire series that is valid in the
entire thing and each of them fluctuate in time according to their own policies; policies in
the sense in a random manner. There are various ways of structuring this, there are
various models of doing it. One of the most common models that are used is Wide Sense
Stationarity Uncorrelated Scattering model which is followed in such analysis. So, we
will just briefly tell you the effect of such a thing.

(Refer Slide Time: 28:48)

670
So, what we have is this expression which you can easily recognize from the previous set
of equations, that we had been talking about. We had made the assumption that let these
different tau n’s be replaced by tau cap. Now, we are saying that no, let us go back and
keep this original tau n and see what happens. So, simply you are going to expand this
expression. So, you can you can decide to omit this because, it is just rewritten over here,
we have the same expression over here. So, you would simply have these things as
delays, delays and these coefficients. So, we have already explained that at each delay
you are going to get adding up of all the different rays that come at the same delay.

So, any one of them, if I look at this would correspond to g of t comma tau 1, this thing
would correspond to g of t comma tau 2 and so on and so forth. So, basically this is g of t
comma tau 1 multiplied by delta tau minus tau 1 multiplied by delta tau minus tau 2 and
so on and so forth. Now, if you take the Fourier transform, Fourier transform of this it is
a linear operator plus Fourier transform of this plus Fourier transform of the next and so
on and so forth. Each one of them are flat that is for sure, but they come with a certain
phase factor, it comes with a certain phase factor right. And so, when they add up
together they create a complete different picture.

671
(Refer Slide Time: 30:24)

So, what we will see is that if you look at the graphical representation, if there is only
one tap only one equivalent delay, this is the frequency response that you want to get. If
you have let us say two delays; then the frequency response time snapshot; that means, at
any instant of time at t equals to let us say t 1. It is not tau, it is time it will be this; as the
number of delays resolvable delays increase; that means, in this case if I say I have tau 1,
tau 2, tau 3 and so on the channel becomes more and more frequency selective. Why do
we call it frequency selective? The simple reason is, if I look at this last one or maybe if
we go further this particular one may have tau 1 tau, 2 tau, 3 and so on up to some tau n.

These set of frequencies we just change the color to match it, are allowed to pass through
with a certain amount of gain. If we look at another set of frequencies here, these set of
frequencies are kind of relatively attenuated with respect to other frequencies. So, again
we choose back the color, these set of frequencies are allowed to pass through with less
attenuation and these set of frequencies are kind of subdued or they are more attenuated.
So, there is selectivity across the frequency compared to flatness across the frequency
between the two conditions. So, this is again a very very vital situation that we have to
use while studying the different effects.

So, we stop this particular lecture over here and we will continue with the one more
lecture at least to consolidate these issues, before we can get into a study of MIMO
communications.

672
Thank you.

673
 Evolution of Air Interface towards 5G
Prof. Suvra Sekhar Das
G. S. Sanyal School of Telecommunications
Indian Institute of Technology, Kharagpur

Lecture - 35
Channel Models for Performance Evaluation - Part – 3
(Spatial Channel Model)

Welcome to the lectures on Evolution of Air Interface towards 5G. So, we are looking at
the propagation characteristics, we have looked at the large scale propagation models, we
have started looking into the small scale models. In that we have looked at the flat fading
condition, as well as the frequency selective fading conditions. So, we are now ready to
move forward towards studying the MIMO channel, but before we proceed there are a
few more minor things, which we one should one should look at.

(Refer Slide Time: 00:41)

674
So, here we take a brief look at it. So, we have discussed the frequency selectivity in the
previous lecture and what we need to just take a further look at some of the additional
things, when we combine the different aspects together for the different channels that we
have. So, we will get a profile which is better described in this particular image. So, what
we have essentially is that we have been talking about a situation, where an impulse is
launched and we get echoes.

So, we will choose a different color, we will get echoes at different delays which gives
rise to if you plot in the frequency domain frequency selective characteristics. So, on this
axis there will be H of f ok so, you know that frequency selective characteristics. Now, if
we look at any one delay, so this is the impulse that has been launched and these are the
echoes that come in. So, if we look at any one echo effectively, this is all about the
transmitter and receiver located at the two focal points of an ellipse, which contains the
different scatterers reflectors right, this is what we have said.

The second delay is again for a second tier of reflectors or scatterers, this is also what we
have discussed earlier. So, what it means essentially is that each of the delays and the
magnitude over here is due to summation over several of the components. And we have
accepted this particular model and we studied this under the flat fading system. So, if we
look at any one particular tap, we find that is the summation of several such coefficients
and this can be broken down into two parts g I and a complex because of this particular

675
complex part g Q, where g I one can write it as summation of C n cos phi n and g Q can
be easily written as summation of C n sin phi n.

So, because we have a large number of summations over here, each of these individually
can be modeled as Gaussian random variables. And hence when we have g of t which is
can be represented as g I plus j g Q in the complex form, each having normal random
distribution, mod of g will follow Rayleigh distribution. Under the assumption that this is
zero mean, as well as this is zero mean. And they be in quadrature we will get that the
modulus is Rayleigh distributed and the phase of g you will find it as uniformly
distributed in the range of minus pi to pi. This is a standard result; we are not going to
derive it in this course, details are there in the other NPTEL course on MIMO
communications.

So, if we focus on any one particular tap or any one particular delay and its time
evolution, we will find that the signal changes with time. And this is well captured within
this model, through the development of phi n which is a function of time, the model we
have seen before. So, the phi n which is a function of time there are two parameters one
is f c tau n that is related to the delay and there is f Dn times t. So, this is the term which
allows the entire thing to grow with time.

And what we have is several such different components because of different values of n
and just to remind you f Dn is equal to f max times cos theta n and cos theta n is due to
the angle of propagation that means, v is propagating along this direction that means, the
object is propagating along positive x axis and the waveforms are coming at an angle
making an angle theta n with the particular receiver.

So, under this consideration what we find is that the Doppler frequency is present in the
phase term, which allows it to grow. And you have different Doppler frequencies coming
from different directions. So, if f m is the max Doppler frequency because of cos theta n
term there is an effective different value of Doppler frequency. So, each tap experiences
several such Doppler frequencies added together to get the cumulative effect that we see
over here.

So, had there been only one Doppler shift we would have got a single tone corresponding
to that Doppler shift, but here since we have different values of n up to a very large
number, you are going to get different such cos theta n and hence different f D n that

676
means, you are going to get several such frequency components thereby giving rise to the
Doppler spectrum and not just the Doppler shift this is something important to consider.

So, then if we have such a situation, let us look at what this would result in when we
study that we look into the correlation analysis of the signal that means, we are generally
interested to study the received signal correlation.

(Refer Slide Time: 06:14)

So, we usually let that s tilde t in our model to be equal to 1. So, if you get back to the
model and we study the correlation analysis. So, if we look at the correlation analysis,
what we do is we would like to take r t that is the received signal.

677
(Refer Slide Time: 06:35)

And we would have the correlation of the process r t which is defined by phi rr of delta t,
which is given by this particular expression. So, if we analyze this particular expression
now, because that is written in these terms there is a sequence of steps which one can
follow, one would end up in a situation we just like to show you the result.

678
(Refer Slide Time: 07:06)

Where the end result of this would appear in a form as given here that the correlation
coefficient of the baseband equivalent component appears as zeroth order Bessel
function of the first kind, parameterized by f m delta t where f m is basically f D max and
delta t is the lag that is the correlation. So, with the correlation we can study the time
evolution and if we take the inverse Fourier transform of this, sorry if we take the Fourier
transform of this, we will get the power spectral density of the Doppler spectrum that we
are talking about it.

679
(Refer Slide Time: 07:48)

So, if we proceed further what we get, what the picture that we see over here is the
autocorrelation function. So, in the autocorrelation function we find that the correlation
function drops with increase in delta t for a fixed value of f m, effectively meaning that
at a particular offset of delta t for a given f m, there is a certain correlation value. And
this correlation value, let us say it is 0 point; in this case it is if it is 0.7. So, this delta t
value at 0.7 is the 70 percent coherence time.

(Refer Slide Time: 08:36)

680
For this particular situation that we have been analyzing, if we proceed further and look
at the Fourier transform of the same.

(Refer Slide Time: 08:41)

681
Where we lead is a spectrum characteristics which is a very famous Jakes spectrum. And
under these conditions if one has to find the coherence time that can be calculated as 9 by
16 pi fm, sorry it cannot be written like that 9 by 16 pi fm. So, if I know the value of f m,
I can roughly calculate the time duration over which the receive signal is coherent with
itself; so that means, when we go back to our earlier description that means, when we are
here in this particular model. So, this particular extension in time that means, this
fluctuation in time that we had drawn earlier, so this is a time evolution.

So, if we take the correlation of this time evolution, we will end up in a pattern as shown
in the previous graph. And we will be able to read off the coherence time corresponding
to the value of coherence over here, so then in this case it is 0.9 t. So, this will tell us
over how much duration of time is the channel coherent with itself that is it does not
change significantly. So, this is capturing the time domain fluctuations along with this
because of this power delay profile that means, because the channel is having delays,
resolvable delays and if you take the Fourier transform you are going to get frequency
selectivity.

In a similar manner, one would like to find the bandwidth or the set of range of
frequencies over which the channel is relatively flat and this description is given by the
term coherence bandwidth and it can be calculated as E of if this is the Fourier transform
f H conjugate f plus delta f, and then one would find the value of this separation delta f
for which this gets to a particular value.

So, what one can find is that the coherence bandwidth with 50 percent correlation can be
roughly calculated as 1 by 5 tau rms, where tau rms is the rms delay spread of this
particular power delay profile. If one is interested in calculating the 90 percent coherence

682
bandwidth, one is going to use the description 1 by 50 tau rms. So, tau rms can be
calculated from the power delay profile kind of description which is given over here.

(Refer Slide Time: 11:43)

So, if we accept these things, then so in this what we have is for a particular situation that
is if we are taking the exponential power delay profile that means, expected value of h

683
tau squared is given in this form that means, e to the power of minus tau by tau naught,
here tau naught is the one which characterizes the rms delay spread. And in that case,
one would be able to easily calculate the power delay profile or the RMS delay spread
analytically. Otherwise, this is the set of expression one has to use in order to calculate it
calculate the tau rms.

So, what we see over here is tau m is the mean excess delay of the channel and tau
squared bar is the weighted delay of the channel that means, you take the tau squared
multiplied by the power of the channel at that particular delay, integrate over the entire
range of it, normalized by the energy of the channel; so that is how one would calculate
the tau rms, once one calculates the tau rms, then one would be able to calculate the
coherence bandwidth in this manner. So, once one calculates the coherence bandwidth,
then one would be able to get a few things.

(Refer Slide Time: 13:06)

684
So that means, first one has coherence time and second one has coherence bandwidth,
coherence time is given as 9 by 16 pi fm and this is given by 1 by 50 tau rms. So, this
essentially gives us the range of frequencies over which channel is not fluctuating and T
c, so this is B c, gives us the delta time over which channel is not fluctuating.

So, if we are taking a time frequency grid which is contained within B c and T c, we are
looking at a portion of time frequency which is not fluctuating with time. And this is flat
in frequency and slow in time, which is most of the things that we are going to be
concerned with.

(Refer Slide Time: 14:08)

So, moving ahead when we combine everything together; so, the combined picture that
we get is depicted in this particular figure. So, let us look at any one particular image that
is the rural area. So, if we look at the rural area, we have the delay axis along this and
what we find is that along the first delay that Doppler is Jakes spectrum, which is again
Jakes spectrum along all delays as shown in this. However, on the first delay there is a
strong specular component which is the line of sight component.

685
If we look at the typical urban profile, what we will find is that at different delays there
are average echoes. And at each delay, there are different kind of Doppler spectrum that
is present and these are usually from measurements. And the earlier few delays
encounter Jakes spectrum and the later few delays encounter double sided gauss
spectrum. So, like this you can characterize the overall channel power delay profile and
what we will be concerned is with the situation, when the symbol duration is much much
greater than the tau max and the signal bandwidth that means, the bandwidth of the
signal is much much less than the coherence bandwidth.

So, if these two conditions are satisfied, then we are situation where the signal is not
experiencing fluctuations in the frequency or fluctuations in time that means, within that
small region the channel is as if held constant and most of our discussion will be with
these set of assumptions, all right. So, with this we have the basic profile of the things
that we require and then we move on to discuss some of the additional components that
are required to understand the MIMO propagation.

(Refer Slide Time: 16:15)

686
So, what we have discussed till now is the time frequency analysis. So, thereafter we
have to move to the space dimensions. So, from time frequency we have to go to the
space dimension, so that means as if we have an antenna over here, we have antenna
over here; so what about the signal which is received let us say I call it y at x and y at x
plus delta x, which is this separation is given as delta x. What we had studied till now, is
if y of t is available can we say anything about y plus t plus delta t and this was achieved
through the correlation analysis. And what we found is that the correlation follows the J
0 function because of certain set of assumptions, which are under laid within that
analysis.

So, now what we do over here is we consider, so we use that same analysis to the space
dimension. So, what we consider is that the mobile is moving with velocity v, which is
within our scope. And in time delta t, it moves a distance l which is v times delta t, which
you can also write as delta x ok. Now, since the Doppler frequency f m is given by this
term therefore, you can write v in terms of the other parameters. And hence this l or delta
x you can easily write as, f m upon c multiplied by c, because this is the v term v

687
multiplied by delta t. So, this is the v term that we have over here, so that v term is this
term multiplied by delta t.

So, now what we have is f m multiplied by delta t right; so, f m multiplied by delta t can
be translated to l or delta x multiplied by f c, because f c is in the denominator gets
multiplied and c comes to the denominator side. So, we have f m delta t is equal to this
and then since you have in the denominator c by f c or f c by c in the numerator. So, f m
delta t can be written as l upon lambda or you can also write it as delta x upon lambda.

So, now what we see is that instead of measuring the signal at two different intervals of
time, if we say that in this time interval something has moved across this distance delta
x, then we can potentially reuse this entire expression that we had got and replace this f
m delta x by this particular term. So, what we have in the next few statements is that the
correlation which we have designed; which you have derived between the signals with
the separation of delta t is this expression within which we are going to replace f m delta
t and what we get back is the expression over here.

In other words, we are saying that the correlation of two signals spaced apart is given by
spaced apart by delta x is given by this expression, under certain set of assumptions that
means, when the signal is coming from all directions with equal probability under this set
of assumptions. So, what we conclude from this set of assumptions is that if we set the
separation between the two positions or if we in other words if we look at two antenna
positions and consider the signal in those two physical locations, and if these two
physical locations are separated roughly 0.38 lambda, we will find that the correlation
goes to 0; or approximately we can say that when the separation between the spacing is
lambda by 2, we get signals which are uncorrelated right.

And if they are zero mean Gaussian random variables, then we are going to get
independent. This is also one of the big assumptions or the setup that we consider in the
analysis of MIMO that we are going to describe very shortly.

688
(Refer Slide Time: 20:17)

So, there are a few more things like we have RMS delay spread. So, what we have
discussed is that Doppler leads to coherence time, delay leads to coherence bandwidth
right, this is the delay tau max I have written influences so tau max is basically
connected to tau r m s and this is connected to actually Doppler spread.

Similarly, what we have over here is angular distribution in case of spatial dimension.
So, these were the things which we discussed in the time frequency plane, but when we
are going to the spatial dimension, what is happening is that the signals which arrive at
the receiver antennas, they can come from different angles. So, these signals they can
come from various different angles with a certain spread in this angular dimension,
which can be described by theta rms ok.

So, this theta rms is now connected to something known as the coherence distance. So,
we have D c which is called the coherence distance. So, instead of T c, B c, we have D

689
sub c indicating coherence distance which is connected to the term theta rms which is
nothing but the angular distribution of the received signal. So, when the signals are
coming from various directions, the signals would form a power angular spectrum which
is described by the picture which is given over here.

So, in a similar manner like one has calculated the tau rms, one can calculate the theta
RMS as is shown over here right. So, if one calculates the theta RMS, then from this one
can find out a similar thing the coherence distance. So, coherence distance is the distance
over which the signal is correlated to itself.

So, if we go back over here under the set of assumptions that the signal is coming from
all directions with equal probability, under such assumptions what we have seen is that at
a separation of lambda by 2 you get uncorrelated signal. So, if you are within that
separation, then you will get highly correlated. Now, unlike in time frequency when we
go for MIMO signal analysis, we would generally look at conditions where the received
signals in two different antennas would be uncorrelated whereas, in the time frequency
we would like to take that grid in time where the signals are highly correlated with each
other.

(Refer Slide Time: 23:08)

690
So, moving ahead we have a certain set of assumptions which we summarize as a
channel which contains which is supposed to be wide sense stationary, uncorrelated
scattering that means, wide sense stationary means the correlation function is not a
function of time that means, it is dependent only on the time shift, wide sense stationary.
Uncorrelated scattering means that the signals coming at different delays are not related
to each other.

(Refer Slide Time: 23:36)

691
And along with this, we have something called homogeneous channels. So, with the
homogeneous channels what is assumed is that the statistical behavior of the h
component, which is given by h tau, t comma d; tau means the delay, t is a function of
time because of Doppler and this is the spatial separation is locally stationary in the
space over several tens of coherence distance; that means, within a few tens of coherence
distance. The distribution of this is not changing or it is not changing over within that
spatial distance.

So, under that assumption if we are calculating the correlation at the location d and d
plus delta d we would call it, the lag correlation coefficient that means, it is not
dependent on d, but it is dependent only on the separation of the antenna elements. So, in
other words what we are saying is that the channel if it is wide sense stationarity
uncorrelated scattering with homogeneous assumption. We have the frequency domain
correlation or the coherence bandwidth is not dependent on the frequency, but only on
the separation between the frequencies. Coherence time is not dependent on the time, but
only on the lag in the time and coherence in the spatial domain is not dependent on the
location, but between the antenna separations.

(Refer Slide Time: 25:05)

692
So, combine together what we have is a channel which is wide sense stationary
uncorrelated state scattering with homogeneousness. So, there is also one more important
set of things that we considered, while taking into account the MIMO channels is that
there is a narrow band antenna array assumption. The narrow band antenna array
assumption means that the signals which are arriving at the first antenna and the last
antenna element of the antenna array are not different from each other than a phase term.

693
(Refer Slide Time: 25:44)

So, effectively what it means is that effectively what we get to is that the, I mean if you
go into the details of it what you finally end up is that, the propagation time between the
first antenna element and the second antenna element. So, in this picture we have made
the assumption theta that means, the time it takes to propagate from this to this suppose,
we mark it as T z.

And if we have T s as the symbol duration, so we say that it is under the narrow band
antenna array assumption if the bandwidth of the signal is much much less than 1 by T z.
So, if we translate this what we get is 1 by T s, where T s is the symbol duration; this is
the symbol duration is much much less than 1 by T z or in other words the symbol
duration is much much larger than the propagation time between the two antenna
elements right. So, all these conditions have to be taken into account, before we get into
the study of MIMO channels.

694
(Refer Slide Time: 26:45)

So, a quick discussion about how we model the signal so, in case of SISO links we have
one transmit, one receive antenna. The first class of channels is the SIMO channel, where
we have M R number of receive antennas. The second class of course, we look at is the
MISO case, where we have multiple input and a single output; here we have a single
input and a multiple output and finally, we look at a MIMO case.

695
So, in the SIMO case what we have single input multiple output. The received signal at
the i th receive antenna is equal to the h tau comma t. This is the SISO channel
coefficient as we have seen, convolved with the signal. And this kind of signal has to be
received at the different M R antennas ok.

So, now if we go for a MISO system that means, multiple input single output; what we
have over here is that the impulse response between the j th transmit antenna and the
receive antenna is given by h j tau,t all right. So, let all the antennas are sending signals
at the same time. So, when the signal is received, so what you find is that s j is the signal
that is being sent from the j th transmit antenna. And h j is the channel impulse response
between the j th transmit antenna and the receive antenna. So, now all these signals add
up together and they are combined at the receiver right. So, you can write all these
different equations in a matrix vector notation and things will be easier.

(Refer Slide Time: 28:23)

696
So, then we move on into the situation where there are multiple transmit antennas as well
as multiple receive antennas. So, together it forms the MIMO system under that what we
have is h 1,1 indicating the channel impulse response between the received antenna
element 1 and transmit antenna element 1; this is the channel impulse response at
received antenna 1, transmit antenna 2 and so on and so forth. This is the received
channel impulse response at receive antenna 1 and transmit antenna M T.

In a similar manner, if we go down the column, this channel impulse response received
in antenna 2, while transmitted from antenna 1. So, if you are able to write down the
equations, so for any one receive antenna we have a summation of the signal which is
convolved with the corresponding channel impulse response and it is summed over the
M T transmit antennas.

And then in the matrix notation you can write, so this y i is for all the different receive M
R number of antennas. So, when we write it in a matrix form you can write that the
vector y, which is a column vector is this channel impulse response matrix convolved
with the transmitted vector s t, where s t is described by this vector which is the signal
vector that is being transmitted from the M T transmit antennas. So, once we write in the
linear equation form in the matrix notation, we will be able to handle the entire analysis
of MIMO using linear algebra.

697
(Refer Slide Time: 30:10)

So, one of the important results of the MIMO channel that we will be looking at is
known as the classical IID channel that means, we are characterizing this particular H
channel and the classical IID channel would be called the spacially white channel and
denoted as H w. So, in this the set of assumptions are that expected value of H W that
means, each of the elements is zero that means, each of these coefficients are on an
average zero; so there is zero mean.

We also have the power of the individual elements are 1, this is matching with the
description of large scale and small scale fading and the correlation between two
different elements are 0, if they are not the same element and otherwise it is 1. So that
means, if you take the covariance matrix of a spacially white channel, you are going to
get an identity matrix right; otherwise it will be the covariance matrix. So, in general the

698
elements of H w are such that the expected value of H w, H w hermitian is an identity
matrix.

(Refer Slide Time: 31:24)

So, now the other important fact that remains for us to be described is that in case the
elements of H are correlated, then how do we capture it? So, first thing what we do is we
translate the matrix to a vector using the vec operation, which simply stacks the columns
one on top of the other. And we can write that the vec of H that means vectorial form of
H, which contains the correlated variables is some R covariance matrix to the power of
half that means, square root of that multiplied by the vec H w channel that means, from
H w we can generate a correlated MIMO channel matrix.

And the correlation is described through this spatial covariance matrix R, which is a
property of a particular propagation area or a particular situation. So, this is the general

699
model. So, here this will be generated using zero mean Gaussian random variables, while
when it is multiplied by R half, you get H where a expected value of H H hermitian is no
longer an identity matrix, but that will be R which is the matrix right. So, effectively R is
expected value of vec of H vec of H hermitian ok.

So, this model can be relaxed and a simpler model can be used, where this covariance R
is split between the transmitter and receiver and you can generate the H coefficient. And
this is usually known as the Kronecker model, because the relationship between capital R
that we have described earlier and the transmitter receiver correlation can be described
through this Kronecker product. And H w is full rank matrix with probability 1.

So, if we have since now we have defined these different matrices, we should be able to
discuss the different performance of MIMO schemes with a prior understanding of these
descriptions about the channel.

Thank you.

700
 Evolution of Air Interface towards 5G
Prof. Suvra Sekhar Das
G. S. Sanyal School of Telecommunications
Indian Institute of Technology, Kharagpur

Lecture – 36
Mimo Signal Processing (Receive Diversity)

Welcome to the lectures on Evolution of Air Interface Towards 5G. So, till now we have
seen various waveforms, and then we have also characterized the communication
channel how it is modeled. So, now, it is time that we look into the different multi
antenna transmission schemes which are helpful in providing higher spectral efficiency
in meeting the new requirements of data rates and spectral efficiency.

(Refer Slide Time: 00:41)

701
So, we have been discussing about the classical IID channel in the previous lecture and
briefly we will mention it once again. So, that there is continuity. So, one of the
important things is we assume that the delay spread is negligible; that means, there is the
channel impulse response is very very narrow. So, it is almost approximated to a delta
function with only a delay. And that means it is flat in frequency.

And we will also assume that it is slow fading; that means, over time the channel is
fluctuating at a rate which is much much smaller than the symbol duration. So, these are
some of the important assumptions. And then we talked about wide sense stationary
uncorrelated scattering and we also introduced the homogeneous channel and then the
narrow band antenna area assumption. So, these things have been discussed in the
previous lecture.

And we also talked about the classical IID channel where it means where we note the
classical IID channel with the H w indicating it is spatially white. So, this H w channel
has certain properties which define H w channel. So, some of the common properties
with the other situations are that the individual elements are zero mean of unit power,
while when we take the covariance we will find that the R HH should be equal to an
identity matrix because the diagonal elements will be one from this and the non-diagonal
elements would be 0 from this, right. So, that is what defines the classical IID channel
which we will be using.

(Refer Slide Time: 02:29)

702
We also talked about the spatial fading correlation, where we said that if H is a correlated
channel it is usually modeled in form of vectorization of H which is provided through the
relationship R raised to the power of half; that means, our half and vec of H w. So, you
generate a spatially white channel given a spatial covariance matrix, you can generate the
matrix of H coefficients which are correlated. And we will see the impact of correlated
channel coefficients.

Although this is a general model, we also said that is simpler and less generalized model
is this where the correlation is split between that at the transmitter and receiver where the
entire covariance matrix is related to the Kronecker product of the R t and R r, right. So,
that is how we have described it and we also mentioned that H w is full rank with
probability 1. So, these are some important things that we should remember while
continuing with the description.

So, we continue with this description and we move forward with a few more essential
things.

703
(Refer Slide Time: 03:47)

So, just a side note the 3GPP has provided a description of the full dimension MIMO
channel, ok. So, with the description that we have given, now one should be capable of
going through the details and understanding all the propagation aspects that are provided
for MIMO.

And we will also try to provide some of the generic results that we have obtained from
that particular model at an appropriate time.

(Refer Slide Time: 04:11)

704
A few more interesting important ones that needs to be defined is the squared Frobenius
norm of H. This is important this is what will be used throughout in the next part of the
analysis, where it is denoted as H with double line on both the sides and a subscript of F
and squared, and its meaning is it is the trace of HH Hermitian.

So, this is the Hermitian operation, which in turn means that you are essentially adding
up all the elements squared together. So, which is can also be interpreted as the total
power gain of the channel. So, that is a critical factor. And what we can also see is that
mod H F squared or the Frobenius norm squared of the channel which is the trace of HH
Hermitian is composed of the square of the power of individual terms. Now, h i,j are
random variables and hence mod h i,j squared should also be random variable which in
turn means that the summation would also be random variable, ok.

So, that means, H F squared is also a random variable. And it can be also seen that mod
H F squared since it is the trace of HH Hermitian can also be written as sum of the
eigenvalues where of HH Hermitian. If lambda i s are the eigenvalues of HH Hermitian
then from this definition one can also write that Frobenius norm squared of H is equal to
sum of the eigenvalues of HH Hermitian. And the eigenvalues of HH Hermitian would
be square of the singular values of H. So, in other words we are kind of connecting the
singular values to the Frobenius norm or whatever way you want to look at it. So, this is
something that we will be using very soon.

705
(Refer Slide Time: 06:17)

And the quantity of interest to evaluate diversity performance and that is what is written
over here is the moment generating function, ok. So, this structure will be used and we
have already established that H F squared is a random variable. So, we need the moment
generating function of H F squared. And it is denoted in this particular case as psi sub H
F squared of nu.

Now, assuming Rayleigh fading, we have described the Rayleigh fading condition. R
there is a covariance matrix is expectation of the vec of H times vec of H Hermitian that
is what is already defined in previous set of discussions. So, in that case with all the other
above assumptions H F squared nu is defined as; that means, the moment generating
function of H F squared is defined is this value. With this expression there is expectation
of the exponentiated nu which is the parameter and H F squared the random variable. So,
this particular structure will be used throughout whenever we are discussing the error
probability. This only helps us in getting an easier expression for error probability when
we are talking about diversity gain.

706
(Refer Slide Time: 07:33)

So, this term as we are seeing can be written as 1 upon determinant of I M T M R, we

have M T M R because we have this HH Hermitian and H F squared. So, H F squared as
you are clearly seeing that it contains of M T M R components, nu times R, R is the
expected value of vec. So, basically if you look at R, R is of size M T M R cross M T M
R because each individually these are M T M R, M T times M R, basically M T times M

707
R cross this thing cross 1, ok. So, what you can see is that R is an M T cross M T M R
plus M T M R matrix and hence you have the determinant of this quantity where the i is
added of the same order.

And the determinant since this is an identity matrix; that means, all diagonal elements are
1 and this has eigenvalues which are lambda i of R, you can write the same through this
expression which will be used. Again, as of now we will just use this expression we will
take it for given. I mean if you expand this you are going to get these results. And we
will be using these set of results in calculating the error probability, ok.

(Refer Slide Time: 08:59)

708
So, then we move forward to discuss the spatial diversity which is of our main interest at
least as of now. And we begin with the description of general diversity. The general
diversity means that there is some transmission transmitted signal s over some channel h
i and what is received is y i rather i equals to 1. It is sent through another channel h 2 and
what is received is y 2 and so on and so forth. And it is resend through m number of
channels you are receiving h M.

So, it is the same signal s which is being sent over multiple paths or multiple received
signal is there belonging to the same information s. And that is what is captured over
here, that the receiver sees y i which is the received signal, i is the index which runs from
1 to M. So, one can translate this to receive antenna branches, transmit antenna branches,
time slots, frequency slots. So, that is why we are doing the general diversity discussion.

And we have E s over M, because E s over M is the transmitter symbol energy for each
diversity branch. That means, if the total energy is E s for s for each of the branch you
would be having E s by M, E s by M, E s by M. So, that the total energy at the
transmitter is E s is not violated when comparing against a single link which has a total
power of E s. So, we are comparing two situations where the transmit power is divided

709
into M parts sent over parallel channels compared to the situation where you have E s
being sent over one single channel. Of course, h i is the channel transfer function and
noise is the zero mean circular symmetric complex Gaussian noise, right, ok.

So, the received signal are combined, so since we have all these different received
signals y 1, 2 up to y M, we would like to combine them and one of the process of
combining is known as the MRC combining, maximal ratio combining. So assuming
channel knowledge available at the receiver you would take h i, conjugate it, and
multiply by y i and add over all the receiver branches.

So, if you do that that is what is written in the expression next to it. What you are going
to get is, this is going to give you some over i, h i conjugate. If you expand y i, y i from
this you are going to get root over E s by M h i s plus n i and thereby if we look at the
desired term E s upon m goes outside the summation you are going to get mod h i
squared times s, s will also be outside the summation and you are also going to get
summation h i conjugate times n i, yeah, so times n i, right.

So, if we look at this term over here this is the desired signal with a certain weighted
power and you are adding it over 1 to M. A very gross view, if all of these values are 1,
if these are 1 then the total power is E s and then we have the total received power that is
the same as the SISO case.

So, now, if you look at the post processing SNR from this expression, if you calculate the
post processing SNR you are going to get the sum over h i squared that is from here you
can clearly see that 1 upon M, 1 upon M over here some over h i squared is here, right.
So, these are the two things that you can clearly see which describes the received SNR.

And then we have the next term rho which is E s by N naught has given over there, right.
So that, so that we now have the entire expression of the SNR of the received signal. We
have seen how the signal is processed at the receiver as well. And from this one can
calculate the probability of error using the expression as given there, where any bar is the
number of nearest neighbors from the constellation. So, you can have QPSK
constellation or a 16 QAM constellation, right. So, what you will be concerned is with
the number of nearest neighbors. So, in this case these are the number of nearest
neighbors.

710
And d min squared is the minimum distance of separation of constellation. So, if this is
the minimum distance of separation. This is not the minimum distance these are the
minimum distance of separation, so that is d min squared. Eta is the SNR of our concern.
So, eta is the one which is going to be there. So, we have all the terms now, and then we
can calculate the probability of error. So, now, one can clearly see that once again h i is a
random variable and therefore, as said earlier some of h i mod squared is also a random
variable which implies, but this is a constant term that is rho is a constant term that eta is
also a random variable. So, eta is a random variable which comes in here that in turn
means that probability of error is also a random variable.

So, since if the probability of error is a random variable then there is hardly much that
you can do about it, except that you can provide the statistics and in this case what we
would be interested in is the average probability of error. So, let us look at calculating
the average probability of error for this particular situation.

(Refer Slide Time: 15:11)

711
So, now to calculate the average probability of error we will use the Chernoff bound
where what we find over here it is in terms of Q function and Q function is in terms of
error function, so that is in the integral form. So, we use in the Chernoff bound and
provide this approximation for Q function. That is Q of x is less than or equal to e to the

712
power of minus x squared by 2 and x that is over here is all the terms that is over here
there is square root of eta d min squared by 2. So, x is equal to square root of eta d min
squared upon 2. So, that is what is x, ok.

And so, we now have the approximation when it is applied, we are going to have any
bar. Instead of the Q function we have e to the power of minus this whole term squared.
So, that whole squared means d min squared by if you look at the thing over here it is 2
so, eta that that is what we had over here, eta is E s by n naught ok, and there is a row
term and we have 1 upon M mod h i squared.

So, from that we get this summation mod h i squared and 1 upon M and we have rho
which is E s by N naught and this 4 is because of 2 is getting multiplied with this 2, so
we have this 4 term. So, since we have now identified all the terms of this expression we
move on to calculate the average probability of error.

So, the average probability of symbol error is given by P e bar which is expectation of
probability of error. So, now, one would be able to connect to this expression and see
that we have e to the power of minus nu times mod h F squared, right. So, this is the
expression N e bar P e. So, from this we have to next go into expectation of N e bar e to
the power of minus nu mod h F squared because here h F squared is equal to sum over i
equals 1 to M mod h i squared, ok.

So, since we have that, so we can easily see that this entire summation is now replaced
by the term here that is below this entire summation is replaced by this term. And nu the
next parameter that we have is all the other terms rho d min squared upon 4 M, right. So,
now, you recollect that this is like the MGF of h, ok. So, the same expression that we had
seen earlier that is it looks like this expression. So, we use the result from this, so it is
basically the MGF of Frobenius Norm squared of H.

So, if we use the result, we will be applying it over here; that means, nu would come as it
is and lambda i of R, right. So, what we see that nu has come in its entirety, ok and when
we go back this determinant gets translated to this product term and in our case here, we
have only M we do not have an M T and M R, we only have M. So, you have an M term
over here N e bar comes out over there and now comes the lambda of R, lambda i of R
corresponding to this i s. So, R is the expected value of vec of h times vec of h hermitian.

713
If we assume that these branches that is what we are going to take are uncorrelated; that
means, they are independent, I mean if we take independent that would result in
uncollected branches in that case, we will be getting the eigenvalues as 1 and hence you
have a 1 multiplied over here and the expression fits in. Now, if we let the SNR becomes
very very high, what we will find is that we can neglect this 1 with respect to this term
and you are going to get P bar which is the N e bar comes here and this term which is a
product of the terms inside this which has a constant term raised to the power of M and if
you bring them to the numerator you get a minus M. So, effectively what this means is
that if we take the log of it and then this minus M is going to come on the outside minus
M log of this expression indicating this is the slope of the curve in the log scale of
probability of error.

So, in other words when we talk about the diversity gain; so, let us erase all the ink on
this slide, yeah. So, when we talk about diversity gain what we mean is that the exponent
that is associated with the SNR term that is inside the bracket, ok. So, that is the diversity
gain.

(Refer Slide Time: 21:05)

714
So, now, let us look at a few other interesting outcomes of this expression. So, as we let
M tends to infinity; that means, as we let the order of diversity become higher and higher
and high, so we have described the order of diversity as M. So, as we increase the
number of received branches or number of independent transmission we can apply the
limit that 1 plus x upon n to the power of n can be approximated as an exponential. So, if
we apply it over here, right, we see M in the denominator and we also see M in the,

715
because this term is you can write it as 1 by 1 plus rho d min squared by 4 M, whole
raised to the power of M, right.

So, that now is what we are approximating over here to get an exponential. So that
means, under M tends to infinity the error probability expression can be approximated to
an expression which looks like this which is the approximate symbol error probability for
an AWGN link. And what we have from this result is that as we increase the order of
diversity towards infinity what we get is the symbol error rate which goes towards the
AWGN link.

Now, a careful note we remember we have not increased the power per branch of
diversity; So, per branch of diversity is E s by M and hence the total received power is E
s, it is not more than that. So, we are talking about the pure diversity, only diversity case.
So, if there are other gains the results would be different. So, when there is only diversity
with just by making by increasing diversity you can achieve the error probability of
AWGN which is the best situation that one can think of, ok.

So, what we have over here is a set of results which indicates the curve that I am tracing
is for M equals to 1 in other words it is for the Rayleigh fading channel one can think of
this as the Rayleigh fading channel with a SISO link, ok. And then what we have is the
next line this is for M is equal to 2; that means, 2 order diversity and this curve is quite
visible. And the next one that we have over here is for M R equals to 4; that means, there
are 4 receive antennas it is slightly a different figure and then what we have over here is
the AWGN curve. So, this is the one for AWGN.

Now, why this crosses over? Because this particular result is for receive diversity which
we are going to see shortly but what we find is that M equals to 1 is there and AWGN is
over here. So, if we have pure diversity or curves are going to bend in this manner for M
equals to 2, 3, 4, 5, and as you increase slowly, they are going to merge with AWGN as
M tends towards infinity, ok.

716
(Refer Slide Time: 24:43)

Moving forward so we can see that the error probability average error probability
expression is written in this form where this M exponent of M indicates the order of
diversity is given over here and the multiplicating factor is the coding gain, right. So,
sorry this should be the coding gain not that one that is we need to correct this particular
part, ok. So, we will correct that particular this is a constant sorry, yeah. So, we have the
coding gain associated with it all, right.

So, what we see is that diversity gain effectively gives you a increase in the slope of the
curve and coding gain gives you a lateral shift of the error probability curve. So, any
expression which is bringing your increase in the slope it is the order of diversity and
that component which is giving you a lateral left shift is basically the coding gain part.

717
(Refer Slide Time: 25:57)

718
So, now we move on to the receive diversity. So, in case of receive diversity what we
mean is that there is a transmit antenna and there are receive antennas, ok. And these
signals are received whereas, only s is sent this is h 1, this is h 2, h 3 and so on up to h M
R and this is y 1 that is received, y 2, y 3 up to y M R that is received. And hence the

719
channel vector can be written as h 1, h 2 up to h M R transpose meaning you are having
h vector is equal to h 1, h 2 up to h M R like that, ok.

So, to maximize ok, the received signal again what do we have y 1 is equal to h 1 s plus
noise 1, y 2 is equal to h 2 s plus noise 2, like that y M R is equal to h M R s plus noise
M R, M R indicating the received branch number. And if you write these equations in a
vectorial form you are going to get y equals to h s plus n, these are all vectors of order M
R cross 1, right. So, that is written over here in this expression in a vectorial notation,
bold, small indicating vectors and this is the normalized transmit power. So, we have a
single transmit antenna hence the total transmit power through that antenna is E s which
is the square of which is the square of this particular term.

To maximize the received SNR, MRC combining is used maximal ratio combining
which is given by h Hermitian times h; that means, if you look at this h, h Hermitian
would be h 1 conjugate, h 2 conjugate up to h M R conjugate. So, when we multiply this
with this, ok, what we are going to get is sum over h i mod squared i equals to 1 to M R
which is nothing but the Frobenius norm squared of h, and that is what we have got over
here this is the one that we had seen earlier also. So, the next expression at the receiver is
this and we also have h Hermitian multiplied by noise, so that term continues. So, from
this we have to calculate the probability of error.

So, if we assume that h is equal to h w, that means if we assume a rich scattering

environment in that case again, we will be able to calculate the probability of error as an
expression which is given over here, right. The difference what you see with respect to
the previous thing in the denominator term there was an additional term of M which is
missing over here. And the reason is at the transmitter now we have E s the total power
being transmitted from one of the branches the power that is received in this branch is
also E s times h 1 squared.

The power that is received in this branch is this E s times h 3 squared, right. So, the
difference with the previous mechanism is that in the previous mechanism we said that
each of the branches receive a power which is E s upon M, but here it is receiving the E s
upon M multiplied by h s squared. So, that term is not over here the entire power E s is
received in each of the branch.

720
So, naturally one can think that we are actually increasing the total received power, and
that is pretty obvious because you are having more number of antennas, you are
accumulating more amount of energy that is a natural translation compared to the
previous situation. So, hence that is the difference in this equation.

So, for high SNR that means, when rho is greater and greater than 1. The approximation;
that means, this is this term is neglected again just as we have done in the previous case
we get N e raised to the power of minus M R. So, the difference is we do not have the M
term over here, that term is missing compared to the previous term. So, diversity order is
M R because we have this thing and for h w that means, for especially white; the reason
we have talked about h w because we have again taken R is equal to identity matrix, ok.

For h w expected value of h F squared is M R, that one can see. If one takes the
expectation over here, so basically go back and take the expectation over here that would
mean you are taking the expectation of you are taking the summation outside and h i
squared. So, we have seen earlier for h w it was mentioned that E of h i squared equals to
1. So, each of these elements are equal to 1 and hence this is equal to M because you
have M summations i equals 1 to M, M times 1 which is equal to M and here it is M R,
so you have M R, all right.

And the average SNR is expectation over eta. So, we have the expression of eta over
here ok that can be calculated directly from this. So, again since we have h F squared E
of h F squared is M R. So, we have M R times rho. So, which means that rho which is
equal to E s by N naught is now getting multiplied by M R; that means, the average
received signal power has increased with respect to noise power by a factor of M R and
hence there is an array gain is the thing that we add in this picture.

There is an array gain in the picture, in this scenario which increases the average
received signal strength compared to the previous case which we were talking about
general order of diversity. So, we have two aspects now one is the array gain and the
other is the diversity gain. So, we have both these things when we are talking about
receiver diversity.

We stop this particular lecture over here, and will continue with this general framework
of analysis for all the things in future.

721
Thank you.

722
 Evolution of Air Interface towards 5G
Prof. Suvra Sekhar Das
G. S. Sanyal School of Telecommunications
Indian Institute of Technology, Kharagpur

Lecture - 37
Mimo Signal Processing ( Transmit Diversity )

Welcome to the lectures on Evolution of Air Interface towards 5G.

(Refer Slide Time: 00:33)

723
So, we have started discussing about multi antenna signal processing and in the previous
lecture we have discussed about the diversity mechanism. We started off with the
discussion on general diversity, we will just briefly look at that and then conclude with
the other mechanisms.

So, in the discussion on the general order of diversity we did mention that we study our
system with the understanding that each of the diversity branch has a power of E s by M.
So, overall with M branches there is a power of E s.

(Refer Slide Time: 00:55)

724
And in that procedure we also studied about the way we should calculate the error
probability and finally, we concluded that as the order of diversity extends towards

725
infinity, the probability of error gets asymptotically closer and closer towards an AWGN
link that is the best possible link one can imagine.

So; that means, by simply diversity one can make the error probability be as best as
possible. This was the one of the first conclusions and for all of these we have used the
Chernoff bound as well as the MGF of the Frobenius norm squared of h.

(Refer Slide Time: 01:29)

We also described that in the previous expression on probability of error we have the
exponent of SNR which implies the diversity gain and the multiplicative factor implies
the coding gain and they have the consequence as M increases; that means, as M
increases the slope of the error probability curve becomes steeper and steeper and as the
coding gain increases the curve shifts more to the left indicating that at lower SNR one
can achieve a better probability of error.

So, simply this probability of error is achieved at a lower SNR because of coding gain
compared to the normal link and at any given SNR at any given SER if this is the
probability of error that we are talking about requires a certain SNR without any

726
diversity gain, because of diversity gain what we will find that the SNR required is
significantly lower, coding gain adds on top of it.

So, had the curve been like this then we would have said that there is a coding gain and
hence the required SNR would have been here. So, with diversity gain as we are
increasing the slope; as we are increasing the slope with higher and higher SNR the gains
are more and more and more. So, that is what is to be remembered whereas, with coding
gain with SNR it is the same gain that appears.

(Refer Slide Time: 03:19)

727
We did talk about a receive diversity; that means, the scenario where there was one
transmit antenna and multiple receive antennas and number of receive antennas indicated

728
by M R. What we figured out is that from the error probability expression diversity order
is M R because the average probability of error expression had M R in the exponent.

And when you calculate the SNR from this expression I mean this is the received signal
expression which can be used to calculate the SNR. So, basically from this when we go
there you are going to calculate the SNR. To calculate the SNR you will be getting E s
from this term, E s is already there mod of s squared is equal to 1, mod of h F squared
and in the denominator you are going to again get E n I mean mod of h F squared whole
squared and you are going to get mod of h F squared.

So, these terms will cancel out, you want to get E s by E n into h F squared which would
mean that you have h F square times rho that is what we have over here and h F squared
from this if you apply h F squared on this; this would turn out to be sum of h i squared, i
equals 1 to M R.

So; that means, if we now apply the expectation on eta we are going to get expectation of
sum over h i squared i equals 1 to M R which would mean expectation which would
mean the summation would go outside. The expectation of h i squared. For h equals to h
w we said this term is equal to 1 i equals 1 to M R. So, what we have is summation 1, i
equals 1 to M R which would simply mean M R.

So, that is what we have over here. So that means, the average SNR has an M R factor on
top of the AWGN SNR which means that there is an array gain. So, we have 2 important
things; one is the diversity gain and two the array gain; when we are talking about pure
receive diversity.

729
(Refer Slide Time: 05:43)

730
731
So, then we move on to look at some other mechanism; that means, can we shift the
diversity to the transmitter. So, the basic setup that we have is let there be two transmit
antennas.

And let there be one receive antenna and let this link be h 1 and let this thing be h 2. So,
what we have is h 1 as signal transmitted from h 1 as the channel gain from one antenna
to the receiver, the other antenna to the receiver and from both of this if we send s what
we are going to receive y is equal to s times h 1 plus s times h 2 plus noise.

(Refer Slide Time: 06:39)

732
So, which you could write it as of course, there is the scaling of energy so, what you can
write it as root over E s by 2 which is the energy term taken outside and h 1 plus h 2 with
a common term of s. So, now, h 1 and h 2 are both zero mean circular symmetry

733
Gaussian random variables and therefore, you could replace these and there is this 1 by
root 2 term by a term which is this.

Now, this 2 term comes because we had said that E s by 2 and E s by 2 will be the power
equally divided amongst the two antenna branches and a square root of that is the
amplitude factor. So, what we have is equally divided power. Now when we add them
together at the receiver what we find is that just carefully look at this. So, the sum is a
random variable with now each both of them are IID in that case you are going to get an
equivalent h with the sigma root 2 times that of the previous one which cancels out and if
you now focus on this expression this is exactly similar to a SISO equation and hence
there is no diversity gain with this mode of transmission if you are sending signal s from
both antennas.

So, this mechanism is not a good mechanism and hence we would have to go for a better
mechanism which is this celebrated Alamouti scheme. So, the Alamouti scheme is a very
very famous scheme and will briefly outline the scheme which is very well established.

(Refer Slide Time: 08:15)

734
So, it uses two time intervals in the first time interval you send signal s 1 from antenna 1
and signal s 2 from antenna 2. In the second symbol duration, so, this duration one can
take it as T s. In the second symbol duration from the first antenna one would say send

735
minus s 2 conjugate and s 1 conjugate from the other antenna. So, these are the
transmission mechanism.

(Refer Slide Time: 08:51)

736
So that means, the first time interval this is the signal and the second time interval 2nd
time slot right and we can write that as the 1st time slot so that means there is two time

737
duration which is required for processing. And one of the strong assumptions is that the h
vector remains constant over time over T 1 plus T 2 right or which is equal to over 2 T s.
So, this is one assumption in this whole set of things.

So, the signal received in the first antenna is s 1 that is s 1 multiplied by h 1 that is over
here plus s 2 multiplied by h 2. So, look at this so, the first time interval this is at t equals
to 1 you have s 1 through this, s 2 through this all right. So, then in the second interval
what we find is that you have s 2 conjugate with a minus and s 1 conjugate hence the
time interval 2 the signal received is minus s 2 conjugate through channel 1.

(Refer Slide Time: 10:17)

738
739
If you follow this path; plus s 1 conjugate multiplied by h 2, s 1 conjugate multiplied by s
2 plus noise. So, that is how you have both the signals.

(Refer Slide Time: 10:49)

740
And therefore now you have to process these two signals at the receiver to for processing
it appropriately you keep y 1 unchanged, but you allow y 2 conjugate to be taken in the
processing. So, because the conjugation would mean that h 1 would become conjugate

741
and you are not going to get anything over here. So, this thing is going to go away and
this thing is also going to go away. And you are going to get a conjugate of h 2 and n 2
conjugate now since n 2 conjugate and n 2 would not have any difference in the
distribution because of circular symmetricity. So, now, what we have is y 2 conjugate we
collect the minus sign and associate it with h 1.

And then what we have is h 1 over here is h 1, h 2 is h 2 multiplied by s 1 s 2, s 1 s 2 in

the second equation also we have s 1 s 2 coefficient of s 1 is h 2 conjugate. So, we have h
2 conjugate, coefficient of s 2 is minus h 1 conjugate so, we have minus h 1 conjugate
and of course, this equation is fine. So, the vectorial notation we have y vector is equal to
of course, this root over E s by 2 is there, this matrix you would take it as a effective
channel matrix because now you are receiving over two transmit intervals and hence this
can be thought of as being received at another instant of channel.

So, together it forms the effective channel matrix which is now a 2 cross 2 matrix 2
indicating the time index and this 2 indicating the two space index. So, we have space
time code; this is the most elementary coding in this mechanism and s 1 and s 2 is the
signal vector that is what we are required to send and n is the noise. So, in a very crisp
notation we have the expression as given by this.

(Refer Slide Time: 13:17)

742
And once it is given in a linear equation then all the things that we have been doing can
follow directly. So, we will write the received signal as this y equals to E s by root 2 H

743
effective s plus n. And the processing at the receiver is given by z equals to H effective
Hermitian times y which is the MRC that is what we have been doing all the while which
maximizes the output SNR and that means, E s by root 2 remains as it is over here H
effective times H effective Hermitian this gets multiplied by H effective this whole term
gets multiplied over here.

What we have over here is, H effective times H effective Hermitian gives us the
Frobenius norm squared of F times I under the set of assumptions that we have already
taken and that if you look into this matrix it is an orthogonal matrix. And one of the vital
reasons for this is that h at time instant 1 h 2 at time instant 1 and h 1 at time instant 2, h
1 at time instant 2. So, in this notation something has been carefully introduced. This is
the signal which is the symbol 1 this is what is the symbol 2; this sub index is for time
whereas, this sub index is for space. So, these things have been mixed in a way so that it
is kind of a bit deceptive. So, to be very clear one should write it the appropriate indices
in the appropriate rotation.

And this is again time at the position which is before this because we are having s 1
symbol coming in time 1 and s 2 symbol coming in time 2 then this s 1 and s 2 together
are transmitted in a manner that s 1 s 2 and then you have minus s 2 conjugate, s 1
conjugate. So, one must be careful with these few notations that we are using over here.

So, because of the set of assumptions like h is static; that means, h 1 t 1 is equal to h 1 t 2
which we have already said, we get this matrix where these t terms are not present in any
of this and they have remained constant. So, we get by this; by the structuring of the
problem we get it as an orthogonal channel.

Now, because of orthogonality, the matched filtering or the MRC operation that is
happening over here gives us the optimal receiver; we do not have to worry about it.

744
(Refer Slide Time: 16:45)

745
So, what we get because of the processing that we have here yeah because of the
processing that we have over here what we see is that from this each of the received
receiver processed things; that means, i is equal to 1 and i equals to 2, we have each i is

746
getting h F squared. That means, each symbol is going through the channel h 1 as well as
the channel s h 2 simply because you can see that the first antenna is getting to send the
symbols s 1 and s 2, the second antenna is also sending the symbols s 1 and s 2 and this
is being sent over two intervals of time.

And since the energy is split to E s by 2 E s by 2 over two interval of time, but again at
the receiver you are combining them, you are not losing out on the energy front, but each
signal is travelling through two antennas, physically if each of the symbol travels
through two antennas you are getting notionally a diversity order of 2 and that we will
see how it appears numerically also.

So, n i is the processed noise n i tilde process noise of the ith symbol and hence the
received SNR from this expression one should be able to calculate the received SNR as
we have done earlier as h F squared by 2 times rho. So, one may be wondering about this
2 factor, but one may note that h F squared contains mod of h 1 squared plus mod of h 2
squared. Now on an average if this produces a value of 1 and on an average if this
produces a value of 1; this entire thing on an average is going to produce an SNR which
is rho.

So, average SNR has not increased, because on the receiver side you have only 1
antenna, if the number of receive branches are more then you get an array gain. So, there
is no increase in array gain, but if you at the probability of error using the methods we
have calculated we have used earlier;

747
(Refer Slide Time: 18:53)

You will find the exponent getting a factor of 2 we are of course, calculating the average
probability of error. And hence the diversity order is 2 and as we have said the expected
value of h F squared being 2 and that is what we apply over here. So, you are taking the
expected value of eta if you take the expected value of eta that is what is over here you
get the value of rho which you have just shown that is for SISO.

So, if you compare the different performance this line which I am trying to sketch is the
one for SISO link and this the second line, that I am trying to sketch is the one for the
Alamouti scheme that we have described. So, there is an increase in the slope whereas, if
you are using pure receive diversity; that means, you are having an extra antenna at the
receiver then this is the new line that is what we are getting. So, what you can clearly see
that both of them have the same slope, but there is an additional shift due to the array
gain which is present in the system.

748
So, what we conclude is that because of one received branch you have only the diversity
gain and, but it is better compared to a SISO scheme and it is useful in the sense that
instead of doing all processing at receiver you can transfer the processing to the
transmitter side. There are various other advanced space time codes which have been
developed over years.

(Refer Slide Time: 20:33)

The next scheme that we would like to discuss is the one where channel knowledge is
available at the transmitter. Now what we have discussed over here is that we are not

749
using this h information over here. It is not being made available, but h information is
being made available at the receiver because you are seeing that you are doing H
effective multiplied by y at the receiver side, but the transmitter side you are not doing
any particular such processing. So, this is very very advantageous because the advantage
is simply because no feedback is required. It is a very very simple mechanism, very very
powerful mechanism but of course, it had its limitation.

Now instead of that if we change the situation and say suppose feedback is available; that
means, say feedback is available and in the modern communication systems that what we
are talking about feedback is one of the fundamental mechanisms to provide a higher
spectral efficiency. So, feedback is provided either in the time division duplexing mode
and they use the reciprocity of the channel or it is sent back through the frequency
division duplexing in the reverse channel.

So, in all cases we will assume that h is known at the transmitter. The received signal in
that case would be given by the expression as outlined in the box that I am drawing,
where we have introduced this w which is an additional vector which is the transmit
weight vector. So, what we have is if you are sending s 1 from first antenna s 2 from
second antenna s 3 from the third antenna. So, then you would multiply each of them by
sorry I mean we are talking about the single stream.

So, we will not have this; you can simply have w 1 w 2 w 3 and so on. You can have this
particular situation w 4 right and you can have such situations. So, when you have such a
situation then effectively what you get is the signal that means, I am going to have w 1 s,
w 2 s, w 3 s and so on and so forth.

750
(Refer Slide Time: 23:33)

So, when we are transmitting; let us go to the transmitter structure. So, when you are
transmitting from the transmit antenna side so, now these are coming back for some
reason. So, you have w 1 multiplied by s, w 2 multiplied by s, w 3 multiplied by s and so
on and so forth, and they are going through the channel h 1, h 2 up to let us say h M T to
the receiver. If the receiver has only one receive antenna the situation is what possible
choices of w can be made and what is the processing gain that is available at the receiver
are the questions that need to be answered at this point of time.

So, there are various mechanisms for this and one of the mechanism that we have over
here is the MRT or Maximal Ratio Transmission; that means, we choose this weight in

751
the form h vector Hermitian divided or it is normalized. So, we have seen that h in this
case is h 1, h 2 up to h M T let us say. So, when you take the Hermitian and normalize it
is h 1 conjugate of course, by the normalization factor h 2 conjugate by the normalization
factor and so on and so forth. This gets multiplied by s so each of these terms are the w
terms which now lead to the situation that we have just described.

So, now you can clearly see that if w 1 is equal to h 1 conjugate by some normalizing
factor when it goes through the channel the signal at this point is h 1 mod squared by c
from normalizing factor. The signal coming from the second antenna would be added h 2
mod squared upon c and so on and so forth and all of them are going to have s as the
common term so that means, if we take s divided by c that means c we take out common
what is left inside is the Frobenius norm squared of the channel again.

So, what we see is that the SNR at the receiver so, if we choose w in this particular case
in this particular way the SNR at the receiver can be computed to be h F squared which
is same as the situation what we have done for the received diversity thing. So, again the
expected value of h F squared would be M T in a similar manner and the average SNR
would be M T times E s by N naught rho is E s by N naught we should not forget this
particular thing and the average probability of error if we calculate exactly following the
same mechanism we will find M T coming to the exponent indicating that the order of
diversity is M T.

And hence what we have is the performance which should not be any different from the
receive diversity case. So, if full CSI is used and maximal ratio combining is used then
we are going to get the transmit MRC’s performance which will be same as that of the
receive MRC performance without changing; without providing any extra transmit
power. That means, you are transferring the complexity of this processing to the
transmitter side yet getting all the advantage that are possible.

752
(Refer Slide Time: 27:03)

The next important scheme that we look at is known as the Dominant Eigen Mode one
can also think of this as the digital beam forming, one can also call it as the baseband
beam forming so, let us look at how does it work.

753
So, we have M R receive antennas we have M T transmit antennas, the received signal y
that is there with us is written as ok; so, I should mention that we are talking about the
scenario of MIMO; that means, previous cases we have talked about receive diversity,
then we have talked about transmit diversity.

So, in receive diversity we had single input multiple output, in transmit diversity we had
multiple input and single output and now we have the case which is multiple input
multiple output. So, how do we handle this; that means both diversity the transmitter and
receiver and we have also assumed that CSI is available at transmitter; at receiver it is
always assumed to be available right. So, we are continuing with the CSI available at the
transmitter.

So, under this case because you have multiple transmit antennas the H matrix will now
be M R cross M T we have discussed how the received matrix would be that is h 1 1
indicating received signal in antenna 1 from transmit antenna 2, h received in signal
antenna 1 from transmit antenna 2, signal received in trans in receive antenna 1 from
transmit antenna 2 and so on and so forth and this forms the channel vector for the M T
cross this is basically 1 cross M T, M T transmit antennas and then we have received in
antenna 1 transmit receive antenna 2 transmit antenna 1, receive antenna t 3 transmit
antenna 1 and so on up to h M R 1. So, basically you have h 1 M T and then you fill up
the entire matrix and the last entry would be h received in M R antenna and transmitted
from M T antenna. So, this is your H matrix right.

So, we have M R cross M T, this is an M R cross M T matrix as you can clearly see w is
M T cross 1 as we have discussed, but we have to find what w compared to the previous
situation and also we have to find the g which is required to be at the receiver right. So,
we are kind of doing a same kind of linear processing, but we have to choose the g that
we are going to use on the y. So, what we have over here is basically the y.

So, then what we see is that H, which is the channel matrix can be decomposed into the
singular value decomposition using the singular value decomposition. And sigma
contains the singular values and we have already mentioned that the singular values
squared would be equal to the lambda i, where lambda i are the Eigen values of R, where
R is the expected value of vec H vec H Hermitian.

754
So; that means, we are actually talking about the channel strengths involved in this; so,
this a singular value of decomposition. So, what is known is this eta which is the SNR
the combined expression would be in this form one could easily derive this without any
complexity is maximized, if you set the received vector to U because you are doing this
U g Hermitian processing.

And if you would set the transmit vector weight vector to V. So, let us see what would
happen, what is going to happen is the received signal. So, if we process it over here H is
broken down into U sigma V Hermitian and w would now be V and the g that is at the
receiver would be U and this Hermitian would come over here to put; to be put as a
Hermitian. So, let me erase this H right this is your Z plus U Hermitian times noise; this
is what you are going to get because the noise is over here.

So, now what we see U Hermitian U is an identity. So, you are left with sigma V
Hermitian V is again another identity plus processed noise; this is a unitary matrix. So,
that some variance is not going to change.

Now, sigma is a diagonal matrix and hence when we do diversity mode or dominant
Eigen mode from this we do not choose the entire matrix V, not the entire matrix U
because you have a weight vector which is M T cross 1 and V over here would be of the
order of M T cross M T; I mean if you take it as a square matrix then it is; this will
become an M R cross r sigma will be r cross r, this would be r cross M T. So, what we
have over here is we will have M T such columns. So, instead of that you have to select
only one column of V and one column of U. Now which columns would you select; you
would select the columns corresponding to the maximum value of sigma which is going
to maximize the eta.

So, if we select the maximum; the vectors corresponding to a sigma max what you will
end up is in the value of z. So, this diagonal entry would now contain only one value that
is sigma max because there is only one vector and there is only one vector over here. So,
the received signal would be root over E s sigma max times s plus eta. So, this is the
maximum strength of the channel that is what you are exploiting and then you can
calculate eta as lambda max times rho where lambda max is equal to sigma max squared
and we have already described this Eigen value of HH Hermitian.

755
So, this way we can extract the maximum order of gain from a MIMO channel if we
have multiple antennas at both the transmitter side as well as at the receiver side while
there is CSI information available at the transmitter. There is various such mechanisms,
we stop our particular lecture over here; we will continue with the discussion in the next
class.

Thank you.

756
 Evolution of Air Interface towards 5G
Prof. Suvra Sekhar Das
G. S. Sanyal School of Telecommunications
Indian Institute of Technology, Kharagpur

Lecture - 38
Mimo Signal Processing ( Capacity )

Welcome to the lectures on Evolution of Air Interface towards 5G. So, we have been
discussing about the multiple antenna signalling schemes which enable us to have high
reliability as well as provide better spectral efficiency. And we are looking at the
diversity schemes, we have looked at receive diversity, we have looked at transmit
diversity; both without channel state information at the transmitter as well as with
channel state information at the transmitter.

And then, we have started looking into the diversity schemes where both the transmitter
and the receiver has multiple antennas. The scheme we have been discussing is dominant
Eigen mode.

(Refer Slide Time: 00:52)

757
In the previous lecture, we have described all the details procedures; where we said that
we look at the channel, in terms of its eigen value decomposition, whereby at the
transmitter side we pre-code using V and we post-process using U hermitian and since it
is a diversity mode that is only one value of signal is said or one signal is sent from the
diagonal eigenvalues or the diagonal singular values.

We take the one corresponding to the maximum eigenvalue for this, we choose the
vectors from U and V which correspond to the maximum eigenvalue and use them for
processing. So, that particular one is used in the g whereas, this one is used in the
transmitter so, the vectors are formed accordingly. So, at the transmitter you have w,
which is defined below and at the receiver you process with g; so, g hermitian that is
what we said with U makes it one for this entry because that is what we are doing.

At the transmitter side, since we are sending only one value and there is only one column
of the vector being unitary. This also leads to one and hence, there is sigma max; so, the
received signal is written in this form where n indicates noise, and sigma max so,
basically the SNR is equal to E s into sigma max squared upon En squared right; that is

758
what we have. So, sigma max squared is the one, which influences the SNR and sigma
max squared is equal to lambda max which is the maximum eigenvalue of HH hermitian
and hence SNR can be written as lambda max rho.

(Refer Slide Time: 02:59)

So, let us look at the performance of such a scheme. So, this flat line is the one for the
flat curve rather is the one for SISO link then, we have the result for two cross two
Alamouti scheme and then finally, we have the result for dominant Eigen mode for a two
cross two system; so, which clearly proves that, this particular mode of transmission
provides the best reliability in terms of error probability compared to other mechanisms
which use two cross two transmission receiving system.

759
(Refer Slide Time: 03:37)

So, after studying the error probabilities, we now look at the signal correlation model;
that means we have talked about the channel correlation or spatial correlation and see
how does it affect the performance of the system. So, the average probability of error, we
have described this in all our previous discussions is given by particular expression over
here and what we see is that, there is the eigen values of R matrix which is present. So,
we have a two cross two system in this case, and the eigen values of R are determined or
are influenced by the correlation which is present in this R matrix.

760
In case of H w channel, we have stated that lambda i’s are equal to 1; whereas, in case of
correlated channel this will be not equal to 1 right so, let us see that. So, under high SNR
approx assumption; that means, when rho is significantly high under that case, this
expression can become N e as we see over here; remains as it is, and from the
denominator term we can get this is we can get this out of course, it is kind of upper
bounded. So, this term comes over here for high SNR approximation. This is a constant
term; so, basically under high SNR, you are going to get this product, i equals to 1 to 4
under high SNR this approximately equal to rho d min squared by 8 multiplied by since
you have the i over here lambda i of R ok.

So, that is; so, let us clean it and write it again. So, what we have there is a rho d min
squared upon 8 multiplied by lambda i of R and since, this is a constant term it can be
brought out; that is what has happened and in case of which is non identity of R. So,
what we will get is this raised to the power of rank of R because this product will only be
the rank of R right otherwise the rest of them are 0. So, you are using only those within
the rank of it.

So, for H equals to H w of course, we have said this is identity according to which we
have derived the earlier result and when R is fully correlated, R is all 1 matrix so; that
means, there is only one Eigen mode and hence, you do not get any diversity. So, to see
the effect of covariance or correlation, which is non-identity; you take a situation for
simplicity that MR equals to M T equals to M. So, that the analysis becomes easier and
then, the eigen values of R; capital R matrix are represented by this expression which is
kind of standard based on what we have been doing.

And they are constrained to this right, that is the constraint that we bring into the system
meaning that the channel is restricted to a power of M right, channel does not provide
any extra power than M. And using the arithmetic geometric mean inequality, which
states that the arithmetic mean is greater than or equal to the geometric mean so, we
apply it over here. So, in this case we have sum of lambda i over M lambda i of R i
equals 1 to M is greater than or equal to product of lambda i i equals 1 to M raised to the
power of 1 by M.

So, from this, what we find that this term is equal to 1 and hence, what we have is the
product of eigen values is less than or equal to 1. So, that is the result that is shown here

761
right. So, now, what we see is that, the product of eigen values that is less than 1. So, we
have that term here which is 1 upon pi lambda i R i equals 1 to rank of R right. So, that is
what we have.

So, what it means is that, this denominator term because there is this inverse over here.
This term is greater than or equal to 1; that means, the whole ratio is less than or equal to
1 right. So, if the denominator is greater sorry, we wrote it wrong; this denominator is
less than or equal to 1; that means, this ratio is greater than or equal to 1 so; that means,
this multiplicative factor is something which is greater than or equal to unity, to be equal
to unity under the case of Hw channel.

So, this probability of error expression, which we are outlining with the box is multiplied
by a factor which is greater than 1 which in turn means that the average probability of
error increases if R is not an identity matrix. So, if R is not an identity matrix in that
case, we see that the error probability increases. So, to check the performance what we
see that, under no spatial diversity we get the SISO link, what we see over here is that,
this line that I am drawing is the one which is without any spatial diversity.

And the new curve that I am tracing is the one which is with IID; that means,
Independent Identical or Identically Independent fading, which means that is
independent there is no correlation. So, because of a certain amount of correlation, what
we find is that the error probability curve has shifted upwards. So, there is an upward
shift in the error probability curve; which I am tracing by the blue coloured ink and
thickening the line; so, that clearly shows that the error probability increases because of
correlation present.

So, correlation is not beneficial for error probability and whatever error probability one
receives under Hw channel becomes only worse; so that means, it increases when it is
not an Hw channel right. So, that is the important summary that we get in studying the
signal correlation. So, once we have discussed about the diversity.

762
(Refer Slide Time: 10:56)

It is very important we move into the next set of things that is the capacity, which is one
of the most interesting aspect why MIMO is so popular.

Of course, there is one more interesting aspect in the new generation that is beam
forming, But the biggest advantage that MIMO has brought in over the last few
generations of communication systems is enhancement is in capacity. And we are going
to study the system under frequency flat fading conditions; this is what we have
mentioned earlier. So, also slow fading condition and all the MIMO assumptions that we
have made before. So, for a typical MIMO link a M T matrix and what we have is M R
cross M T matrix.

763
(Refer Slide Time: 11:41)

y is a MR cross one receive vector s is an M T 1 cross sorry M T cross1 signal vector ok.
So, what we have is the received signal in its linear equation form y vector is some
scaling H matrix s vector plus noise and it is also given that R ss is the receive or the
signal covariance matrix with a constraint that trace of R ss is equal to M T, this is an
important constraint. So, the total average transmitted energy constraint; that means, we
do not want to use excess transmit excess transmit power and what we see over here

764
from this part, is that the transmit power is equally divided amongst the M T transmit
antennas that is what we have over here.

And then, if we constrain that trace of R ss is equal to M T, then we will ensure that the
total transmit power is restricted to Es; that means, we can compare the performance
with SISO link. So, the capacity of a MIMO channel is the one given by maxim, which
maximizes the mutual information between the received signal and the transmitted signal
over the distribution of the transmitted signals. So, f s is the probability distribution of
the vector s.

So, this is a standard result which we will accept, we cannot afford to go through the
derivation of this it is available in standard textbooks. So, now let us focus on this mutual
information expression. The expression for mutual information is given as the entropy or
the differential entropy of y because this is a continuous random variable, take away the
conditional differential entropy of H; that means, the differential entropy of y given s
right. So, that is the expansion of the mutual information.

And we have also defined both the necessary terms s, the signal s and noise are
independent. This is one of the assumptions, it is kind of obvious, but still it is important
which leads to the condition that H of y given s because y is equal to h s plus n. So, we
could write that differential entropy of y given s is equal to that of h n right.

So, because we are saying that h s plus n conditioned on s this is what we are trying to
evaluate. Now, since n and s are independent here you do not have any uncertainty. So,
what is left with is uncertainty between h of n given s. So, h of n given s is basically H of
n right that is what we have over here. Now, we get back to the original equation that is
this one. So, we have I s semicolon y, which is the mutual information between transmit
and received signal can be expressed as H y minus H n, where H indicates the
differential entropy of the received signal and H n receives the differential entropy of
noise.

So, now, if we see the capacity expression, it is maximization of the mutual information
right; that means maximization of this term. If we look at the right hand side, we do not
have any control on the differential entropy of noise it is a natural event. So, we only
have control possible control over differential entropy of the received signal. So,
therefore, we say that the mutual information is maximized by maximizing the

765
differential entropy of the received signal because the received signal is connected or is
controllable through the transmitted signal s with this we proceed.

(Refer Slide Time: 16:12)

So, the differential entropy of noise is mentioned over here which is fundamentally
controlled by N naught which is the noise power spectral density, I MR or you can say
that MR is another parameter, but we have seen that as MR increases, the received signal
to noise ratio increases. So, I would like to have MR as much as possible.

766
So, therefore, we use this definition of differential entropy for noise. Similarly, the
differential entropy for y can be written as given over here, where R yy is the term is the
covariance of the received signal that is expectation of yy hermitian. So, now let us
expand yy hermitian over here that is, if you take y equals to square root of root over E s
by M T H S plus n. So, you want to multiply this by the hermitian of the same term. So,
you are going to get noise hermitian; you are going to get root over E s by M T s
hermitian h hermitian. So, this product is what you are going to get.

So, if you expand the terms, you are going to get E s upon M T and then you are going to
get H S S hermitian H hermitian plus you are going to get n n hermitian and you are
going to get to the cross terms that is HS n and of course, the root part is there and the
root over Es by n naught times H S sorry, S hermitian H hermitian noise and of course,
the hermitian. So, these are the terms that you are going to get and then, you have this
expectation operator.

So, if you apply the expectation operator, it would not apply on this that is constant. H is
given that means, for a particular value of H. So, E would operate on SS hermitian and E
would operate on this as well as E would operate on this; so, E what we have stated that
S and n are independent. So, what we would get is E s times En, we have said that En is
0 and hence, this term would go to 0; the third the fourth term would also go to 0.

So, we are left with the first and second term that is E s upon M T H. So, E of SS
hermitian we have defined earlier as Rss H hermitian plus E of nn hermitian. Again you
can write this as R nn which you can write it as I N naught of course I MR times N
naught. So, what you see over here this term is available here and this term is available
here. So, we have got the expression of R yy.

So, now if we have to maximize the differential entropy of y, what we are left with is; we
have, we are left with this expression where H is something, which is not in our control it
is from the channel. Noise is something which is not in our control, it is again from the
channel. The only thing that is left with us in our control is R ss; therefore, we can say
that as you are seeing that differential entropy is given as log determinant.

So, the log determinant of R yy so, what you have is log of determinant of R yy minus
log determinant of you can say R nn you say that way. So, you have determinant of R yy
upon determinant of R nn and a log outside that. So, if you expand this in terms of these

767
expressions you will end up in the expression over here, where there is I MR E s by M T
N naught H R ss H hermitian.

And therefore, you can state the capacity as the one, which maximizes the mutual
information that is maximizes this entire expression over trace of R ss or over R ss with
the constraint that trace of R ss is equal to M T. So that means, the capacity expression to
make it look clean, we have as given there so; that means, it maximizes this expression
just change the pen colour; it maximizes the expression over here. Of course, it is the log
determinant over R ss with a constraint that trace of R ss is equal to M T all right. So,
this is also called the error-free spectral efficiency. So, in all the analysis of MIMO that
we do here on will be using this particular expression for all our right.

(Refer Slide Time: 21:30)

768
So, the first thing that we discuss is the situation, where channel state information is not
known to the transmitter; that means, CSI is not available at the transmitter right. So, if
CSI is not available, then that means, at the transmitter side one, does not have any
information about the channel this is opaque, one does not know what is going on in the
channel. So, there is no specific information about the channel. So, the best that one can
do is set R ss equals to I MT right; that means, you just divide the power equally and you
have the; you have no other option to do and s is non-preferential; that means, you do not
have any partiality over the selection of s.

769
(Refer Slide Time: 22:29)

So that means, you have already chosen a condition on R ss. If we go back; we find that
your trace has to be constrained to MT, but R ss can be of any structure. So, the
particular structure of R ss that we have identified is I MT. All the diagonals are one and
the matrix is of size M T cross M T or M T order identity matrix whose trace is definitely
equal to M T.

So, now, we see that so, the constraint is gone. So, C is equal to log determinant of; so, in
this we had R ss and since, that is set equal to I MT it kind of vanishes from the equation

770
and the rest of the equation as it appears over here is the expression for the capacity
under such situations. What we now do is HH hermitian is a symmetric matrix and
therefore, it can be factored into a structure like Q lambda Q hermitian, where Q are
orthogonal matrices and lambda contains the eigen values of HH hermitian right.

So, now we can write the capacity as log determinant; that means, we have not changed
this part I MR also remains as it is, E s by M T N naught remains as it is, and HH
hermitian gets replaced by QQ hermitian; Q lambda Q hermitian. Using an identity of
determinant and also using the condition that QQ hermitian equals to I MR; that means,
we will swap these two positions, you are going to get QQ hermitian and then, again you
are going to swap the positions. You are going to get Q hermitian Q that will be let equal
to identity.

So, what you will be getting is log determinant I MR E s by N naught, you will be left
with lambda. This entire matrix as you can see is a diagonal matrix because this is a
diagonal matrix with constant multiplicating terms. So, I MR is all ones and this matrix
is E s by M T N naught and lambda 1 lambda 2 so on. So, that is it so; that means, this
whole matrix is a diagonal matrix, whose determinant is a product of 1 plus E s by M T
N naught times lambda i, i equals to 1 to rank of R. So that means, the rank of R you can
set it equals to R.

So, determinant of this and a log base 2 so determinant sorry, determinant gets changed
to a product right. So, this would translate to sum of log base 2 1 plus Es; well of course,
erase these things.

771
(Refer Slide Time: 25:52)

So, that you get a cleaner place E s by M t N naught multiplied by lambda i and i goes
from 1 to r which is the rank of the matrix and this is the expression that you have over
here right. So, where r is the rank of the matrix and lambda i go up to r and E s by M T is
the transmit power right. So, what we see is that, if we look at this particular part; this
particular part is a SISO link that is; this is the capacity of a SISO link and we are

772
summing over the capacity of a SISO link each of the SISO link has a strength
corresponding to lambda i. So, that means, we can say that in this case it is the sum of
the capacities of r number of SISO links or SISO channels each with a power gain of
lambda i.

That means, the very important situation that we see is MIMO opens up multiple scalar
special data pipes or modes and this is exploited in providing high amount of spectral
efficiency. In SISO, you have only one data pipe where your SNR is inside the
logarithm. Here what we see is that this is broken down; the signal power is broken down
and we have added them; that means, the summation is outside the log so; that means,
now the power is distributed to different SISO links. Each SISO link having a certain
amount of gain and the transmitted power against each SISO link is an equal power that
is E s by M T.

So, all one needs to do is to compare this and see whether it gives an increase in power
and the clear cut answer is this gives a much increase in signal in spectral efficiency.
There is much larger value of spectral efficiency than a SISO link, which has all the
power entrusted inside the logarithm. So, this helps us grow beyond the logarithmic
growth of spectral efficiency.

So, this is a very important result that we have arrived at, we will continue to discuss the
capacity of MIMO channel, when channel is known to the transmitter as well as look at
the beamforming techniques which help in providing high capacity for MIMO with
advantage of millimeter waves where you can provide much more focused beam in the
next lecture.

Thank you.

773
 Evolution of Air Interface towards 5G
Prof. Suvra Sekhar Das
G.S. Sanyal School of Telecommunications
Indian Institute of Technology, Kharagpur

Lecture - 39
Mimo Signal Processing (Capacity & Massive Mimo)

Welcome to the lectures in Evolution of Air Interface towards 5G. So, in this journey so
far we have discussed various things of the 5th generation communication system
starting from the requirements the evolution of different standards. And then we have
talked about different mechanisms by virtue of which the new requirements can be made.

We have also talked about various waveforms then we looked at the propagation
characteristics how the models are available what kinds of documents you refer to. And
then we are looking at a very important class of techniques which would help in
improving the spectral efficiency, which is been there and would also continue in 5th
generation or in general in any broadband wireless communication systems wherever
high spectral efficiencies requirement and that is MIMO.

We have talked about the diversity mode of communication which helps in improving
the bit error rate and we have started looking into the capacity which enhances the
spectral efficiency in bits per second per Hertz. So, we have discussed about one
particular method in enhancing capacity by sending parallel data streams. So, we have
identified that the MIMO signal systems where there are M T number of transmit
antennas and M r number of receive antennas can open up r which is the rank of the
channel matrix number of spatial SISO data pipes.

So, one can imagine like parallel pipes going on and each can communicate and each can
have a capacity of a SISO link with a power proportional to the lambda which is the
eigen value of the HH Hermitian or sigma squared which is the singular value the sigma
is the singular value of the H matrix that is the MIMO channel matrix. So, now, let us get
back to that particular discussion.

774
(Refer Slide Time: 02:04)

So, what we said is that the situation when there is no preferred direction; that means,
when we do not have channels state information then the best we can do is set the R SS
that is the covariance matrix of the transmit power to I M T and based on the expressions

775
that we have discussed earlier the capacity would be as given in this particular
expression.

And then we also saw that HH Hermitian which is a Hermitian matrix can be expanded
in terms of Q lambda Q Hermitian with the property that Q Hermitian Q is M R and the
expression simply translates to this and using the determinant identities and the
relationship of Q we find that further the expression can be written in this form. So, what
we see there is an lambda which is the diagonal matrix, this is also a diagonal matrix and
hence this whole thing is a diagonal matrix is what we have discussed.

And determinant of diagonal matrix would be the product of the diagonal terms log
product. So, log product of diagonal terms this is what we had written. We had assumed
let M be the number of links or rather i is equals to 1 to r and then what we have got is
since there is a log, it can be expanded as summation of logs. So, this expression if you
look at it carefully contains within it a SISO link capacity and we are adding up this r
number of SISO link capacity and hence we have said it is a sum it is adding up the
capacities of r SISO links each with the power gain of lambda i.

So, that is what we see that the SNR over here is this and E s by M T is by virtue of
dividing the transmit power equally amongst MT number of transmit antennas. So, what
we concluded was that this is the MIMO system which opens up r spatial pipes. And how
to use this if we have to see that let us open up a new screen.

(Refer Slide Time: 04:16)

776
And what we will find is that suppose you have a certain number of antennas at the
transmitter and there are a certain number of antennas at the receiver and the H matrix
lies in between. So, in that case if we are sending signal S 1 S 2 up to S r let us say or S
M called simplicity when it goes to the channel the signal that is received in each of the
antennas are y we could write it as M R or M T in this case.

So, we would write Y is equal to H which is H matrix times s plus noise right. So, now,
what we see is that this is the M R cross M T matrix and you can for sake of simplicity
let us take it as n for the non square matrix of course, you could do the pseudo inverse
and this is M cross 1 and this is also M cross 1 this is also M cross 1. So, let us say all
both the sides of M.

So, now, what we are effectively doing is sending different signals now if you compare
this with the earlier mechanism of STBC we had sent S 1 and S 2 and again we had sent
in 2 time intervals t 1 and t 2 whereas, here in the same time interval t 1 you are sending
different symbols each of this S i element of the constellation point. So, each of them can
be selected from the complex constellation right.

So; that means, each one would be a complex value x i plus j y i indicating one of these
values and they will be going out. Channel as we have already said it will be again
complex values noise is also same. So, now, in order to recover S S cap we can use
various different mechanisms. So, we would say H equaliser times Y and one of the

777
simplest equalisers in this case would be H inverse if it is a square matrix otherwise, it
would be a pseudo inverse right which would take us through that.

So, if we execute this expression what we get is that H inverse H S plus n since we have
taken square and assumed it to be invertible, we would get it as S plus n this vector so;
that means, each of the elements that we receive are the transmitted element plus the
noise element right.

So, we must remember that each y i is sum over H if this is one h 1 k let us say h 1 k k
equals to 1 to M T, but I am writing M over here S k plus noise 1 and then you could
simply generalise it by writing Y i is equal to H i k so; that means, each of the received
signal i equals to 1 2 up to M R, but I am writing it as M so; that means, each contains
inter symbol interference as you can clearly see. But if this channel is invertible then we
would be able to recover everything and there is no ISI and this kinds of mechanism is
kind of zero forcing where we are forcing the interference to 0 and getting a coefficient
of 1 against the desired symbol.

Instead of using H inverse one can use H pseudo inverse we have also said Heq could be
also based on MMSE criteria, but otherwise one can go for advanced non-linear
processing also at the receiver end, but the scheme is very famous because of its
simplicity and this usually known as the V BLAST or the vertical BLAST.

BLAST the name coming from bell labs layered space time communication system. So,
this is the very simple system of communicating where we send parallel data streams or
parallel symbols which go through this channel and they can be recovered depending
upon the channel characteristics right.

So, this is what matches with the definition of whatever we have discussed over here
right. So, let us see that. So, we have discussed about a very common method of
transmitting and sending in parallel data pipes while channel is not known at the
transmitter. So, then we move further to the situation where the channel may be known at
the transmitter.

778
(Refer Slide Time: 10:13)

So, that is CSI is available at the Tx, we have already explained how CSI can be made
available at the CS at the transmitter. So, there could be various method just to
summarise one could be in time division duplexing mode assuming channel reciprocity
and in FDD mode that is Frequency Division Duplexing it could be through feedback.

779
Now, these all sound good, but this sounds to be very very easy and very nice way of
doing it, but we must remember that we are talking about point point link. So, in case of
point to multipoint or multipoint to point or multipoint to multipoint there is the notion of
interference which is not reciprocal in both the directions ok. So, in case of interference
it may not be reciprocal in both the directions. And hence we may not be able exploit this
kind of thing and there this explicit feedback is very very important. Explicit feedback
means you have to give a feedback although there is a term called as explicit feedback
which is used in different ways.

So, here we assume that CSI is available at the Tx either through feedback or the
principle of reciprocity and this is what we do over here. So, the channel we have seen
this mode of analysis earlier when we said dominant ideal mode this H can be
decomposed into its singular value decomposition as we have over here U sigma V
Hermitian. So, sigma contains the eigenvalues sorry the singular values and U and V are
unitary matrices which contains the vectors corresponding to these singular values.

So, now, if you look at the received signal the received signal is H times s, but at the
transmitter we do some precoding as you can see there is this V vector that is the
precoding ok. So, S is the signal V times S produces the S which we had been using in
our earlier notation and this kind of precoding can be called as SVD based precoding.

And similarly at the receiver what you see is that this is corresponding to Heq in the
previous discussion that we had. So, now, if we concentrate on the set of equations we
have U Hermitian from this from this we are getting U Hermitian multiplied by if we
look at H H get expanded as U sigma V Hermitian and V is the precoding at the
transmitter plus U Hermitian noise because of receiver processing.

So, now what you see is that U Hermitian U is identity V Hermitian V is an identity we
have left with sigma times S. So, that is what we get over here sigma times S. So, sigma
times S sigma is diagonal matrix as we are stated over here right. So, we have sigma 1
sigma 2 and so on and S is what we have S 1 S 2 so on. So, effectively what it means and
of course, this is y so, y 1 y 2 and so on. So, if we break down the elemental equations
we will find y i is equal to of course, this is the scaling because of the energy
normalisation times, we have stated earlier that lambda i is equal to sigma squared i

780
where, the lambda i are the eigen values of H H Hermitian and sigma belongs to H a
singular values of H.

So, from instead of writing sigma we will write it as square root of lambda times S i plus
n i tilde n i is the noise for that particular received signal path. So, now what you see is
that the received signal can again be broken down into r number of spatial data pipes
once again and hence in a similar manner you would be able to get the capacity
expression as we are discussed earlier is a sum.

So, we are getting the sum operation over here of log because we had log determinant
inside the log we are getting a diagonal because look at this is the diagonal this is causing
the diagonal matrix there was I MR that would have been there. So, now, the expression
is E s because of this because it is taking a SNR expression the square root is gone where
N naught because of the noise part ok.

And we are saying lambda i there were square root. So, now, it is lambda i, but we have
included gamma i as the new entry into the system if you compare this expression with a
earlier expression, earlier expression we had used R SS is equal to identity matrix. But
here since CSI is available CSI is available at the transmitter we have the option of
accessing the modes. Modes means the spatial modes ok.

So, we are able to access the spatial modes, but in order to access the spatial modes this
is the power control or the power sharing you can say for each of the mode. So, this is
one of the resources which have been used and what we see is that, here it is mentioned
gamma i is E of expected value of the sigma power of the power in the i th branch.

So, now what you will find is that R SS which was set as I earlier this is not what we will
use in this particular case earlier we have used because CSI is not available at the
transmitter. So, now, what we will get back to is R SS would be the diagonal matrix
which will contain these elements which is E of s i squared like that these entries will
happen; that means, R SS if we recall the expressions that we had discussed earlier.

781
(Refer Slide Time: 17:40)

We said that you maximise over the choice of R SS subject to this constraint when CSI is
not here not available we had set R SS to identity, but now CSI is available. So, there is a
particular choice of R SS which can be determined which can be used. So, R SS is
basically covariance of the received signal. So, this is here and of course, the signals are
independent hence these elements would be 0, but I mean we are getting a diagonal
values which are the powers of the each of the paths.

So, what we have as the capacity expression finally, is the maximum value of this such
that this constraint is held true. So, we had to we are left with finding the power

782
distribution within the powers constraint that is what is the problem. So, this in this
expression we had simply quoted power control, but still the values of these have been
found out. So, that is the next stage of operation while implementing this.

So, just statement before you move forward these kind of mechanism are called SVD
based precoding and as you can see in the diagram the S signal is multiplied with the V
vector. So, basically when we write down we write it S multiplied by V and then it is
going to the channel where it is getting multiplied by H and then at the receiver you are
multiplying by U Hermitian and then what you all getting it is S tilde cap correct.

So, that is what we are having and this, what we are given over here each of the data
pipes have this kind of amplitude or power and we are left with the amount of power that
we dedicate to each of these links.

(Refer Slide Time: 19:37)

783
So, the gamma i optimal can be found in this manner where this plus sign indicates
positive values; that means, if x is greater than 0, if this argument is greater than 0, then
you take the value if it is less than 0 then you just apply 0 over there and this is for all the
r streams because we have r data pipes ok of course, this constraint is maintained.

So, we are not going through the details of how to find this out this is available in the
reference material. So, the optimal energy allocation is found through iterative water-
pouring ok. So, we will just explain what it means. So, what you do is that you set p to 1
through iterations and you calculate this expression. Once we have calculate this
expressions then you can feed this mu into this expression which is derived from the
expression above ok.

So, now we will go through this iterations and you can find out gamma i in case the
solution is less than 0 we are not going to use it if it is only positive, then we going to
keep it. So, that is what it says if this value is less than 0 discard this channel put this
equal to 0 rerun the algorithm p implemented by 1. So, get slowly the non negative
values or the values which are greater than 0 as your remaining streams.

So, let us see how does it look like. So, if we look at the expression we have a mu take
away something. So, mu is the constant term. So, we have the mu threshold across the
different spatial modes and each of the spatial mode has M T N naught by E S of a

784
lambda. So, if you look at that particular term M T N naught by E S lambda i. So, this
you can easily write it as 1 upon E S by M T N naught times lambda i.

So, now carefully look at the expression here this expression is the channel strength. If
we go back and see this expression here or if we go back and see the expression there;
that means, if we see this expression we said it is the channels strength that is what we
have to mentioned in this particular statement there.

So, what we see is that we are taking away this entity from mu. So, let us write mu over
here mu minus this. So, inverse of the SNR. So, inverse of the SNR for that particular
link inverse of the SNR what is the meaning of the inverse of the SNR? So, what we
mean over here that if gamma of lambda i is very large then this value is small right.

So, that means, we give the power which is as close to mu as possible if lambda is small;
that means, when channel power is small then this entire thing is very large if this
number is very large this entire expression is very small; that means, the power you are
allocating is very small. In other words if lambda i is high you allocate gamma i which is
high if lambda i is small then you allocate gamma i which is small and this is the famous
water-pouring algorithm.

So, what we see is that this quantity indicates the noise. So, larger the channel strength
lesser is the noise more is the power to be allocated. So, with respect to some threshold
that is what we have said as mu the amount of power that we are going to fill in is
proportional to the channels strength right.

So, after you do everything only all the total amount of power that is going into the
channel or the signal to noise ratio or the total amount of power they maintain the same
value which is mu and whatever is in the denominator term is a significance of amount
of noise.

Now, if the channel weak very very weak like these channels then you will going to get a
negative value in these expression if it is a negative value do not use that channel; that
means, a channel is too weak to be used. So, this is the another level of mechanisms that
has to be added on to this.

785
So, now if we get back, so, we have got the gamma i values this is gamma 1 gamma 2 to
gamma r. So, this is fine you can calculate the capacity, but in both the schemes; that
means, whenever you are doing.

(Refer Slide Time: 24:58)

Either you go for BLAST or you go for SVD precoding. So, in this case you use an
identity matrix here you use R ss R ss is determined through the gamma i opt through the
algorithm we have described and now what we see is that in each of the cases in both the
solutions we had only talked about the power.

Now, once the power is known data rate also have to be decided for practical
communication systems; that means, the set of constellation that you are going to choose
has to be decided; that means, depending upon the SNR whether you are going to use a
QPSK or whether you are going to use a 16 QAM or whether you are going to use a 64
QAM that depends upon the signal to noise ratio of the particular link.

So, what we mean to say is that, depending upon the particular links’ SNR which is
determined by the earlier expression you can choose different constellation for different
streams. So, this is called per stream rate control right ok. You have got per stream rate
control and together you can achieve high spectral efficiency. Now one important thing I
would like to mention over here in SVD based precoding if we go back what we find is
that, there is this precoding matrix V which we are talking about.

786
So, if you look at this precoding matrix V you have S vector which is nothing, but s 1 s 2
up to s r; that means, r data sets each. So, we select r number of columns over here. So,
basically v 1 1 v 1 2 let us say v 1 M T like that v 1 r up to v 1 sorry v this should be v 2
1 this should be v M 1 and this should be v M R.

So, we select r such columns. So, this is the precoding matrix and this is dependent on
channel state information. So, this is absolutely dependent on channel state information.
So, if we have channels state information the precoding matrix weights are decided
based on the H. So, if H is known at the transmitter then only we can achieve this
scheme and if H is not known one can go for BLAST now these two mechanisms are
extreme ends on one end we do not have any information at the transmitter the other end
we have full information at the transmitter, but now what we see is that something else
can also be done. So, let us see what can be done.

(Refer Slide Time: 28:55)

What can be done is we have the transmitting antennas we have the receiving antennas
right and what is happening is H is a matrix. So, we have the symbols s 1 s 2 up to a
certain number let us say L and then they are getting processed through the precoder. So,
we have selected in the previous case the columns from the V matrix which are
generated from the H matrix ok.

So, this means there is a perfect match with the channel coefficients because at the
receiver you are again using a linear processing; that means, you are using a post

787
processing is the post processing matrix where you are taking U 1 vector U 2 vector of
course, you have the Hermitian up to U r vector let us say So, now the number of entries
or number of elements is equal to the number of antennas where as the number of data
streams is less than or equal to the rank of the channel.

(Refer Slide Time: 30:30)

So, we have this S vector we have that goes into the precoder which goes to the antennas
this is what we have drawn this goes to the channel and what we mentioned is these
columns contain entries which are of M T length; that means, if there are M T number of
transmit antennas and S has S L number of symbols where S is less than or equal to M T
which you can put as less than or equal to M R and then everything would hold out.

So, now this we have said depends entirely on the channel the other case is extreme
where there is no preference. Now the question is can we do something better I mean
why something better because the amount of feedback is very high in this case is
extremely high.

So, now what people have thought of intelligent ways of doing things is that we could
have various precode books designed; that means, we would call them as code books

788
which would contain complex weights and there could be various such matrices ok. And
if we have let us say capital N number of such matrices we would require log of N with
the base of 2 number of bits to be used in identifying what operation is to be done at the
receiver and these are not dependent on the channel these are predefined right.

So, what the receiver does based on H. So, if we say that the received signal can be
written as S vector with some precoder matrix W then it goes to the channel and then
there is noise. So, the receiver can think of doing a processing in this manner and the
receiver needs to find out the index of this matrices which would maximise the SNR or
maximise the capacity or would minimise the BER depending upon the requirements.

Now, once the index of the W matrix is identified because the transmitter and receiver
both know these matrices. The receiver has to feedback only the index of W matrix; that
means, which matrix is to be used the transmitter would use that matrix at the
transmitter. The receiver would use a corresponding matrix of the receiver a very general
thing would be there would be pair of the matrices W and W and W tilde we can say that
right.

And one could use in either way. So, effectively in the previous case when we are doing
SVD in the SVD case you are sending back H matrix now if it is let us say 16 cross 16;
that means, there are 256 elements right. You know 256 elements each elements would
contain 2 entities because of complex so; that means, you have 512 real entries. And if
you would sent at even 10 bits you would have 5120; that means, nearly 5 kilo bits of
information we fed back for processing whereas, if you compare with the scheme over
here if I have N number of such precoding matrix I just have to use log N base 2.

So, even if I have let us say 250 if I have 256 let us say then this is equal to 2 to the
power of 8 ok. So, if it is 2 to the power of 8 yeah. So, then I will require only 8 bits of
information so; that means, I require only 8 bits of feedback over here compared to the
huge amount of feedback over there. So, of course, with the reduced feedback the quality
of SNR and the channel capacity will be significantly reduced, but this is one important
strategy which is necessary to realise large scale communication systems ok.

So, with this let us move on to see some of the code books that are used in LTE and
similar things are extended in the newer generation. So, I will just show you a few
samples of such code books that are used.

789
(Refer Slide Time: 35:18)

So, let us look at this particular slide which talks about code book index number of
layers; that means, if there is only 1 layer 1 layer meaning that 1 layer means sorry let us
take a right pen 1 layer means that you have only one spatial pipe right.

So, oh sorry this is the number of layers so; that means, it is the number of spatial pipes
so; that means, L what we have indicated earlier is basically the number of layers. So,
although we can have a large number of antennas we may use choose to use only one
data pipe. So, when we choose to use only 1 data pipe what do we do that precoder
should contain only 1 vector and there would be only 1 signal over here.

So, this signal gets multiplied by all the elements of this vector and then they go through
the transmitter similarly you have the vector processing at the receiver and you extract
signal at the receiver, this particular case is similar to the dominant eigen mode, but there
this vector is chosen from the channels’ SVD, but here we are saying that you can have
different channel vectors. So, these are the different channel vectors.

790
So, if we have to send back channel vector, we would require at least two elements to be
feedback and I mean the number of complex bits would be significantly large compared
to the option that we are having over here. So, sees with choosing between only 4 you
require only 2 bits of information to the feedback if you are sending 2 layers this
particular example has code book defined over there.

So, if I am using the code book over there. So, if I am using code book index 0 or three
we are actually not using any codebook. So, I think of an identity matrix where as if you
are using codebook value of 1 or 2 you are choosing this or this matrix respectively right.
So, if we move further.

(Refer Slide Time: 37:41)

What we find is that this contains the different code books that are available. So, number
of layers is denoted as M. So, it could be 1 layer 2 layer 3 layer or 4 layer and then there
is a particular mechanism of generating these matrices through these u i vectors and then
all one has to choose is which particular matrix one is sending. So, out of 16 possible
options if one has to choose then one requires only 4 bits to send them.

So, now just imagine this that you have a matrix where you have 2 columns only so; that
means, and if there are 4 antennas. So, you will taking basically 2 vectors which take 2
data inputs and send them out over 4 such antennas. So, when you write down the
expression you have s 1 s 2 as a vector multiplied by these w 11 w 21 up to w 41 and w
12 w 22 up to w 42 and this goes into the channel. So, that is how the processing is done

791
and how one chooses this particular weight matrix is the proprietary mechanism by
which one can do it. So, in this way one can take advantage of exploiting the different
MIMO spatial data pipes that means.

(Refer Slide Time: 39:20)

One would take advantage of the data pipes and one can expand the spectral efficiency.

792
(Refer Slide Time: 39:28)

So, in these two figures we see the result of the case when channel is unknown to the
transmitter and when channel is known to the transmitter for the situation of M T equals
to MR equals to 4 as your number of antennas increase you get a different kind of result,
but what we see over here is for low SNR conditions there is a gap in the channel known
to the transmitter compared to the channel known, but for high SNR condition there is
not much difference between this. So, high SNR condition means that ES upon MT N
naught is very high.

So, that is very high 1 upon ES by MT N naught this whole thing is very low which
means mu minus this is very high and there is not much difference between each of the
modes that we are going to use and as your SNR increases there is not much a gain that
one would get if one uses full CSI at the transmitter. So, it is something to be
remembered.

We also talked about the 10 percent outage capacity. So, there we see that the difference
is much more notable, but I mean depending upon the situation one has to choose the
appropriate mode of operation. So, when we use the code book it is not a full CSI, but a
partial CSI information about the channel.

(Refer Slide Time: 40:47)

793
The next important thing that we would like to see is the effect of spatial fading
correlation we had seen such a thing for the diversity performance we will now see it for
the capacity results. So, H can be expressed in this form we had discussed this discussed

794
these things earlier and we assume M R equals to M T equal to M and then what we see
is that HH Hermitian that we had over here. Remember we had HH Hermitian. So, if you
expand H it is R half H w R t half right and if you look at this that will be R t half H w
Hermitian R r half Hermitian right. So, R t half R t half Hermitian would give you R t
that is what you have and then you have H w H w Hermitian rest of the terms you can
easily figure out into this expression.

At high SNR conditions; that means, when the rho is very very large this can be
represented in this manner with a log determinant because we are neglecting the effect of
I 1 over here in the diagonal elements which is very very large and you have R r and R t
through I mean determinant identities you can just swap these things and you get this R t
over here sorry R t over here and R r half and R r half Hermitian would come there. So,
what you would see is that the capacity can be approximated to the capacity of the
spatially white channel, but there are this additional terms of log determinant if R r and
log determinant of R t.

This would mean that R r and R t would affect the capacity in a similar manner if you
look at it their affect is similar. So, we study one of them like before we have to put this
constant that sum of lambda i of R is equal to M using arithmetic mean geometric mean
inequality which we had seen earlier for the diversity case what we get is this result this
was also seen earlier.

So, now, if the determinant of R r is less than 1, log determinant, so, let us clear out
everything this entire thing is less than or equal to 1; that means, thing is only less than 0.
Similarly, if this is also less than or equal to 1 with determinant; that means, this would
be less than or equal to 0.

Now, at when these are identity in that case the determinant would turn out to be 1 and in
that case the log of determinant will be 0 and will be left with the capacity of a H w
channel which is true when R t or R i R r equals to 1 identity when they are not so, since
log determinant of them are negative, we see that the capacity drops in case of spatial
fading correlation.

795
(Refer Slide Time: 43:55)

So, what we see over here is that for a particular configuration that we are showing the
results we find that the spatial correlation has a detrimental effect on the capacity. So, the
capacity falls significantly 3.3 bits per second per Hertz if you just have 3.3 bits per
second per Hertz now you multiply let us a 20 mega hertz right. So, you can get almost
66 mega bits per second loss in this particular situation right. So, what we see is that
correlations increases the probability of the error and decreases capacity. So, net effect
uncorrelated channel gives you much much better performance than a correlated channel.

So, correlation only effecting us detrimentally if we know the details, then we can take
advantage of designing the transmission mechanism schemes which can provide us with
a higher spectral efficiency.

796
(Refer Slide Time: 45:02)

So, last thing that I would like to show you before we conclude in a in a minute from
now the capacity of spatially white channel for large M this is the motivation for
studying massive MIMO. So, what we see is that if we let M T equals to M R equals to
M again for simplicity and also we let R SS equals to identity of size M.

Using this strong law of large numbers as M tends to infinity you can get this thing. If
you open up these things you will be get H 11 H 21 this whole matrix and H Hermitian
would be H 11 H 21 and so on Hermitian. So, when you multiply these matrices you are
going to get diagonal terms which contain the product of the streams and the off diagonal
would be the cross terms. If it is spatially white with large size of M each of the diagonal
entries would turn out to be almost same as expected value of h i h i mod squared and
hence this matrix would turn out to be a identity matrix, this particular part you can
check as an assignment for yourself.

797
So, now, if you look at the capacity expression we have HH Hermitian with M T below
and R SS has been assumed to be set as identity. So, now, what we see is that inside you
have HH Hermitian by M T HH Hermitian upon M T we said you are going to get it as I
M T which you can check out during the derivation for yourself and it is not very
difficult it is few steps and you can get it very easily using the central limit theorem or
law of large numbers. So, you are going to use the law of large numbers you will get that
and then with this I M T. So, inside what do we have I M R plus ES by N naught plus of
course, we are talking about M we are talking about M this thing determinant and a log.

So, this is an entire diagonal matrix and if you see each of the entries each of the entries
are 1 plus ES by N naught. So, this is the SNR of an AWGN or of a SISO link one could
say right and of course, one is going to get the yeah one is going to get the if we have
made this assumption there is no other problem only left with ES by N naught. So, this
expression is the capacity or the spectral efficiency of the SISO link that is what we get
from here.

And now since we were talking about determinant. So, we basically have the product of
these things because that is the diagonal matrix determinant is the product of these things
1 to M and you have a log. So, this would be summation of log 1 plus ES by M naught
since this is the constant term i equals to 1 to M, you need to get summation i equals to 1
to M multiplied by inside of course, 1 log 1 plus rho. So, this would result in M
multiplied by log 1 plus rho and that is what you have.

So, what you get finally, is M times the capacity of a SISO link, this is the biggest
motivation one of the biggest motivation of massive MIMO that is as you keep
increasing the number of antennas one would for an H w channel of course, we are
talking about the H w channel one would tend towards a situation that you have SISO
links and you are getting M times the capacity without any increase in transmit power.

So, transmit power remains the same as SISO, but you have an M factor increase. So, all
the spectral efficiency that we required can be simply got by linear scaling of the SISO
capacity with simply large number of antennas. So, this means as M tends to infinity the
channel becomes deterministic we will discuss that simply because of this identity
operation and it increases linearly with M which in other words mean than for every 3

798
dB increase in SNR capacity increases by M bits per second per Hertz instead of
logarithmic increase.

So, it is huge impetus in providing huge amount of spectral efficiency requirements for
all future techniques and hence in the 5th generation system massive MIMO is one of the
major communication techniques which we briefly overlook in the next lecture along
with some more advanced mechanisms.

Thank you.

799
 Evolution of Air Interface towards 5G
Prof. Surva Sekhar Das
Department of G. S. Sanyal School of Telecommunications
Indian Institute Technology, Kharagpur

Lecture - 40
Hybrid Beam Forming mm Wave

Welcome to the lectures in Evolution of Air Interface Towards 5G. So, we have been
discussing the issue of increasing the number of antennas to very large numbers. So, we
will just revisit that quickly and proceed on to the next few set of things.

(Refer Slide Time: 00:31)

So, what we have been talking about is the case of spatially white channel, where we are
saying that if we increase the number of antenna elements to very large values, then what
ends up. So, originally this was proposed as Large MIMO you can look up the internet
for literature on Large MIMO and almost at the same time or later on the term massive

800
MIMO became very very popular. And however, the earliest possible literatures you can
find using this set of keywords and of course, a huge amount of literature. Following that
on almost on the same time you will find with the keywords massive MIMO. Now of
course, there are a huge amount of work that has developed based on the term massive
MIMO and certain newer concepts.

So, what we have said is that if you set the number of antennas going to very large value,
we have defined we have said in the last discussion that, take this as an assignment and
you will find that 1 upon M H w H w Hermitian tends towards an identity matrix by law
of large numbers. And then we had discussed that if you set R ss equals to I as given
over here, these few terms as we are encircling would turn out to be an identity matrix.

(Refer Slide Time: 02:03)

So, inside the expression what you will find is you are getting I M plus E s by N naught I
determinant log base 2 so; that means, it is a log base 2 product of 1 plus E s by N naught
which turns out to be log base 2 1 plus E s by N naught summation i equals 1 to M which

801
is log base 2 1 by E s by N naught multiplied by M, because this is a constant term and
hence what we see there is an M fold increase in capacity over a SISO link and we said
this is a major gain that one gets when using very very large number of antennas.

So, some of the assumptions play a vital role over here; so what we find is that as M
becomes very large, the channel becomes more or less deterministic, which is understood
from this expression. That means, as M becomes large this tends towards identity matrix;
that means, the diagonal elements are all having the same power and the rest of the non
diagonal elements are 0 and this is what you get at the receiver processing or in the
capacity expression, this whole thing right.

This is one of the very important gains. So, one is not affected by the channel variability.
The capacity increases linearly so one can simply get the desired spectral efficiency by
increasing M and in turn which would boil down to this few set of conclusion; that
means, every 3 dB increase in SNR capacity increases by M instead of a logarithmic
growth. Now, along with this a few other considerations that we must make at this point
is a few more things.

(Refer Slide Time: 03:57)

One, when we are using SVD we said it is also a kind of beam forming that is what we
are doing; because the precoding matrix V is matched to the channel. So, one can think
of an arbitrary shape beam that you are able to form based on the particular cluster
realization of the channel which we will see shortly. So, when V is arrived at from the

802
channel you get exact matching with the channel whereas, if you are choosing from
codebooks you have certain predefined matrices, and you are choosing the one which is
the best matrix for the particular realization.

You can imagine the whole situation like this. So, this entire set of things can be thought
of as kind of beam forming as you increase the number of antenna elements, you have a
much greater control on the kinds of beam that you can form; you can match it more and
more closely to the channel. And if it is codebook then you are much wider option to
choose from where by one can expect that one of the code books is going to match very
closely with the channel.

So, now this code so as you increase the number of antennas, if you look at the channel
estimation procedure the number of pilot training symbols that are required that is
number of time stamps or time instants grows linearly with M. That means, your training
period becomes bigger and bigger and bigger, but of course, if you use OFDM, then you
have one advantage that if there are a large number of carriers within the coherence
bandwidth you can assign one carrier to one antenna. And thereby reducing the training
time interval required by spreading the training sequence in the time as well as in the
frequency domain; however, the number of pilots required would grow with the size of
the system, that is one aspect that we should keep in mind.

The other aspect we have already mentioned the channel variability reduces. So, thereby
you get closer and closer to the best performance matching towards in AWGN link. The
third thing is if we increase M we have to also accommodate it in the size. So, if we look
at the 2 gigahertz range of frequencies, rather the sub 6 gigahertz then the antenna
spacing as we have said earlier is required to be lambda by 2 in a general situation in
order to make the links uncorrelated, because uncorrelated gives you the better advantage
as we have just now seen.

So, even then with these set of frequencies the lambda spacing is in order of centimeters.
So, if I have to place 512 antenna elements, it becomes a very very large dimension in
space. And if it is a very large dimension in space then it becomes system which is not
realizable and probably in some situations the narrowband antenna array assumption may
also break. Whereas, there has been a lot of interest in going towards the millimeter wave
band of frequencies, millimeter wave bands of frequencies are around 30 gigahertz and

803
60 gigahertz. These are some of the ranges of bands which are usually made available for
the mobile communication system.

So, there if we compare the wavelength there is a factor of 10 to 20 fold reduction in the
wavelength, thereby reduction in the antenna spacing as well as the component size and
antenna dimensions get significantly reduced in the millimeter wave band. Thereby
naturally enabling massive MIMO, another important fact which we will see is that in
these millimeter bands the number of such clusters which provide the angle of arrival for
different rays are also significantly less compared to the sub 6 gigahertz band.

So, thereby you have a more sharper beam to be formed in case of millimeter waves;
overall millimeter waves is kind of a enabler for massive MIMO systems it makes things
much more feasible compared to sub 6 gigahertz band. So, what we will do is we will
quickly take a look at some of the aspects of the millimeter wave band and then we will
get back to the details of these things.

(Refer Slide Time: 08:47)

So, in the millimeter band when people have moved towards the or they are excited
towards millimeter band; because the sub six gigahertz is highly occupied and the
bandwidth available is also very very less. So, people are moving towards band which
are between 30 gigahertz and 300 gigahertz.

804
(Refer Slide Time: 09:01)

So, the size of elements would be much much smaller, within a very small dimension
one would be able to encompass a very number of antenna elements, thereby enabling
the use of massive MIMO.

(Refer Slide Time: 09:13)

So, in a typical configuration of MIMO architecture, one has the transmitter and receiver
locations and the rays emanating from the transmitter come to the receiver after
reflection diffraction of scattering through different clusters. In millimeter wave the
number of such clusters are much less compared to the sub 6 gigahertz band in the same

805
propagation environment. For example, the room that you are sitting in if you use a sub 6
gigahertz band the number of multi-paths, the number of angles that you are going to get
signals from would be much more in sub 6 gigahertz band than in the same room just
when you shift the frequency to millimeter band.

Now, we would like to recall that we said in the time frequency relationship tau rms
delay spread affects the coherence bandwidth. The Doppler spread affects the coherence
time and the theta r m s that is the angular spread affects the coherence distance. Now, if
we design antennas what we will find is that the theta rms when it is less coherence
distance is large right.

So, if we space antennas in order of lambdas so we are not putting absolute separation
we are talking about lambda separation then, if theta r m s; that means, if signals are not
coming from all directions with equal probability then lambda by 2 spacing does not
hold anymore right; we have shown this thing earlier. And now what we find is that if
the number of clusters are less the direction spread or the angular spread of arrival of
signals at the receiver would be much less compared to that of the other situation.

So, in sub 6 gigahertz we said there are much more number of clusters right. So, signals
are going to come from all directions, this is the kind of thing that we had shown
whereas, in the millimeter band of frequencies they are going to come only over a few
set of such directions; and hence the theta rms is relatively lower in case of millimeter
band of frequencies.

So, then this tells us that the covariance or the correlation would be higher; in case of
millimeter wave for the similar antenna spacing when determined they are expressed in
terms of lambda separation but in absolute terms this is different. But you have another
advantage that if the separation requirement is larger since we are going to millimeter
band we can afford to have a larger separation.

806
(Refer Slide Time: 12:05)

So, we move forward with this and there is a detailed description of the propagation of
the channel profile in case of millimeter wave; because we are kind of towards the end of
this we are not discussing the details.

(Refer Slide Time: 12:21)

807
But all I am telling you at this point of time is there a detailed description of the power
angular spectrum that is exactly what we were talking about; that means how the power
is distributed how the power is distributed over the angle. Using these one can calculate
the covariance matrix of the channel as a function of separation distance between or as a
function of separation distance between the antenna elements with respect to the lambda
spacing right. And this is of course, influenced by the theta rms which is in this path.

So that means, one can finally, calculate R H H covariance matrix given the power
angular spectrum of the channel. The expressions that we show over here are arrived at
from various descriptions of power angular spectrum, which is provided in the evaluation
methodologies of the different communication standards especially we are talking about
the millimeter band, but this analysis is general for any set of such MIMO
communication links.

(Refer Slide Time: 13:29)

So, another important factor in millimeter wave is the line of sight factor, which is called
the Rician K factor, this is also an interesting fact which are like to point out over here.

808
In case of millimeter wave a major amount of power is carried by the line of sight
because there is huge attenuation upon hitting upon a particular surface. So, usually the
first multipath, the first path which arrives in the channel impulse response is the line of
sight component. You probably know that the Rician K factor is usually described in
these propagation detail characteristics of 3GPP ITU and 802.11ad which is particularly
for its millimeter wave as well as for other substance gigahertz bands; what we have
done an analysis is because you have a lot of directivity in these links and one is
expected to use directional antennas.

We have been able to compute analytically the impact of such usage of directional
antennas under specific channels which are governed by the parameters of the third
generation partnership project or ITU or 802.11 series of documents. That means, we are
talking about practical channel models there are many theoretical works which provide
power angular spectrum description.

But they are primarily motivated with the analytical tractability of those equations
whereas, the models which we have just mentioned from the practical measurement
works which are like 3GPP and others. They mainly use the method of simulation,
because those PAS are not mathematically generally mathematical tractable.

So, we have analyzed these kind of channels in two aspects; one is the addition K factor;
that means, generally you would be given a K factor, we use the K factor in calculating
the bit error rate or the SIR and hence the spectral efficiency. What we show is that it is
not sufficient to use only the K factor that is present in these documents; there is a lot
more details that one has to consider which is described in the papers that have been
sited in our work. So, one can feel free to get into those papers and find out all the
details, we will simply summarize and show the different effects.

809
(Refer Slide Time: 15:53)

So, the paper we are talking about is the analytical calculation of Rician K factor for
indoor wireless channel models right; what can easily access that paper and get into the
details.

(Refer Slide Time: 15:59)

810
What we are going to show is that two situations; one is when there is line of sight which
is determined by the case A and when the signal is coming from this direction and that is
case B.

(Refer Slide Time: 16:13)

So, what we show here is results in the sub 6 gigahertz and for millimeter wave band;
and these set of results as you can see are for configuration B and these set of results as
you can see are for configuration A alright.

So, what do I find is that in configuration B the provided value of K factor makes a good
sense whereas, if you are in configuration A then we clearly find that the Rician K factor
sorry I mean we just made a wrong statement; these set of lines are the ones which
provide the Rician K factor. So, this is the curve which is for the given Rician K factor
which is matching closely with the case of A whereas, if you are in the case B, I mean if
you just go back to case B, case B is when you are tilted in some other directions;
because the devices they do not know they can be configured in any orientation. In case
the beam pattern is not oriented towards line of sight you are not going to get the K
factor which is given in these documents.

So, in that situation you will be significantly away in the bit error rate performance
estimation. So, we are talking about the expected value of performance if I use the K
factor given in the channel models. So, all that we are saying is you need to do a detailed

811
modeling which has been given in details in the paper; if you use the expressions and
details that are available there you will find a more accurate performance estimation.

The importance of such works is that you can get a theoretical or analytical performance
estimation without needing a huge amount of simulation, which are generally the
practice in order to estimate the performance of such systems. So, because of not much
available time we will cut short this discussion over here and we will move forward to
some additional results on such effects.

(Refer Slide Time: 18:31)

So, will also talk about another work over here, you can find the publication which I
have underlined over here; now this work is again in a similar line that we have taken the
propagation characteristics are described in the 3GPP MIMO system; because if one has
to evaluate the performance of these 5G systems and others one has to take the
propagation characteristics as described in this 3GPP documents ITU documents or even
wants the performance evaluation for 11 series one must take the standard specified
simulation channel models.

So, if you take this channel models you have to go through a huge amount of simulations
to get a realistic performance result. If you use theoretical works other papers again as
mentioned they will provide you PAS which is not matching with the 3GPP PAS and
hence, the performance estimate will not match that of the simulated performance
estimates that from the 3GPP PAS.

812
So, this particular work finds out the spatial correlation for the 3GPP PAS thereby
enabling a analytical performance evaluation of such channels which are generally done
using simulation, thereby reducing a huge amount of simulation time, we will show you
only the fundamental result and the things which matter to our present discussion.

But I would highly encourage people to get into this document and find out how these
results can be used in your performance evaluation, in reducing the simulation time by a
significant margin; whereas, at the same time you are going to get the results for these
practical channel models.

(Refer Slide Time: 20:21)

So, if we look into the description of the channels you will find a picture which looks
like this, which provides the detail propagation modeling scenarios one has to implement
in analyzing the performance of a particular MIMO scheme one come comes up with.

So, if you use the simulation models as described in this and evaluate your scheme then
you would be assured how good or bad is your scheme with respect to 5th generation
communication system. So, let us look at the correlation performance of such schemes
we will not get into the details of the procedure and the details of the models which I
leave to you to find out.

813
(Refer Slide Time: 20:57)

So, the expression of the channel as given in the document is this which is a cumbersome
the expression as given in the channel model. So, one has to typically implement these
channel models in order to get the channel coefficients. So, these are the channel
coefficients which we have been talking about evolve in time they evolve in space and
thereby give you the covariance.

So, R would be equal to expected value of vec H vec H Hermitian that still holds right.
So, through all this process will tell you what kind of R evolves out of these channel
models So, we will keep the detailed description and will go to some of the important
results that we get out of this. So, what we show is that we look at one such result.

814
(Refer Slide Time: 21:47)

So, we have certain set of results for the 2.4 gigahertz band of frequencies which is
effectively the sub 6 gigahertz band, and we have another set of results which is
millimeter wave band right.

So, what we find is that this group of curves which are being identified are when we
have 64 number of antenna elements and we have also identified another set of curves
which are with 16 antenna elements right. So, now let us look at one such curve if we
look at this particular one this is for a sub 6 gigahertz using the expression that we have
derived. And these circles are the ones for sub 6 gigahertz through simulation; that
means, using the 3GPP models.

So, what we see is that the analytically provided performance matches that of the 3GPP
result right what we see over here. Whereas, the theoretical PAS which is the Von-
Mises Fisher PAS has a performance gap at higher SNR it gives us a 4 bits per second
per hertz gap. Now, again if you multiply 100 megahertz you are going to get 400 mega
bits per second gap with respect to a real situation. Whereas, if you use the analytical
method that we have developed and the paper is available, you would not get a
significant notable gap between the performance estimation only advantage that you get
is a very quick result, through analytical expressions of capacity that we have already
described in the few earlier slides. Now if we look at the 28 gigahertz set of frequencies.

815
So, let us change the color and again what we find is that this one. So, that is these set of
ones are the ones for the millimeter band of frequencies ok; what we see is that when N
is equal to 64; again the simulated and the analytical they are in close match. That
means, whether you do the cumbersome simulation using 3GPP channel or use the
expression that we have developed which uses only parameters of the channel model you
are going to get a performance estimate which is not going to be different.

You can easily predict the performance using analytical techniques within few seconds
whether simulation is going to take a huge amount of time. When you compare this
result with that of the theoretical PAS again you will find a significant difference and this
difference is huge; that means 14.2 bits per second per Hertz.

Now look at this we are talking of millimeter band, so, we are talking of a 2 gigahertz
channel bandwidth. So, 14.25 multiplied by 2 into 10 to the power of 9 this clearly
means roughly 30 gigabits per second gap between an analytically provided PAS and the
simulated PAS whereas, based on the parameters provided by 3GPP using the result that
we have derived; if you get the analytical result then you can see that there is no gap in
performance. That means, you can easily predict the performance even in millimeter
band when using large number of antennas, massive MIMO configurations very easily
capturing the realistic effects of the correlation.

The other fact which is also pointed out from this particular figure is that is a very
interesting fact we are talking about N equals to 64 antennas so kind of large number of
antennas. And these set of curves are for the 2.4 gigahertz whereas, these set of curves
are for the millimeter band ok.

So, what we find is that because the clusters are less, the angular spread is less the
correlation is very high and hence there is a difference in the performance. But one
should not take the result as it is one should remember that, when we are going for
millimeter wave in the same space where in we are putting 64 antennas for the sub 6
gigahertz one may be able to put a very large number of antennas within that same space.
And hence the capacity would jump significantly higher than that of the sub 6 gigahertz
band.

When you have a very large number of antennas the beams that one is forming is again
huge and hence one can get even large performance gains. So, this summarizes the

816
different issues that are involved when you are actually evaluating a large MIMO system
with realistic channel models, the difference between sub 6 gigahertz and millimeter
band of frequencies which one needs to consider in details in predicting the performance
of such systems. So, we will proceed with certain more discussions on this particular
aspect.

(Refer Slide Time: 27:41)

So, we go ahead with the massive MIMO systems. So, some of the challenges of massive
MIMO are, huge amount of signal processing at transceivers which you can easily guess
as the size of antenna increases, simply because the matrix that we have to operate
become significantly large. These large number of RF chains that come into play not
only that, beyond the signal processing and device design issues there is communication
system design issues. So, if one has to design pilots which are orthogonal. So, for point
to point communication there is one kind of effect.

So, you have one transmitter and one receiver you are only affected by the number of
antenna elements that you have, if you have multi-user it is not only one antenna, one
user you have each user with connecting to a large number of antennas. Now, if you go
to multi-cellular you have even more transmitting antennas or base stations around the
place. So, what we find is that training becomes a very very critical problem in this
particular dimension and people have been working towards it finding better solutions.
So, that things can be implemented it is a whole field by itself and unfortunately we

817
cannot cover this in this short time limitation that we have this particular course. So, I
would like to only highlight that in massive MIMO there are these few sets of problems
that one needs to be looking at while designing or implementing the solutions.

(Refer Slide Time: 29:17)

People have thought of analog beam forming to reduce the problem over here as well as
people have gone towards other problems also.

(Refer Slide Time: 29:25)

So first when you look at analog beam forming, spatial multiplexing is not feasible under
such conditions. Beam training of course, we have said is time consuming multi-user

818
MIMO is not possible under such cases ok. And the typical other problems of massive
MIMO which we have highlighted in a short discussion in the previous slide is
highlighted with larger number of points over here which is for your consumption;
amongst which some of the important aspects other ones which I am highlighting. This
factor is also critical as one goes towards millimeter wave system right. So, there are a
whole bunch of issues which needs to be addressed when implementing such systems.

(Refer Slide Time: 36:17)

Digital beamforming is a solution, but digital beamforming has a lot of problems, digital
beam forming allows multi stream we have seen how does multi stream works multi-user
MIMO we have not discussed in details, but one can get into it and find out and there is
lot of feasibility potentials in this, but it is constrained by the typical list we have already
highlighted. That means, large power, signal processing complexity, channel estimation
complexity and so on and so forth.

819
(Refer Slide Time: 30:45)

So, one goes towards implementing hybrid beamforming; that means, you have a mix of
digital and analog will again give only a brief overview of such things over here. So, in
hybrid beamforming precoding is done in analog domain as well as in digital domain
taking advantage of both the things. That means, from digital domain you can form more
signal processing in analog domain you can reduce the number of RF chains thereby
taking advantage of both.

So, the number of RF chain is relatively small it provides both beamforming gain as well
as multiplexing in multiplexing gains, comes from the digital beamforming gain comes
from analog. Multi-user MIMO is supported because of the digital part and precoder
combiner design is very complex because now you have a precoder for the base-band
digital design part as well as you have a precoder for the RF part.

Because RF weights have to be taken and again, these are preferably done using code
books, because of the amount of overhead that needs to be sent across. In comparison
there has been also proposal for beam-space MIMO, which we will look at shortly as
well. So, in a typical hybrid beamforming architecture, you have a baseband beam
forming.

820
(Refer Slide Time: 32:01)

So, you have precoding matrix and you have an RF codebook matrix. So, this is the
transmitter side and you can choose a certain number of special streams; at the receiver
side, again you have the weight matrix in the RF domain as well as you have a weight
matrix in the baseband domain right.

So now, one is not restricted to choosing only from one set, but one has to choose from
two sets which enhances the complexity of decision making problems. But anyway it
helps in alleviating some of the problems of large MIMO while giving some of the huge
benefits that massive MIMO promises. Details can be found in this particular paper and
many other references.

821
(Refer Slide Time: 33:01)

So, we will go beyond these things and will now briefly talk about the beam space
MIMO using lens antenna this is primarily from the paper which is given below
millimeter wave MIMO with lens antenna array it is a very interesting work. So where
some kind of an electromagnetic lens is thought of in front of the antenna; and there is
kind of a hemispherical space behind the lens where antenna elements are connected.

So what it does effectively is that, the multi-paths that arrive so, let us go here. So, when
signal comes from large distance from the antenna after going through the lens it
converges to a particular antenna element; if the rays are coming from different
direction, the length those particular rays would converge to another antenna element and

822
so on and so forth. So, what we see is that these elements are coming at an angle of theta
1 whereas; these ones are coming at an angle of theta 2.

(Refer Slide Time: 34:09)

Effectively meaning that if there are clusters at different angles the paths along those
angles would go to different antenna elements. That means, each of the multi-paths from
the cluster can be resolved and that can be used for path division multiple access
compared to the space division multiple access and many other techniques. This is also a
very very promising technique and it is highly recommended that one can explore these
techniques, in providing much much simpler solutions. The biggest advantage of this
scheme is that one need not do the separation of the paths in the digital domain because
the architecture that has been proposed in this particular work, enables an analogue
domain separation of the path.

823
So, that reduces the signal processing complexity in a significant and a huge manner. So,
when this becomes practically feasible, a massive MIMO would again get a new
dimension and the benefits would obviously, come to the users. So, now we would not
discuss more details about these things, I would leave it as an open issue and we will go
on to see certain more things alright. I think we can summarize our discussion over here
when we have been talking about the millimeter wave and massive MIMO structures.

So, what we will rather discuss is that so far, the MIMO gives us a huge amount of
benefit in terms of reliability through diversity, spatial multiplexing gains are possible,
but you need precoders to achieve the different objectives, we have talked about code
books. And then we have said that, if you increase the number of antenna elements, you
can actually achieve the scalar or the linear increase in capacity over a SISO links.

So, that is why MIMO was very very popular, you can do beamforming using precoding
which can be matched to the channel or based on codebooks. We have also said that
when you increase the number of antennas there are a lot of problems and millimeter
wave seems to be a matching solution for implementing massive MIMO.

But again millimeter comes with a lot of problems of its own and towards enabling
massive MIMO through millimeter wave, people have thought of hybrid architectures,
which include analog beamforming as well as baseband beamforming. There is a huge
amount of literature, it is a detailed almost a detail subject by itself now, but it uses all
the basic fundamentals that has been discussed earlier. But there are of course, different
mechanisms and algorithms which are used in finding the different solutions. Beyond the
hybrid beamforming there is also proposal for lens MIMO which is able to resolve the
different paths or the cluster directions based on the physical mechanism of the antenna
design itself.

So, this particular area is evolving, there are many solutions and 5th generation
communication system is expected to use the massive MIMO solutions. But these are of
course, deployment specific there are of course, still challenges to be solved, but a huge
amount of potential gains that can be arrived at from these techniques. So, we would
conclude our discussion on the MIMO processing techniques with this in this particular
series of lectures. And we will continue with the discussion of one very important access
mechanism called the non orthogonal multiple access in the next lecture.

824
Thank you.

825
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