Abstract

Third Generation Partnership Project Long Term Evolution is the evolution of the Universal
mobile telecommunication system which will make possible to deliver next generation high
quality multimedia services according to the users' expectations. Since downlink is always an
important in coverage and capacity aspects, special attention has been given in selecting
technologies for Long Term Evolution downlink. Unlike 3rd generation standards which use
code division multiple access technique, Long Term Evolution makes use of Orthogonal
Frequency Division Multiplexing for downlink.Recent theoretical studies of communication
systems show much interest on high-level modulation, such as M-ary quadrature amplitude
modulation, and most related works are based on the simulations. Simulation for M-ary
quadrature amplitude modulation techniques is done. We present a comprehensive
investigation of the Long-Term Evolution performance analysis, where the Bit Error Rate,
and throughput performance results of Long-Term Evolution physical layer provided. The
simulation results in terms of the constellation diagram and the Bit Error Rate curve under
various conditions are presented and analyzed.This thesis investigates the performance of
orthogonal frequency division multiplexing of Long Term Evolution physical layer using 16
quadrature amplitude modulation and quadrature phase shift keying modulation. The
numerical results obtained by Matlab Simulation are then demonstrated on Bit Error Rate and
signal to noise ratio graphs. Additive white Gaussian noise and Rayleigh fading models are
also used to determine the performance of Long-Term Evolution in presence of noise and
fading.
 CHAPTER ONE

1. INTRODUCTION
1.1. Background of the Project
Providing higher-speed data transmission has always been the most concerned objective of
the 4th generation of mobile communication standards. That is why these standards have
constantly been suffering from prohibitive cost, splintering of technology standards and lack
of user interest. Evolved UMTS Terrestrial Radio Access Network is one of the 4th
generation mobile communication standards for mobile communications introduced by 3 rd
Generation Partnership Project. Unlike 3rd generation standards which use CDMA
technique, LTE makes use of Orthogonal Frequency Division Multiplexing for downlink.The
demand for high speed and widespread network access in mobile communications increases
everyday as the number of users’ increases and applications are constantly developed with
greater demand for network resources. As a result of this trend, mobile communications have
experienced significant developments which are the result of tremendous research that has
been carried out. The 3GPP LTE is the system that marks the evolutionary move from third
generation of mobile communication UMTS to fourth generation mobile technology.The
physical Layer will provide peak data rate in uplink up to 50 Mb/s and in downlink up to
100Mb/s with a scalable transmission bandwidth ranging from 1.25 to 20MHz to
accommodate the users with different capacities. For the fulfillments of the above
requirements changes should be made in the physical layer example new coding and
modulation schemes and advanced radio access technology. In order to correct error code and
improve the spectral efficiency in downlink direction, OFDMA, together with multiple
antenna techniques and turbo coding are exploited.Under the 3G or UTRAN evolution study
item, LTE was initially referred to as the Evolved UTRAN access network in 3GPP reports,
documents, and specifications. On the Core Network side, the evolution towards the Evolved
Packet Core is known as the System Architecture Evolution. The Evolved UMTS is thus the
combination of the E-UTRAN access network and the EPC Core Network, known as 3GPP
UMTS in standard documents. In order to ensure the competitiveness of UMTS for the next
years and beyond, concepts for UMTS LTE have been investigated. Objective is a high-data-
rate, low-latency and packet optimized radio access technology. LTE support an
instantaneous downlink peak data rate of 100Mbps within a 20 MHz downlink.
With the fast development of modern communication techniques, the demand for reliable
high data rate transmission is increased significantly, which stimulate much interest in
modulation techniques. The requirements for spectral and power efficiency in many real-
world applications of the modulation lead to the necessity of using the modulation
techniques other than binary modulation. Modern modulation techniques exploit the fact
that the digital baseband data may be sent by varying both envelope and phase or
frequency of a carrier wave. Because the envelope and phase offer two degrees of
freedom, such modulation techniques map baseband data into four or more possible carrier
signals. Such modulation techniques are known as M-ary modulation.M-ary modulation
schemes are one of most efficient digital data transmission systems as it achieves better
bandwidth efficiency than other modulation techniques and give higher data rate. In order
to improve the performance of M-ary modulation techniques, always a need of studying
and analyzing the unwanted effects caused by different factors on their characteristics
exists.QAM is the encoding of the information into a carrier wave by variation of the
amplitude of both the carrier wave and a “quadrature” carrier that is 90° out of phase with
the main carrier in accordance with two input signals. That is, the amplitude and the phase
of the carrier wave are simultaneously changed according to the information needed to
transmit. It is such a class of nonconstant envelope schemes that can achieve higher
bandwidth efficiency than M-PSK with the same average signal power.The main role of
the LTE physical layer is to translate data into reliable signal for transmission across a
radio interface between the enhanced NodeB and the user equipment. It involves basic
modulation, protection against transmission errors multiplexing schemes as well as the
antenna technology that are utilized. Multiplexing is a technique for sending multiple
signals or streams of information on a carrier at the same time. The antenna technology
involves the different configurations, schemes and techniques that can be incorporated
into antenna systems to fulfill recommended requirements or to achieve desired goals.
OFDMA has been discovered to be a beneficial multiplexing scheme for LTE downlink
with many advantages such as improved spectral efficiency, less complex equalization at
the receiver, flexible bandwidth adaptation, etc. With respect to antenna technology,
MIMO antennas play a significant role in the attainment of the performance goals of
3GPP LTE. And SC-FDMA is the multiplexing scheme used for uplink transmission in
LTE. The LTE air interface consists of physical channels and signals. Physical channels
carry data from higher layers including control, scheduling and user payload or data while
the physical signals are used for system cell identification, radio channel estimation and
system synchronization. This thesis work is targeted or primarily based on LTE downlink
transmission, therefore the bulk of the work is on the physical layer with focus on
OFDMA and digital modulation.
LTE is the next major step in mobile radio communications, and will be introduced in 3 rd
Generation Partnership Project. LTE uses Orthogonal Frequency Division Multiplexing as
its radio access technology, together with advanced antenna technologies. 3GPP is a
collaboration agreement, established in December 1998 that brings together a number of
telecommunications standards bodies, known as ‘Organizational Partners’. The current
Organizational Partners are ARIB, CCSA, ETSI, ATIS, TTA and TTC. Researchers and
development engineers from all over the world representing more than 60 operators,
vendors and research institutes – are participating in the joint LTE radio access
standardization effort. In addition to LTE, 3GPP is also defining IP-based, flat network
architecture. This architecture is defined as part of the System Architecture Evolution
effort. The LTE–SAE architecture and concepts have been designed for efficient support
of mass-market usage of any IP-based service. The architecture is based on an evolution of
the existing GSM/WCDMA core network, with simplified operations and smooth, cost-
efficient deployment. Moreover, work was recently initiated between 3GPP and 3GPP2 to
optimize interworking between CDMA and LTE–SAE. This means that CDMA operators
will be able to evolve their networks to LTE–SAE and enjoy the economies of scale and
global chipset volumes that have been such strong benefits for GSM and WCDMA.

1.2 Statement of the problem

The 3G technology is less downlink data rate than 4G technologies due to the absence of
OFDM and MIMO techniques.

In 3G technology, high latency connection can cause web pages to load slowly and can
also affect the experience in applications that requires real time connectivity example
voice calling, video calling and gaming application.

1.3 Objective

1.3.1 General Objective

 To study and evaluate the performance parameters of LTE downlink physical layer.
1.3.2. Specific Objective

 To analyze the performance of LTE downlink physical layer using different

modulation schemes.
 To investigate the BER and SNR obtained by using different modulation schemes,
channel and different antenna configurations.

 To simulate of LTE downlink network with the help of MATLAB Simulink.

1.4 Methodology of the project

The first task, we have gathered different data from journals and book as well as google
web pages and select the title with appropriate software. And next, we have coded the
program to it’s desire goals by using different algorithm and also design the simulink
model.

Collect Identify the Related

Select
data problem of work
title
project

Write the
Simulation Select
matlab code modulation
output

Figure 1.1 flow of methodology

1.5 Significance of the study

The 3GPP LTE is a new standard with laudable performance targets, therefore it is of great
advantage for us in order to grasp the knowledge how it works and also, it’s imperative to
evaluate the performance of this new system at an early stage in order to promote its smooth
and cost- efficient introduction and deployment. To analysis the performance of LTE
downlink physical layer using different modulation schemes. This thesis work therefore used
to model and evaluating the performance of LTE under Rayleigh fading & AWGN channels a
high-data- rate, High Spectral Efficiency and less Latency.

1.6 Scope of thesis

This thesis work is targeted to evaluate the performance of the LTE downlink physical layer.
modulations are some of techniques used to overcome the performance of the downlink
network. In this thesis work the performance of the LTE network will be evaluated in
different digital modulation schemes such as QPSK, 4QAM, 16QAM. Matlab software is a
tool to evaluate LTE downlink physical layer using performance metrics such as BER, SNR
and constellation points of modulations that is its graphical representation also described .

1.7 Limitation
We are limited to do MIMO configurations over AWGN and Rayleigh fading channel.

1.8 Thesis outline

The structure of this thesis is organized as follows. Chapter one presents introduction and key
features of LTE downlink system. Chapter two presents details of LTE downlink literature
review and related work. The details description of LTE downlink system design is depicted
in chapter 3. The simulation result of a simplified LTE Downlink physical layer in QPSK and
M-QAM modulation scheme is mainly focus of chapter four. Finally, chapter five represents
conclusion of this thesis and some suggestion for extending the work in the future.
 CHAPTER TWO
2.LITERATURE REVIEW
December 2013, Wen-Bin Yang and Michael Souryal,” LTE Physical Layer
Performance Analysis”, National Institute of Standards and Technology. The 3GPP
Long Term Evolution technology exhibits a major advance in wireless communication
networks to meet increasing demands for high quality multimedia services. Orthogonal
frequency division multiplexing and multiple inputs multiple output are employed to
enhance the performance of current wireless systems. With these and other techniques,
higher data rates and higher capacity can be attained in the LTE network. Results of a
physical layer performance in terms of block error rate and spectral efficiency [1].
March 2013, Samiallah Shahid and Mohammad Saqib, “Designing of LTE-Advanced
Downlink Transceiver on a Physical Layer”, Blekinge Institute of Technology. The
evolved version of Long Term Evolution is LTE-Advanced which is being
developed by the Third Generation Partnership Project. LTE-Advanced will meet or go
beyond the requirements of the International Telecommunication Union for the fourth
generation radio communication standard known as IMT-Advanced. LTE-Advanced is
primarily considered as a part of Release 10 of 3GPP specifications [2].
September 2017, H. Mousavi, Iraj S. Amiri, M.A. Mostafavi and C.Y. Choon, “LTE
physical layer: Performance analysis and evaluation”, King Saud University. 3GPP LTE
was proposed by cooperation between groups of telecommunications consortiums named
as 3rd Generation Partnership Project to improve the UMTS standard. It supports up to
300 Mbps of data transmission in downlink using the Orthogonal Frequency Division
Multiplexing modulation as well as up to 75 Mbps throughput for uplink using SC-FDMA
modulation schemes. In this paper, the study of LTE physical layer performance
evaluation is conducted for downlink transmission utilizing Single-Input and Single-
Output and Multi-Input and Multi-Output techniques. He presents a comprehensive
investigation of the LTE performance analysis, where the Bit Error Rate, Block Error Rate
and throughput performance results of LTE physical layer provided [3].The requirements
for spectral and power efficiency in many real-world applications of the modulation lead
to the necessity of using the modulation techniques other than binary modulation. Modern
modulation techniques exploit the fact that the digital baseband data may be sent by
varying both envelope and phase or frequency of a carrier wave. Because the envelope and
phase offer two degrees of freedom, such modulation techniques map baseband data into
four or more possible carrier signals. Such modulation techniques are known as M- ary
modulation. With the fast development of modern communication techniques, the demand
for reliable high data rate transmission is increased significantly, which stimulate much
interest in modulation techniques [4].

In 2009, H. Holma and A. Toskala, IMT-Advanced was submitted to ITU and new
capabilities of IMT-advanced will support a wide range of data rates with peak data rates
up to 100 Mbps for high mobility requirements and up to 1 Gbps for low mobility
requirements. New IMT- advanced work within 3GPP is called LTE-Advanced [5].

In 2007, E. Dahlman, S. Parkvall, J. Skold “Downlink Transmission Scheme” 3G

Evolution HSPA and LTE for Mobile Broadband. The main characteristics of the 3G
system known as collectively IMTS-2000 are the single family of the compatible standards.
IMT-2000 is a set of requirements which are defined by the ITU IMT stands for
“International Mobile Tele- communication” and 2000 represents both the frequency range
of 2000 MHz and scheduled year of initial trail system. The following are the main
proposals proposed under IMT-2000. All of which are leading the previous existing
standards toward ultimate goal of IMT-2000 [6].

In the existing literature, Kamboj and Kaushik described the basics of the OFDM system
and even though a thorough analysis of the modulation schemes was not carried out,
emphasis was laid on the constellation analysis of the modulation schemes. Insight was
also given on the general study of the OFDM system. The system was also simulated and
some performance criteria of the system such as tolerance to multipath delay spread,
channel noise and start time error were tested and analyzed [7].

2.1 Related work

2.1.1 Orthogonal Frequency Division Multiplexing

In OFDM systems, the available bandwidth is broken into many narrower subcarriers and
the data is divided into parallel streams, one for each subcarrier each of which is then
modulated using varying levels of QAM modulation e.g. QPSK, 16QAM, 64QAM or
higher orders as required by the desired signal quality. The linear combination of the
instantaneous signals on each of the subcarriers constitutes the OFDM symbols. Each of the
OFDM symbol is preceded by a cyclic prefix which is effectively used to eliminate
Intersymbole Interference and the subcarriers are also very tightly spaced for efficient
utilization of the available bandwidth. There are a lot of algorithm and techniques for the
performance and analysis of LTE downlink physical layer. Among this digital modulation
and precoding are assumed to be considered.

OFDM is a broadband multicarrier modulation method that offers superior performance

and benefits over older, more traditional single-carrier modulation methods because it is
a better fit with today’s high-speed data requirements and operation in the UHF and
microwave spectrum

Figure 2. 1 OFDM Spectrum. [7]

OFDM has been adopted as the modulation method of choice for practically all the new
wireless technologies being used and developed today. It is perhaps the most spectrally
efficient method discovered so far, and it mitigates the severe problem of multipath
propagation that causes massive data errors and loss of signal in the microwave and UHF
spectrum.

OFDM is based on the concept of frequency-division multiplexing, the method of

transmitting multiple data streams over a common broadband medium. That medium could
be radio spectrum, coax cable, twisted pair, or fiber-optic cable. Each data stream is
modulated onto multiple adjacent carriers within the bandwidth of the medium, and all are
transmitted simultaneously. A good example of such a system is cable TV, which transmits
many parallel channels of video and audio over a single fiber-optic cable and coax cable.
The FDD technique is typically wasteful of bandwidth or spectrum because to keep the
parallel modulated carriers from interfering with one another, they should have a space with
some guard bands or extra space between them. Even then, very selective filters at the
receiving end have to be able to separate the signals from one another. With digital
transmissions, the carriers could be more closely spaced to one another and still separate.
That meant less spectrum and bandwidth waste.

The serial digital data stream to be transmitted is split into multiple slower data streams, and
each is modulated onto a separate carrier in the allotted spectrum. These carriers are called
subcarriers or tones. The modulation can be any form of modulation used with digital data,
but the most common are binary phase-shift keying, quadrature phase-shift keying, and
quadrature amplitude modulation. The outputs of all the modulators are linearly summed, and
the result is the signal to be transmitted. It could be up converted and amplified if needed.

OFDM works best if hundreds or even thousands of parallel subcarriers are used and this is
because of Fast Fourier Transform. The FFT sorts all the signal components out into the
individual sine-wave elements of specific frequencies and amplitudes a mathematical
spectrum analyzer of a sort. That makes the FFT a good way to separate out all the carriers of
an OFDM signal. The FFT process keep the individual modulated carriers from interfering
with one another. This is where the term “orthogonal” comes in. Orthogonal really means at a
right angle to. The signals are created so they are orthogonal to one another, thereby
producing little or no interference to one another despite the close spacing. In more practical
terms, it means that if the subcarriers spaced from one another by any amount equal to the
reciprocal of the symbol period of the data signals, the resulting sinc frequency response
curve of the signals is such that the first nulls occur at the subcarrier frequencies on the
adjacent channels. Orthogonal subcarriers all have an integer number of cycles within the
symbol period. With this
arrangement, the modulation on one channel won’t produce Inter symbol interference in the
adjacent channels.

Orthogonal Frequency-Division Multiple Access is a multi-user version of the popular

orthogonal frequency-division multiplexing digital modulation scheme. Multiple access is
achieved in OFDMA by assigning subsets of subcarriers to individual users. This allows
simultaneous low data rate transmission from several users. The OFDM signal used in LTE
comprises a maximum of 2048 different sub-carriers having a spacing of 15 kHz. Although it
is mandatory for the mobiles to have capability to be able to receive all 2048 sub-carriers, not
all need to be transmitted by the base station which only needs to be able to support the
transmission of 72 sub-carriers. In this way all mobiles will be able to talk to any base
station. Within the OFDM signal it is possible to choose between three types of
modulation:
1. QPSK (= 4QAM) 2 bits per symbol

2.16QAM 4 bits per symbol

3. 64QAM 6 bits per symbol

The exact format is chosen depending upon the prevailing conditions. The lower forms of
modulation, do not require such a large signal to noise ratio but are not able to send
the data as fast. Only when there is a sufficient signal to noise ratio can the higher order
modulation format is used.

Figure 2. 2 High order modulation techniques work best near the base station. [8]
In the downlink, the subcarriers are split into resource blocks. This enables the system to be
able to compartmentalize the data across standard numbers of subcarriers. Resource blocks
comprise 12 subcarriers, regardless of the overall LTE signal bandwidth. They also cover one
slot in the time frame. This means that different LTE signal bandwidths will have different
numbers of resource blocks.

2.1.2 Benefits of using OFDM

The first reason is spectral efficiency, also called bandwidth efficiency. What that term really
means is that it can be transmitted more data faster in a given bandwidth in the presence of
noise. The measure of spectral efficiency is bits per second per Hertz, or bps/Hz.
For a given chunk of spectrum space, different modulation methods will give you widely
varying maximum data rates for a given bit error rate and noise level. Simple digital
modulation methods like amplitude shift keying and frequency shift keying are only fair but
simple. BPSK and QPSK are much better. QAM is very good but more subject to noise and
low signal levels. Code division multiple access methods are even better. But none is better
than OFDM when it comes to getting the maximum data capacity out of a given channel. It
comes close to the so called Shannon limit that defines channel capacity C in bits per second

as eqn2-1. Here, B is the bandwidth of the channel in hertz, and 𝑆⁄𝑁 is the power signal-to-

noise ratio.

C=B*log ( 1 +� 𝑆 ).................................................equation 2-1

�

OFDM is highly resistant to the multipath problem in high-frequency wireless. Very short
wavelength signals normally travel in a straight line, or line of sight, or LOS from the
transmit antenna to the receive antenna. Yet trees, buildings, cars, planes, hills, water towers,
and even people will reflect some of the radiated signal. These reflections are copies of the
original signal that also go to the receive antenna. If the time delays of the reflections are in
the same range as the bit or symbol periods of the data signal, then the reflected signals will
add to the direct signal and create cancellations or other anomalies. The result is what we
usually call Raleigh fading. The high-speed serial data to be transmitted is divided up into
many much lower-speed serial data signals. Then OFDM sends these lower-data-rate signals
over multiple channels. This makes the bit or symbol periods longer, so multipath time
delays have less of an effect. The more subcarriers used over a wider bandwidth, the more
resistant the overall signal is to the multipath phenomenon. This means the higher
frequencies can be used with fewer multipath effects to worry about. But the really good
news is that they can be used in
mobile situations where either the transmitter or receiver or both are moving and
undergoing changing environmental conditions with good signal reliability.
2.1.3 Downsides of OFDM

Like anything else, OFDM is not perfect. It is very complex, making it more expensive
to implement. However, modern semiconductor technology makes it pretty easy.
OFDM is also sensitive to carrier frequency variations. To overcome this problem,
OFDM systems transmit pilot carriers along with the subcarriers for synchronization at
the receiver. Another disadvantage is that an OFDM signal has a high peak to average
power ratio. As a result, the complex OFDM signal requires linear amplification. That
means greater inefficiency in the RF power amplifiers and more power consumption.
2.1.4 Multipath
Multipath interference is a phenomenon where two or more waves are transmitted at the
same time from a base station and travel through different paths towards the receiving
whereas, before the reception they interfere with each other causing a phase shift.

Figure 2. 3 the effect of multipath on a mobile user

When the waves of multipath signals are out of phase, reduction in signal strength can occur.
This phenomenon is known as Rayleigh fading. Fade describes the loss of signal strength at
the receiver by causing periodic attenuation. In addition, due to the multiple reflections,
the same signals could arrive at the receiver end at different times. This effect arises a
phenomenon called inter symbol interference, where the receiver cannot sort the incoming
information. As a result, the bit error rate increases and distorts the incoming signal.
CHAPTER THREE

3. Design parameters and simulation

3.1 System Model

LTE Signal Input signal

BPSK M-QAM Modulation

Schemes

AWGN Rayleigh Channels

Performance
BER SNR Constellations
Metrics

Figure 3. 1 System model

3.2 Signal Model

The basic OFDM signal comprises a large number of closely spaced Continuous Wave tones
in the frequency domain. The most basic form of modulation applied to the subcarriers is
square wave phase modulation, which produces a frequency spectrum represented by a sinc
or
sin(X)
or function that has been convolved around the subcarrier frequency. A truncated sinc
X

Function is shown in Figure 3.2

 Figure 3. 2 Spectrum of a two modulated OFDM subcarrier [9]

The rate of change of the phase modulation will determine the position of the zero crossings
in frequency. The trick that makes OFDM a practical transmission system is to link the
subcarrier modulation rate to the subcarrier spacing such that the nulls in the spectrum of one
subcarrier line up with the peaks of the adjacent subcarriers. For standard LTE each
modulating symbol lasts 66.7 µs. By setting the subcarrier spacing to be 15 kHz,
which is the reciprocal of the symbol rate, the peaks and nulls line up perfectly such that at
any subcarrier frequency, the subcarriers are orthogonal; i.e., there is no interference between
them. This can be seen in Figure 3.2

Rb, maps n-bit words on to 𝑀 = 2𝑛 symbols splits the resulting symbol stream into N
Orthogonal frequency division multiplexing takes a digital information signal with bit rate

parallel streams and modulates each stream onto one of N different carriers. The N

OFDM symbol period, 𝑇OFDM = 1⁄R

frequencies chosen for the carriers are such that the carriers are mutually orthogonal over one

OFDM
allowing independent recovery of each
parallel information stream.
In Figure 3.2 each subcarrier has the same magnitude, which is the case when any of the
LTE- supported constant amplitude modulation formats are used: Binary Phase-Shift Keying
and Quadrature Phase-Shift Keying. It is also possible for the subcarriers to vary in amplitude
since LTE also supports 16 Quadrature Amplitude Modulation and 64 Quadrature Amplitude
Modulation. Compared to the 3.84 Msps of UMTS, the 15 ksps subcarrier symbol rate of
LTE is very low, but in the same 5 MHz channel bandwidth, LTE can simultaneously
transmit 300 subcarriers to provide an aggregate 4.5 Msps rate. Thus on first inspection,
CDMA and OFDM have similar capacity for carrying data.

Within OFDM signal, it is possible to choose between three types of modulation for the LTE
signal. Such as QPSK, 16QAM and 64QAM

Techniques of LTE
downlink physical layer

Modulation

Techniques

16-QAM 64-QAM
4-QAM

Figure 3. 3 Techniques of LTE downlink physical layer flowchart

3.2.1 Quadrature Amplitude Modulation

QAM is a bandwidth efficient signaling scheme that, unlike CPM, does not possess a
constant envelope property. Unlike CPM waveforms, QAM needs to operate in the linear
region of a power amplifier to avoid any signal compression and hence degradation. For this
reason, among others, when choosing QAM as a signaling scheme, the waveform designer is
foregoing power efficiency for bandwidth efficiency QAM is a widely used modulation
scheme in applications ranging from short-range wireless communication to telephone
systems.
The QAM-modulated signal is given by:

S(t) = 𝑚1(t)𝑐𝑜𝑠(𝛺𝑐𝑡) + 𝑚2(t) sin(Ω𝑐𝑡) (1)

where m1(t) and m2(t) are the messages. S(t) as having a phasor representation that is the sum
of two phasor perpendicular to each other (the cosine leading the sine by π/2); indeed,

S(t) = Re[( 𝑚1(t)𝑒𝑗0 + 𝑚2(t)𝑒−𝑗𝜋⁄2) 𝑒𝑗Ω𝑐𝑡 ] (2)

Since, 𝑚1(t)𝑒𝑗0 + 𝑚2(t)𝑒−𝑗𝜋⁄2 = 𝑚1(t) − j 𝑚2(t (3)

we could interpret the QAM signal as the result of amplitude modulating the real and the
imaginary parts of a complex message

m(𝑡) = 𝑚1(t) − j 𝑚2(t) (4)

The basic process of impressing the parallel symbol stream onto the orthogonal carriers

Figure 3. 4 Conceptual representation of OFDM transmitter [10]

 Figure 3. 5 QAM transmitter and receiver: s(t) is the transmitted signal and r(t) is
the received signal [3].

For quadrature amplitude modulation two carriers shifted in phase by 90 degrees are
modulated, inducing amplitude and phase variations of the resulting signal. At the receiver
end, the phase and the amplitude, or the two quadratures of the field, must be obviously
measured. The constellation points are arranged to have the larger possible distance for easier
discrimination after the channel impairment. However, for sake of an easier modulation
implementation, they are usually arranged on a square grid, with the same vertical and
horizontal spacing. Despite the fact that the square QAM modulations do not exactly
maximize the Euclidian distance between constellation points, they are widely used, because
optical circuits including phase-controlled paths can easily implement them. For an MQAM
modulation, the number of points M of the constellation is equal to a power of 2. So, an
MQAM uses an M point constellation and allows the transmission of n=log2M bits per
symbol. The energy per bit is related to the energy per symbol by 〈EB〉 =ES⁄𝑛.

Figure 3.2 displays the signal constellation for a 16 QAM modulation. A 4 QAM modulation
is a constant envelope QPSK format. As the order M of the modulation increases, we get
closer to an analogic signal, more bits per symbol are transmitted, and the spectral efficiency
is improved. At the same time, the points of the constellation distance dMIN become
smaller,

increasing the sensitivity to noise and signal corruption, and the energy per bit is a lower
fraction of the symbol one. Higher signal level and/or a lower noise accumulation are/is
required to obtain a given rate of error. Since the signal vector no longer have the same
amplitude, we have a lower robustness to optical nonlinearity and the average energy per
symbol is reduced. Assuming an identical probability for the different symbols, a normalized
constellation point Euclidian distance 𝑑𝑀𝐼𝑁 = 2 , and remembering that the sum of the n
first odd integers number is (𝑛⁄3) (4n2 -1)

Figure 3. 6 Signal constellation for a 16 QAM modulation [6]

QAM (quadrature amplitude modulation) is a method of combining two amplitude

modulation (AM) signals into a single channel. This approach helps double its effective
bandwidth. QAM is also used with pulse AM (PAM) in digital systems, like wireless
applications.A QAM modulator works like a translator, helping to translate digital packets
into an analog signal to transfer data seamlessly.QAM is used to achieve high levels of
spectrum usage efficiency. This is accomplished by utilizing both the amplitude and phase
components to provide a form of modulation. In this scenario, the QAM signal comes with
two carriers. Each has the same frequency but differs in phases by 90 degrees, or one-quarter
of a cycle, which is the basis for the term quadrature.One signal is called the I signal, and the
other is called the Q signal. Mathematically, one of the signals can be represented with a sine
wave and the other by a cosine wave. The two modulated carriers combine at the source for
transmission. At the destination, the carriers separate, and the data is extracted from each.
Then, the data is incorporated into the original modulating information.
 Examples of three types of modulation

What is the difference between analog and digital QAM?

Some analog transmissions, like AM stereo, use QAM systems. However, QAM comes into its
own in data applications. This is because it offers a highly effective form of modulation for data
when used in anything from mobile phones to Wi-Fi. QAM is found in most forms of high-speed
data transmission. Analog QAM also enables carriers to transmit multiple analog signals. For
example, QAM is used in Phase Alternating Line and National Television Standards Committee
systems. In this case, different channels provided by QAM enable the signal to carry components
of color or chroma data.A system known as Compatible QUAM is found in AM stereo radio
applications. In this scenario, the different channels enable the required two channels for stereo to
be carried by a single carrier. Digital versions of QAM are often called quantized QAM. They are
built into most radio communications systems that use data.For example, radio communications
technologies ranging from Long-Term Evolution to Worldwide Interoperability for Microwave
Access and Wi-Fi use different types of QAM. As the field evolves, expect to see an increase in
QAM systems in radio communication technologies.
Simulation model

Figure 3. 7 LTE Downlink Simulation design in QPSK

 Figure 3. 8 LTE Downlink Simulation design in QPSK and 16QAM

Raised-cosine filter block

The raised-cosine filter is a filter frequently used for pulse shaping in digital modulation due
to its ability to minimise intersymbol interference.
The raised-cosine filter is an implementation of a low-past Nyquist filter that is one that has
the property of vestigial symmetry. This means that its spectrum exhibits odd symmetry
about where is the symbol period of the communications system.
Bandwidth

The bandwidth of a raised cosine filter is most commonly defined as the width of the non-
zero frequency-positive portion of its spectrum.
BW = (β + 1) , (0 < β < 1)
Rs

Application

When used to filter a symbol stream, a Nyquist filter has the property of eliminating
intersymbol interference,as its impulse response is zero at all nT where n is an integer
except n=0 Therefore if the transmitted waveform is correctly sampled at the receiver, the
original symbol values can be recovered completely.

The proposed OFDM system is simulated using SIMUINK in MATLAB. The performance
results for the system using different modulation schemes are obtained using the OFDM
parameters.

Table 3. 1 Parameters for the simulation of the OFDM model

System Parameters Values

System OFDM

Modulation techniques BPSK/QPSK/16QAM/64QAM/256QAM

Fading channel type AWGN/Rayleigh

Guard type Cyclic prefix

Cyclic Prefix length 25%

Doppler shift 10 Hertz

3.1 Modulation and Coding

One of the main design goals of LTE is to achieve high peak rates, and many multiple
methods are employed in order to meet this goal, a sophisticated way is by utilizing adaptive
modulation. This is the ability to adjust modulation schemes based on signal quality.
Adaptive modulation provides a tradeoff between delivered bit rate and the robustness of the
digital encoding, so as to balance throughput with error resilience. In 3GPP LTE, QPSK,
16QAM and 64QAM are supported modulation schemes. High order modulation like
64QAM work best with strong signals which is usually achieved near the base station while
low order modulation like QPSK possess better signal recovery in poor signal quality areas.
Adaptive modulation is therefore essential in LTE because it provides benefits to users on
both high and low signal strength areas.

LTE-Advanced downlink physical layer works with various modulation schemes, depending
on the data rates and coverage circumstances. Modulations schemes are QPSK, 16-QAM, 64-
QAM.Quadrature Amplitude Modulation is a modulation scheme which conveys data by
changing (modulating) the amplitudes and phases of two carrier waves. These two waves,

usually sinusoids, are out of phase with each other by 90°and thus are called Quadrature
carriers.

The average peak bit-rates and spectrum efficiency can only be optimized by:

 Introducing advanced modulation schemes

 More efficient channel coding
 Increasing symbol rates (in practice, increasing the carrier bandwidth).

QPSK modulation schemes convey data by changing the phase of the two carrier waves.
 3.3.1 M-ARY QAM

QAM is the encoding of the information into a carrier wave by variation of the amplitude of
both the carrier wave and a quadrature carrier that is 90° out of phase with the main carrier in
accordance with two input signals. That is, the amplitude and the phase of the carrier wave
are simultaneously changed according to the information needed to transmit. It is such a class
of nonconstant envelope schemes that can achieve higher bandwidth efficiency than M-PSK
with the same average signal power.

Mathematically, M-ary QAM can be written as shown:

(𝑡) = Ak𝑐𝑜𝑠(2𝜋𝑓𝑐𝑡 + 𝛳𝑙), (1)

k= 1, 2,… M1 𝑙= 1,2,,,,M2

Where

 Ak is the signal amplitude,

 𝛳𝑙 is the signal phase,
 M1 is the number of possible amplitudes of the carrier,
 M2 is the number of possible phases of the carrier, and 𝑓𝑐 is the carrier frequency.
A. Bit Error Rate Probability M-ary QAM

BER is a performance measurement that specifies the number of bit corrupted or destroyed as
they are transmitted from its source to its destination. Several factors that affect BER include
bandwidth, signal to noise ratio, transmission speed and transmission medium. The definition
of bit error rate can be translated into a simple formula:
Number of bit error s
BER =
Total number of bits sent

BER can also be defined in terms of the probability of error (POE) and express
1
POE¿ (1−erf )
2
Eb
N0√
Where erf is the error function, Eb is the energy in one bit and N0 is the noise power spectral
density. At that, the error function erf is different for the each of the various modulation
methods. This is because each type of modulation performs differently in the presence of
noise. It is important to note that POE is proportional to Eb / No, which is a normalized form
 of SNR.

B. Noise

The term noise refers to unwanted electrical signals that are always present in electrical
systems. Particularly, in terms of communication systems, noise can be defined as any
unwanted energy tending to interfere with the proper reception and reproduction of
transmitted signals. In digital communication systems, noise may produce unwanted pulses
or perhaps cancel out the desired ones. Noise may introduce serious mathematical errors in
signal analysis and limit the range of systems for a given transmitted power. It can also affect
the sensitivity of receivers by placing restrictions on the weakest signals to be amplified. All
these are some of the effects of noise on signals and communication systems at large.

In communication systems, the most common type of noise added over the channel is the
Additive White Gaussian Noise. AWGN is the effect of thermal noise generated by thermal
motion of electron in all dissipative electrical components i.e. resistors, wires and so on.
Mathematically, AWGN is modeled as a zero mean Gaussian random process where the
random signal “z” is the summation of the random noise variable “n”and a direct current
signal “a” that is
z=a+n
The probability distribution function for this Gaussian noise can be represented as follows:

( )( z−a ]Where 𝜎 2
σ )
1 −1
P(z )= exp ⁡[ is the variance of n, the higher the variance of
σ √2 π 2
the noise, the more is the deviation of the received symbols with respect to the constellation
set and, thus, the higher is the probability to demodulate a wrong symbol and make error.

3.3 Channel coding

3.3.1 Turbo Coding

Additive white Gaussian noise is a basic noise model used in information theory mimic the
effect of many random processes that occur in nature. The modifiers denote specific
characteristics

 Additive because it is added to any noise that might be intrinsic to the information
system.
 White refers to the idea that it has uniform power across the frequency band for the
 information system. It is an analogy to the color white which has uniform emissions
at all frequencies in the visible spectrum.
 Gaussian because it has a normal distribution in the time domain with an average
time domain value of zero.

In the simulator AWGN& Multipath Rayleigh fading channel models applied. The AWGN
Channel block adds white Gaussian noise to a real or complex input signal. When the input
signal is real this block adds real Gaussian noise and produces a real output signal. When the
input signal is complex, this block adds complex Gaussian noise and produces a complex
output signal. This block inherits its sample time from the input signal. This block accepts a
scalar-valued, vector, or matrix input signal with a data type of type single or double. The
output signal inherits port data types from the signals that drive the block.

The channel coding scheme for PDSCH adopts Turbo coding, which is a kind of robust
channel coding. The scheme of the Turbo encoder is a Parallel Concatenated Convolutional
Code with two 8-state constituent encoders and one Turbo code internal inter leaver.

 Systematic bit stream

 Parity bit stream
 Interleaved parity bit stream
Since the receiver also has the knowledge of the Turbo internal interleave sequence, the
interleaved systematic bit stream will not be transmitted to the receiver. But the data will be
partly utilized at the step of trellis termination. The tail bits are independently appended at
the end of each information bit stream to clean up the memory of all registers, i.e. terminate
the encoder trellis to a zero state. Generally, the length of the tail bits is equal to the number
of registers in one constituent encoder in LTE. The sequence of tail bits is rearranged and 4
tail bits are attached after each information bit stream. Hence, the length of each bit stream
becomes K + 4.

With the three information bit streams, the original Turbo coding rate is 1/3. However, after
padding tail bits, the coding rate will decrease a bit. Furthermore, by puncturing or repeating
the output of Turbo coding, it can accomplish an alterable channel coding rate under different
scenarios. Such process is implemented by the circular buffer at the rate-matching block.

3.4 Receiver
In the LTE downlink simulator, the receiver side simulates the operation of one user
equipment that processes the received signals and interacts with the eNodeB. In the LTE
receiver side there are steps of inverse-OFDM and inverse re- source mapping, the receiver
has to do the channel estimation to provide the necessary channel information to the
following blocks of equalizer. In each TTI, the following blocks of demodulation, inverse
rate-matching and channel decoding will detect each transmitted bits and ask for a
retransmission if any errors remain after the Turbo decoding. Finally, after CRC check the
decoded bits are transferred to OFDM symbols corresponding to a sub-frame are received,
the complete sub-frame is processed in a dual manner as done at the transmitter side. That is,
information from the control plane is used to extract the modulated symbols from their
corresponding resource elements.

3.4.1 Demodulator
To provide a soft bit stream to the soft combining block and the Turbo decoder, the
demodulation part has to work in the soft decision mode within the form of log-likelihood
ratio which reflects the reliability on each received bit. The LLR is the ratio of probabilities
of a 0 bit being transmitted versus a 1 bit being transmitted based on the knowledge of
received signal. In the LTE simulator, the demodulator is achieved by the block of QAM
Demodulator Baseband from the Simulink library. The configuration of demodulation
mapping should be the same as the modulator.
In addition, the decision type of ‘Approximate log-likelihood ratio’ is another option available for the
soft decision of the Rectangular QAM Demodulator Baseband block. The approximate LLR is
calculated by the nearest constellation point to the received signal rather than all the constellation
points as done in LLR. Hence, the output from the QAM Demodulator Baseband block should be
inversed