7

CHAPTER 2

BASICS OF MIMO OPEN LOOP

AND CLOSED LOOP SYSTEMS

The wireless communication has a very antagonistic environment

because the signal transmitted over a wireless communication link is
vulnerable to severe fluctuations in signal level (fading), co-channel
interference, scattering effects in time and frequency, path loss effect, etc.
Above all the availability, limited bandwidth introduces a significant
challenge in designing a system that must provide higher spectral efficiency
and offers high quality links at low cost. Multiple Input Multiple Output
systems (MIMO) is the current wireless trend which provides the spectral
efficiency and high quality links when compared to traditional Single Input
Single Output (SISO) systems. This chapter provides the basics about MIMO
and the techniques to improve the performance of MIMO.

2.1 MIMO -MULTIPLE INPUT MULTIPLE OUTPUT BASICS

An antenna technique in which multiple antennas are used at both

transmitter and receiver is called as MIMO or MU-MIMO (Multi User -
MIMO); there are simple categories of multi-antenna types:

SISO

SIMO
 8

MISO

MIMO

The data speed optimization and error minimization are

achieved by combining the multiple antennas at each end of the
communications circuit. The other forms of smart antenna technology are
MISO (multiple input, single output) and SIMO (single input, multiple
output). Multiple antennas at the transmitter and receiver are used to enable a
variety of signal paths to carry the data, this follows the principle of diversity
in which the receiver is provided with multiple copies of the same signal
which leads to reduce probability that the signal will be affected by multipath
effects and hence improves the link performance by reducing error rate.

There are several types of diversity modes available, they are:

i. Time diversity: Using time diversity, a message may be transmitted at
different times, e.g. using different timeslots and channel coding.
ii. Frequency diversity: In this form of diversity, a message may be
transmitted using different channels.
iii. Space diversity: It is used in a typical terrestrial environment where the
antennas are located in different positions, a message may be transmitted
via different radio paths.

In MIMO wireless systems the basic idea of space-time signal

processing is the use of multiple antennas located at different points. In
between a transmitter and a receiver; the signal can take many paths. Besides
 9

by moving the antennas even at a small distance the paths used will change.
Even though these multiple paths introduce interference in MIMO, by
improving the signal to noise ratio, or data capacity they can be used to
provide additional robustness to the radio link. As a result it is possible to
linearly increase the throughput of the channel. In recent years one of the
more valuable commodities is spectral bandwidth, to use the available
bandwidth more effectively techniques such as precoding is needed.

2.2 MULTI-USER MIMO (MU-MIMO) BASICS

MIMO system which spatially shares the channels by the use of

additional hardware‘s such as filters and antennas without the expense of
additional bandwidth is called as multi user MIMO (MU-MIMO) system.
When using spatial multiplexing instead of FDMA, TDMA or CDMA the
interference between the different users on the same channel is
accommodated by the use of additional antennas. To enable the spatial
separation, some additional signal processing is needed. The two set ups
associated with MU-MIMO are:

i. Downlink or Broadcast Channel (BC)

For the MIMO-BC transmit processing is required. It is usually in the
form of precoding and space division multiple access (SDMA).The channel
state information at the transmitter (CSIT) enables significant throughput
improvements, when compared with the point to point MIMO systems if the
number of transmit antennas exceeds that of the number of receiver antennas.

ii. Uplink or Multiple Access Channel (MAC)

In MIMO-MAC the channel state information at the receiver (CSIR)
is needed. Determining CSIR is simpler than that of CSIT but it needs
considerable uplink capacity to transmit the dedicated pilot signals. It
outperform the existing point to point MIMO if the number of receiver
 10

antenna is greater than the transmiter antennas.

2.2.1 Multi-User MIMO Advantages

Some of the significant advantages of MU-MIMO are:

i. Depending upon the number of base station antennas employed ,the
level of direct gain to be obtained in capacity arising from the multi-user
multiplexing schemes increases.
ii. It is less affected by channel rank loss and antenna correlation.
iii. Without the need for multiple antennas at the user equipment MU-
MIMO achieves spatial multiplexing gain,thereby it reduces the
production cost of remote terminals.

2.3 TECHNIQUES FOR IMPROVING PERFORMANCE OF MIMO

To increase the data rate in wireless communication, Spatial
Multiplexing techniques are used (Tarokh V, 1998) . Fading can be alleviated
by employing receiver and transmit diversity (Alamouti S. 1998), thereby
improving the reliability of the transmission link. By using coherent
combining techniques array gain and signal to noise ratio of the system
increases thereby increases the coverage area (Paulraj & Kailath T 1993). The
following techniques are used to improve the performance of MIMO
i. Diversity
ii. Spatial-Multiplexing
iii. Precoding
This chapter concentrates on two of the above mentioned
techniques – diversity and spatial multiplexing.

2.3.1 Diversity

Aiming at improving the reliability of the system, multiple

antennas are used in a system to provide different propagation paths (spatial)
so that same data can be sent across the different paths, one can send same
data across the independent fading channels to combat fading effect. This
 11

technique is known as spatial diversity or simply diversity technique. Since

multiple copies of the same data are sent across different channels, the
amount of fade experienced by each copy of the data will be different. Hence
at least one of the copies will have good signal quality at the receiver than that
of the remaining copies. This improves the reliability of the system and also
reduces the co-channel interference.

In SISO only one transmit antenna and one receive antennas are
used. This will not provide any diversity as there is no parallel link. Thus the
diversity order is 0. In SIMO system, two copies of the same data is
transmitted by using two transmit antennas having independent fading
characteristics. If one of the links fail to deliver the data, there is possibility
that the other link may deliver the data properly. This improvement in
reliability leads to performance improvement which is measured as diversity
gain. For a system with Nt transmitter antennas and Nr receiver antennas, the
maximum number of diversity paths is Nt×Nr .For SIMO the number of
diversity paths is 1×2=2.Similarly for a 2×2 MIMO system the total number
of diversity paths is 2×2=4.
Fading Channel h1

Transmitter Fading Channel h2 Receiver

Figure 2.1 1×2 MIMO System

 12

Fading Channels
h1

h3 h2

Transmitter Receiver
h4

Figure 2.2 2×2 MIMO System

2.3.2 Spatial-Multiplexing

MIMO systems implemented using spatial-multiplexing techniques

provides degrees of freedom or multiplexing gain in order to improve the data
rate of the system. This is achieved by placing different portion of the data on
different propagation paths (spatial-multiplexing) i.e., each spatial channel
carries independent information. In Orthogonal Frequency Division
Multiplexing (OFDM) technique (Discussed later), different frequency sub
channels carry different parts of the modulated data. But in spatial
multiplexing, several independent sub channels are created in the same
allocated bandwidth. Hence it achieves high multiplexing gain at low wastage
of bandwidth or power. In signal space constellation the multiplexing gain is
also referred as degrees of freedom. For a MIMO system with Nt transmit
antennas and Nr receive antennas the number of degrees of freedom is given
as min (Nt × Nr).Since the spatial multiplexing (Paulraj & Kailath T 1993)
concentrates on improving data rate the degrees of freedom governs the
overall capacity of the system. The difference between diversity and spatial
multiplexing is illustrated in Figure 2.3.
 13

010 0

010 010 010 1

010 0

MIMO with MIMO with Spatial

Diversity Multiplexing

Figure 2.3 Comparision of MIMO Diversity and Spatial Multiplexing

2.4 OFDM

In high data rate applications the symbol duration reduces with the
increase of data rate. Due to the fading effect the systems using single carrier
modulation experience severe inter symbol interference (ISI) which leads to
more complex equalization. Orthogonal Frequency Division Multiplexing
(OFDM) is a digital multicarrier modulation scheme that overcomes the
drawback of single subcarrier modulation by using multiple subcarriers within
the same single channel. Instead of transmitting a high rate stream of data
with a single subcarrier, OFDM makes use of a large number of closely
spaced orthogonal subcarriers that are transmitted in parallel. The basic
concept of OFDM modulation is to divide the entire frequency selective
fading channel into many narrow band flat fading sub channels which carries
a high data rate modulating stream in parallel. Since the carrier frequencies of
each sub channel are orthogonal to each other, even though sidebands from
each carrier overlap they are not affected by inter symbol interference. In
order to accomplish this, carrier spacing is chosen such that it is equal to the
reciprocal of the symbol period (Li Y.G 2006).
 14

Figure 2.4 OFDM spectrum

The basic concept of OFDM is based on Frequency Division

Multiplexing (FDM) technique. In FDM different data streams are mapped
onto separate parallel frequency channels and the channels are separated from
each other by a frequency guard band to reduce the interference between
adjacent channels.The variations of OFDM compared with FDM are listed
below:
 OFDM uses multiple carriers to carry the data stream
 The subcarriers are orthogonal to each other, and
 To minimize the channel delay spread and ISI a guard interval is added to
each symbol.

Figure 2.5 Guard interval

 15

The following Figure 2.6 illustrates the interrelationship between

the frequency and time domains of an OFDM signal. In the frequency
domain, the subcarriers are independently modulated with complex data. To
produce the OFDM symbol in the time domain an Inverse FFT transform is
performed on the frequency domain subcarriers. Then to prevent inter symbol
interference (ISI) caused by multipath fading ,guard intervals are inserted
between the symbols. At the receiver to recover the original data streams an
FFT is performed on the OFDM symbols.

Figure 2.6 Interrelationship between frequency and time in OFDM

2.4.1 OFDM system Implementation

To map digitally modulated input data onto orthogonal subcarriers

a combination of digital signal processing techniques such as Fast Fourier
Transform (FFT) and Inverse Fast Fourier Transform (IFFT) are used. In an
OFDM system, the input bits are combined together and mapped to the
complex source data representing the constellation point. At the transmitter
site the complex source symbols are in the frequency domain by using IFFT
block the data is transformed into time domain. The IFFT takes the N
subcarriers as N source symbols at a time. Each symbol has symbol duration
of T seconds. The IFFT output is the summation of all N orthogonal sinusoids
 16

which will form up a single OFDM symbol. The result from IFFT is
transmitted across the channel. The receiver uses the FFT block to bring out
the frequency domain signal in order to recover the original data.

Figure 2.7 OFDM Block Diagram

2.4.2 Mathematical Representation of OFDM

OFDM can be regarded as a time-limited form of multicarrier

modulation. The complex signals transmitted by OFDM are represented as
. Now the OFDM modulated signal can be expressed as,

for (2.1)

where, and

where Ts denotes the symbol duration and indicates the OFDM sub
channel space. At receiver in order to demodulate the OFDM signal the
symbol duration must satisfy the orthogonality condition i.e., Ts =1 (Li Y.G
2006).

By using the orthogonality condition we have,

=

= (2.2)

where,
 17

Hence the OFDM signal can be demodulated by,

(2.3)

Samples of OFDM multicarrier signals can be obtained using the

inverse discrete Fourier transform (IDFT) of the data symbols. The discrete
Fourier transform (DFT), can be implemented by low complexity fast Fourier
transform (FFT).

2.4.3 FFT Implementation

From the above equation it is understood that the integral function

is needed to compute the OFDM demodulated signal, to reduce the
complexity of integral function Fast Fourier Transform (FFT) is used.

From (2.2) and (2.3), the discrete form of OFDM signal can be
represented as,

where, then

Let, then = IDFT {sk}

where IDFT denotes the inverse discrete Fourier transform. Hence the OFDM
transmitter can be implemented using the IDFT. An OFDM signal with N sub
channels the signal bandwidth is about . The transmission rate of

each sub channel is given as symbols/sec.; hence the total transmission rate

of OFDM signal is symbol/sec. From this the bandwidth efficiency of the

OFDM system can be written as follows,

where, T indicates the actual OFDM symbol duration and it is the sum of
symbol duration and length of cyclic extension i.e., T=Ts+Tg(Li Y.G 2006).

(2.4)
 18

2.4.4 OFDM Advantages

i. OFDM divides the overall channel into multiple narrowband signals that
are affected individually as flat fading sub-channels hence it is more
resistant to frequency selective fading.
ii. Channel interference is band limited so it will not affect all the sub
channels i.e. not all the data is lost hence OFDM is highly resilience to
interference.
iii. OFDM efficiently utilizes the available spectrum because it uses closely
spaced overlapping sub carriers.
iv. The OFDM supports low data rate on each of the sub-channels hence it
provides resilient to ISI.

2.4.5 OFDM Disadvantages

i. OFDM signal has high noise like amplitude variation which leads to
high peak to average power ratio.
ii. OFDM is more sensitive to carrier offset and drift.

2.4.6 Additional Attributes of OFDM System

i. Coded Orthogonal Frequency Division Multiplexing (COFDM):
Includes the error correction coding into the signal.
ii. Flash OFDM: Uses multiple tones and fast hopping to spread signals
over a given spectrum.
iii. Orthogonal Frequency Division Multiple Access (OFDMA):
Provides multiple access facility in telecommunication applications.
iv. Vector OFDM (VOFDM): Uses the concept of MIMO technology to
enhance the signal reception and improve the transmission speed.
v. Wideband OFDM (WOFDM): It uses a large spacing between the
channels so that any frequency errors between transmitter and receiver
do not affect the performance. Widely used in Wi-Fi systems.
 19

2.5 CHANNEL STATE INFORMATION

In wireless communications, the well-known channel property of a

communication link is referred as channel state information (CSI). The CSI
information is used to represent combined effect of fading, scattering and power
reduction with respect to distance and to describe the signal propagation of signal
from transmitter to the receiver. The knowledge of CSI is not needed for SISO
channel because it is constant and does not vary from bit to bit.

In order to split the channel variations into spatially separated sub

channels in a rapid fading channels where the CSI varies rapidly MIMO
technique is used. Thus the knowledge of CSI either at the transmitter or at the
receiver is essential for designing a communication system. The CSI at the
transmitter is referred as CSIT and at the receiver CSI is referred as CSIR
respectively.

The MIMO system is modelled as,

(2.5)
where, y and x denotes the transmit and receive signal vectors and H and n
denotes the channel matrix and noise vectors respectively, The noise vector is
normally considered as a complex normal with mean ‗0‘ and variance ‗s‘.
i.e. (Tulino A, 2005).

2.5.1 Types of Channel State Information

Instantaneous CSI or short term CSI: By using impulse response

of a digital filter the current channel conditions are known. This is used to
adjust the transmitted signal nearer to the impulse response to achieve low bit
error rates.

Ideally it is considered that the channel matrix H is perfectly

known. But in practice due to estimation errors the estimated channel matrix
is given as (Björnson E & Ottersten B 2010),
 20

(2.6)
where, Rerror is the error covariance matrix and Hestimate is the channel
estimation matrix.

Statistical CSI or long term CSI: This method uses the statistical information
such as the type of fading, line of sight (LOS) component, channel gain and
spatial correlation to describe the channel characteristics.

In practise the channel conditions of fast fading systems varies

quickly with the frequency hence instantaneous CSI is suitable for analysis,
whereas inn slow fading systems statistical CSI is used. Therefore the
performance is further improved by combining statistical CSI with
instantaneous CSI (Kermoal J et al 2002).

The channel matrix is given as,

(2.7)

2.5.2 Estimation of Channel State Information

In real time applications the instantaneous CSI is estimated by
using a pilot or training sequence. In this method a known signal is
transmitted and by using the combined knowledge of transmitted and received
signal the channel matrix H is estimated.

Let the pilot sequence be denoted .Where, Pi is the

transmitted signal over the channel. The received signal is thus given as,
(2.8)
where, Pilot matrix P= and noise vector N=

2.5.2.1 Least square estimation (LSE)

The least square estimator or minimum variance unbiased
estimator is (Biguesh M & Gershman A 2006) used if the channel and noise
distributions are unknown. The channel matrix of LS estimator is given as,
 21

(2.9)

The estimation Mean Square Error (MSE) is proportional to

,where denotes the trace. If N is greater than or equal to number
of transmit antennas then is scaled to identity matrix this condition is
used to minimize errors.

2.5.2.2 Minimum mean square error estimation (MMSE)

In this method it is assumed that the channel and noise
distributions are known. By using this priori information the estimation errors
are decreased. This approach is also known as Bayesian estimation.
and

(2.10)
where ⊗ denotes the Kronecker product. The mean square error estimation is
given as

As opposed to least square estimation, If N is smaller than the

number of transmit antennas the estimation error can be minimized. Both
transmit diversity and spatial schemes are categorized as either open loop or
closed loop system depending upon the available CSI.

2.6 OPEN LOOP MIMO

In open loop systems the transmitter does not require any
knowledge of the channel. It is used in systems where the access network
does not have information or feedback from the receiver to do coding
adjustment. The following Figure 2.8 shows a possible setup in spatial
Multiplexing.
 22

Y0(i)

X0(i) M×M DFT M×M large delay N×M

. .
. Precoding Precoding .
. CDD D(i) .
(U) W(i) YN-1(i)
XM-1(i)

M Layers N Antennas
Figure 2.8 Mimo open loop system

2.7 CLOSED LOOP MIMO

On the other hand closed loop systems require channel knowledge

at the transmitter, thus necessitating either channel reciprocity or a feedback
channel from the receiver to the transmitter. Hence, it is used in systems
where the access network executes dynamic adjustment based on feedback
from the receiver. The Figure 2.9 shows a functional view of closed loop
MIMO.
Y0(i)

CP CP removal DFT
X0(i) IDFT
Equalizer
Precoding W(i)

.
. . .
. .
. . .
. . .
. . .
XM-1(i)
IDFT CP removal DFT
CP
YN-1(i)

PMI
Feedback Channel
Channel Estimation
Codebook

Figure 2.9 Mimo closed loop system

2.8 MIMO CHANNEL MODEL

The MIMO system typically contains M antennas at the transmitter

and N antennas at the receiver end. The receiver antenna ‗y‘ not only receives
the direct signal intended for it, but also receives a fraction of signal from
other propagation paths. Thus, the channel response is expressed as a
transmission matrix H. For example the direct path formed between antennas
 23

‗i‘ at the transmitter and the antenna ‗i‘ at the receiver is represented by the
channel response hii. Thus, the channel matrix is of dimension N×M.
Therefore from (2.5) the received signal vector y can be expressed
in terms of the channel transmission matrix H, the input signal vector x and
noise vector n as,

where,

, and

For a simple 2×2 MIMO system, the above equation is rewritten in

terms of linear equation as
(2.11)
(2.12)

In terms of Matrix representation, the received signal vector ‗ ‘ is,

(2.13)

where, is the transmission channel vector

indicates the signal vector
and denotes the noise vector

2.9 CAPACITY OF MIMO SYSTEM

MIMO system is introduced to increase the capacity and to

improve the quality of a communication link. The capacity can be achieved
by spatial multiplexing and quality by diversity techniques. Hence it is
important to identify the capacity equation of a MIMO system over a variety
of channels such as AWGN, fading channels.
 24

2.9.1 Capacity and Mutual Information

A channel is said to be a discrete memory less channel if the noise

term corrupts the input symbols independently. The input and output variables
are random and represented as X and Y. The channel can be expressed by
conditional probabilities. Conditional probability is nothing but for a given set
of inputs to the channel the probability of getting the output of the channel is
given as p(Y/X).

The mutual information is the amount of information that one

random variable contains about the other random variable and it is
represented as I(X; Y).
(2.14)
where, is the amount of information in X before observing Y and thus
the above quantity can be seen as the reduction of uncertainty of X from the
observation of Y. by maximizing this mutual information over all possible
input distributions p(x) we can obtain the information capacity C.
(2.15)

2.9.2 Capacity with Transmit Power Constraint

In practical scenario the capacity is given in terms of the average

power. The average transmit power is given as and the
maximum average power in the transmitter side is Pt.
Hence, the capacity C is,
(2.16)

Thus the channel is considered as a continuous input continuous

output discrete memory less channel (CCMC). For such continuous random
variable, differential entropy hd(.) is considered. Thus I(X; Y) in terms of
differential entropy is as follows,
(2.17)
 25

For simplification it is assumed that the channel is perfectly known

at the receiver, hence the uncertainty of the channel h conditioned on X is
zero and also the noise is independent of the input. Therefore the above
equation can be rewritten as,
(2.18)
where,

=Noise covariance Matrix

and = Input signal covariance Matrix

Substituting the (2.18) in (2.16) we can simplify the capacity

equation as follows,
(2.19)

For a MIMO flat fading channel the channel noise is considered as

uncorrelated noise therefore and is the identity matrix of

dimension × . Thus the channel capacity of MIMO flat fading channel is

as follows,

(2.20)

In places where the channel state information at the transmitter

(CSIT) is unknown where is the × identity matrix.

Depending upon the characteristics of mutual information, capacity

is categorized into two types, they are,
i. Ergodic Capacity
ii. Outage Capacity
 26

2.9.3 Ergodic Capacity

Ergodic capacity is defined as the statistical average of the mutual
information, where the expectation is taken over H.
(2. 21)

2.9.4 Outage Capacity

It is defined as the information rate at which the instantaneous
mutual information falls below a prescribed value of probability expressed as
percentage q (Goldsmith Andrea & Varaiya Pravin 1996).

(2.22)

2.10 RESULTS AND SUMMARY

The MIMO-OFDM system is designed with a maximum channel
frequency of 20MHz, the total number of packets as 200 and 256 FFT
samples according to the design specifications of OFDM system. The
sampling frequency and sampling time periods are 22MHZ and 11μ sec
respectively. The system is analyzed with different types of modulation
techniques based on the channel SNR. Selection of modulation schemes is
based on the following Table 2.1.

Table 2.1 Type of modulation schemes

SNR Modulation Scheme Code Rate

6 dB-9.4 dB BPSK ½
9.4dB-11.2dB QPSK ½
11.2dB-16.4dB QPSK ¾
16.4dB-18.2dB 16QAM ½
18.2dB-22.7dB 16QAM ¾
22.7dB-24.4dB 64QAM ½
 27

Figure 2.10 and Figure 2.11 shows the performance of MIMO

system in terms of channel capacity and BER for different number of transmit
and receive antennas. For SNR=10 dB, the BER of a 4×4 system is
approximately 0.02, for a 4×6 system, it is 0.004 and for 4×8 systems the
BER is about 0.0015. Hence, it is understood that as the diversity increases
the BER performance is also increased. Similarly for example, at SNR =10
dB the channel capacity of a 4×4 MIMO system is 10bps/Hz and an 8×8
MIMO system provides 20 bps/Hz. Hence the 8×8 system outperforms by
66.6667%.
45

40 N =1, N =1
T R
N =2, N =2
35 T R
N =4, N =4
channel capacity(bps/Hz)

T R
30 N =6, N =6
T R
N =8, N =8
25 T R

20

15

10

0
0 2 4 6 8 10 12 14 16 18 20

SNR[dB]

Figure 2.10 MIMO channel capacity without CSI

 28

Figure 2.11 MIMO performance analysis

Similarly, Figure 2.12 depicts the performance of MIMO channel
capacity in terms of cumulative distribution function (CDF) and data rate for
different number of transmit and receive antennas. As the number of transmit
and receive antennas get increased the transmission rate of the MIMO system
also gets increased. For example for a 4×4 system the data rate is
approximately 10 to 15 bps/Hz, for an 8×8 system, it is approximately
between 20 to 25 bps/Hz.
1

N N =2
0.8 T R
N = N =4
T R
N = N =6
T R
0.6 N = N =8
T R
CDF

0.4

0.2

0
5 10 15 20 25 30

Rate[bps/Hz]

Figure 2.12 Distribution of MIMO channel capacity (SNR=10dB)

without CSI
 29

Figure 2.13 shows the performance in terms of channel capacity with

CSI for different MIMO systems with respect to average SNR. For 5 dB
average SNR the capacity of a SIMO/MISO system is approximately 4
bits/transmission, for a MMO system with maximum eigen mode it is 5
bits/transmission, for a MIMO system with uniform power distribution the
bits/transmission is 6 and finally for a MIMO system with water filling power
distribution it is 7 bits/transmission. The result clearly shows that always the
MIMO system with water filling power distribution outperforms the all other
MIMO systems.

25
Capacity (bits/transmission)

20 SIMO/MISO

Max Eigenmode Tx

Eigenmode Tx with Uniform Power

Eigenmode Tx with WF
15

10

0
-10 -5 0 5 10 15 20

Average SNR (dB)

Figure 2.13 Capacity for MIMO systems with CSIT

 30

2.11 CONCLUSION
This chapter thus provides an overview of MIMO systems,
especially MU-MIMO systems, techniques used to improve the performance
of MIMO system. It describes the basics and need for OFDM system in
MIMO, need for channel state information, the channel model and the
capacity of MIMO channel. The BER and capacity of MIMO systems are
analyzed and it shows that the performance of MIMO system is increased as
diversity increases.