Btech report

A NOVEL CHANNEL EQUALISATION TECHNIQUE FOR MIMO–OFDM
SYSTEM AND STUDY OF WPMCM SYSTEM
A PROJECT REPORT
submitted by
CB107EC102 AKASH MOHAN
CB107EC103 AMRITA MISHRA
CB107EC118 KARTHIK M
CB107EC144 PADMA N
CB107EC145 PRASHANTH G
Under the guidance of
Ms. R.Deepa
in partial fulfillment for the award of the degree
of
BACHELOR OF TECHNOLOGY
IN
ELECTRONICS AND COMMUNICATION ENGINEERING
AMRITA SCHOOL OF ENGINEERING, COIMBATORE
AMRITA VISHWA VIDYAPEETHAM
COIMBATORE 641 105
APRIL 2011

AMRITA VISHWA VIDYAPEETHAM
AMRITA SCHOOL OF ENGINEERING, COIMBATORE, 641105
BONAFIDE CERTIFICATE
This is to certify that the project report entitled “A NOVEL CHANNEL
EQUALISATION TECHNIQUE FOR MIMO–OFDM SYSTEM AND STUDY
OF WPMCM SYSTEM” submitted by
CB107EC102 AKASH MOHAN
CB107EC103 AMRITA MISHRA
CB107EC118 KARTHIK M
CB107EC144 PADMA N
CB107EC145 PRASHANTH G
in partial fulfillment of the requirements for the award of the Degree of Bachelor of
Technology in ELECTRONICS AND COMMUNICATION ENGINEERING is
a bonafide record of the work carried out under my guidance and supervision at
Amrita School of Engineering, Coimbatore .
Ms. R.Deepa
Asst. Professor, ECE
Project Guide
Mr. R.Gandhiraj
Asst. Professor, ECE
CERG Coordinator
Dr. V.P. Mohandas
Chairman, ECE
The project was evaluated by us on:
Internal Examiner External Examiner

ACKNOWLEDGEMENT
We express our sincere thanks to our beloved guide Ms. R.Deepa, Assistant
Professor, Department of Electronics and Communication Engineering for being the
pillar of the project with tremendous support and profused moral encouragement
throughout the journey of the project and also being the torch bearer for the rougher
patches of our project.
We would like to thank our Chancellor Satguru Mata Amritanandamayi Devi
for her blessings without which we would not have completed our project.
Our heartfelt gratitude to our Pro-Chancellor Br. Abhayamrita Chaitanya for
having provided necessary infrastructure required for the successful completion of our
project.
We express our sincere thanks to Dr. V. P. Mohandas, Chairman, Department
of Electronics and Communication Engineering who has been instrumental in lending
us a helping hand throughout the completion of the endeavour.
We express our sincere thanks to Mr. P.Sudheesh, Assistant Professor,
Department of Electronics and Communication Engineering, for his moral support
and assistance throughout the completion of our project.
Our sincere thanks to Ms. S.Kirthiga, Assistant Professor, Department of
Electronics and Communication Engineering, for her valuable support and
suggestions during weekly reviews, for completing our project.
We express our heartfelt thanks to Mr. R.Ramanathan, Assistant Professor,
Department of Electronics and Communication Engineering, for his encouragement
and assistance throughout the completion of our project.
We would like to thank Mr. R.Gandhiraj, Assistant Professor, Department of
Electronics and Communication Engineering for being supportive and encouraging
towards completion of our project.
Our heartfelt thanks to Mr. V.Anantha Narayanan, Senior Lecturer and Ms K.
Nalina Devi, Assistant Professor, Department of Computer Science And Engineering,
for their seamless support and encouragement.
Our heartfelt gratitude to Dr. Murali Rangarajan, Assistant Professor,
Department of Chemical Engineering, for having motivated and helped us sail
through the dark patches of the project.

Our thanks to all the teaching and non-teaching staff of our college and to our
friends, who really boosted our confidence to complete the project successfully and
make it a fruitful one.

i
TABLE OF CONTENTS
ABSTRACT iv
ABBREVIATIONS AND ACRONYMS v
LIST OF FIGURES vi
1. INTRODUCTION 1
1.1 INTRODUCTION 2
1.2 WIRELESS COMMUNICATION 2
1.3 WIRELESS COMMUNICATION BLOCK 3
1.4 CHANNEL ESTIMATION 3
1.5 MIMO 5
1.6 OFDM AND WPMCM 6
1.7 ENHANCEMENTS AND CONTRIBUTION 6
2. MIMO 7
2.1 INTRODUCTION 8
2.2 MULTIPLE ANTENNA SYSTEMS 8
2.3 MAJOR ADVANTAGES OF MULTIPLE ANTENNA
SYSTEMS 8
2.3.1 ARRAY GAIN 8
2.3.2 SPATIAL DIVERSITY (SD) GAIN 8
2.3.3 SPATIAL MULTIPLEXING 9
2.3.4 INTERFERENCE REDUCTION 9
2.4 ST CHANNELS AND SIGNAL MODELS 9
2.4.1 SISO CHANNEL 9
2.4.2 SIMO CHANNEL 10
2.4.3 MISO CHANNEL 10
2.4.4 MIMO CHANNEL 11
3. OFDM AND WPMCM 12
3.1 OFDM 13
3.1.1 INTRODUCTION 13
3.1.2 SYSTEM DESIGN 14
3.1.3 ADVANTAGES 17
3.1.4 DRAWBACKS 17

ii
3.2 WPMCM 18
3.2.2 SYSTEM DESCRIPTION 19
3.2.3 ADVANTAGES 21
3.2.4 DISADVANTAGES 22
4. MIMO-OFDM AND MIMO-WPMCM 23
4.1 MIMO-OFDM 24
4.1.3 ADVANTAGES 26
4.1.4 LIMITATIONS 26
4.2 MIMO-WPMCM 26
4.2.2 ADVANTAGES 28
5. CHANNEL ESTIMATION TECHNIQUES FOR OFDM AND
MIMO-OFDM SYSTEM 29
5.1 CHANNEL ESTIMATION BASED ON BLOCK TYPE
ARRANGEMENT 31
5.1.1 MINIMUM MEAN SQUARE ERROR(MMSE)
ESTIMATION 32
5.1.2 LEAST SQUARE ERROR(LSE)
ESTIMATION 33
5.2 CHANNEL ESTIMATION BASED ON COMB TYPE
ARRANGEMENT 34
5.3 CHANNEL ESTIMATION OF MIMO-OFDM SYSTEM 34
6. A NOVEL PRE-DISTORTION TYPE ADAPTIVE CHANNEL
EQUALISATION TECHNIQUE 38
6.1 SYSTEM MODEL 39
6.2 MSD ALGORITHM 41
6.3 THEORY 42
7. SIMULATION AND RESULTS 44
7.1 CONVERGENCE OF MSD FOR THE PROPOSED
TECHNIQUE 45

iii
7.2 BER VS SNR(4-QAM)
FOR THE PROPOSED TECHNIQUE 46
7.3 COMPARISON OF BER VS SNR(2-PAM AND 4-QAM)
FOR THE PROPOSED TECHNIQUE 47
7.4 COMPARISON OF BER VS SNR(2-PSK)
FOR A MIMO SYSTEM WITH AND WITHOUT
PROPOSED TECHNIQUE 48
7.5 COMPARISON OF BER VS SNR (2-PSK) FOR A MIMO-
OFDM SYSTEM WITH AND WITHOUT PROPOSED
TECHNIQUE 49
7.6 COMPARISON OF BER VS SNR(2-PSK) FOR AN OFDM
AND WPMCM SYSTEM 50
7.7 COMPARISON OF BER VS SNR(2-PSK) FOR A WPMCM
SYSTEM FOR VARIOUS CHANNELS 51
8. CONCLUSION 52
8.1 SCOPE FOR FUTURE WORK 53
9. PUBLICATION 55
10. REFERENCES 57

iv
ABSTRACT
In any communication system, the emphasis is on estimating the channel
response so as to retrieve the transmitted input signal accurately at the receiver’s end.
Channel Equalisation at the transmitter refers to pre-distorting the input signal so that
the effect of the channel is nullified during transmission. This approach works out for
slow fading channels where the channel response remains almost constant for a
considerable amount of time (coherence time). Our prime objective in this work is to
adapt a filter with impulse response (F) to the channel impulse response (H) at the
transmitter end. By evaluating the inverse of the filter F and passing the symbols
through a filter designed with frequency response F-1
, we can equalise the distortions
on the input due to channel.
Simulation results show that the Bit Error Rate (BER) performance of the
system is identical with that of the effect of noise, when this technique is implemented
for basic modulation schemes like PAM or QAM. Whereas, when the technique is
implemented for Multiple Input Multiple Output (MIMO) system, or a Multiple Input
Multiple Output (MIMO) system with Orthogonal Frequency Division Multiplexing
(OFDM) modulation, it shows a better Bit Error Rate (BER) performance than that of
the usual way of channel equalization in the respective systems.

v
ABBREVIATIONS AND ACRONYMNS
SISO: Single Input Single Output
SIMO: Single Input Multiple Output
MISO: Multiple Input Single Output
MIMO: Multiple Input Multiple Output
SNR: Signal-to-Noise Ratio
OFDM: Orthogonal Frequency Division Multiplexing
WPMCM: Wavelet Packet based Multi Carrier Modulation
FFT: Fast Fourier Transform
IFFT: Inverse Fast Fourier Transform
ISI: Inter-Symbol interference
IDWT: Inverse Discrete Wavelet Transform
DWT: Discrete Wavelet Transform
LSE: Least Square Error
MMSE: Minimum Mean Square Error
ST: Space Time
SD: Spatial Diversity
SM: Spatial Multiplexing
BER: Bit Error Rate
ICI: Inter-Carrier interference
AWGN: Additive White Gaussian Noise
QAM: Quadrature Amplitude Modulation
PSK: Phase Shift Keying
SC: Sub-Carrier
MSD: Minimum Standard Deviation
PAM: Pulse Amplitude Modulation

vi
LIST OF FIGURES
Figure 2.1: Block diagram of basic MIMO system 9
Figure 3.1: Block diagram of a basic OFDM system 14
Figure 3.2: Spectrum of OFDM signal 15
Figure 3.3: Spectrum of WPMCM signal (8 sub-carriers) 19
Figure 3.4: Block diagram of a basic WPMCM transmitter 20
Figure 3.5: Block diagram of a basic WPMCM receiver 20
Figure 4.1: Block diagram of a MIMO OFDM system 25
Figure 4.2: Block diagram of a MIMO WPMCM transmitter 27
Figure 4.3: Block diagram of a MIMO WPMCM receiver 27
Figure 5.1: Block type pilot arrangement in an OFDM system 30
Figure 5.2: Comb type pilot arrangement in an OFDM system 30
Figure 6.1: Channel paths between two transceivers 40
Figure 6.2: Adaptation of the filter F to the Channel Impulse Response 40
Figure 6.3: System model for the proposed technique at the transmitter side 41
Figure 6.4: Symbol transmission diagram for the proposed technique 41
Figure 7.1: Convergence of MSD for the proposed technique 45
Figure 7.2: BER vs SNR (4-QAM) for the proposed technique 46
Figure 7.3: Comparison of BER vs SNR (2-PAM and 4-QAM)
for the proposed technique 47
Figure 7.4: Comparison of BER vs SNR (2-PSK)
for a MIMO system with and without the proposed technique 48
Figure 7.5: Comparison of BER vs SNR(2-PSK)
for a MIMO-OFDM system with and without the proposed 49
technique
Figure 7.6: Comparison of BER vs SNR (2-PSK)
for an OFDM and WPMCM system 50
Figure 7.7: Comparison of BER vs SNR(2-PSK)
for a WPMC system for various channel models 51

2
Chapter 1
INTRODUCTION
1.1 INTRODUCTION
Communication, the activity of conveying information, is the distinctive ability
which has made possible the evolution of human society. The history of
communication is mankind‟s search for ways to express itself, to share knowledge
and to prosper.
Humans live related to each other. The initial challenge for a man was to put
forth his thoughts. As gestures and body language became inadequate to convey one‟s
thoughts, languages were invented. Language is a tool which portrays thoughts in the
form of words, though not a very effective tool; it has become a basic necessity for
everyone to use it. But as humans explored the world around, more knowledge was
dwelled which were to be shared, and, texts and speech alone became insufficient for
transferring the vastness of what is known.
Better communication techniques were enquired upon and were being
discovered, from Pigeon posts to Persian couriers, from telegraphy to telephony,
every technique connected people separated by lands, further. Our planet started
shrinking as the world of communication began to expand. But nothing changed the
destiny of humanity as much as what James Clerk Maxwell‟s discovery did. Electro-
magnetic waves redefined limitations, it made wireless communication possible.
1.2 WIRELESS COMMUNICATION
Wireless communication is the use of EM waves to transfer data between two
users. Wireless communications has developed into a key element of modern society.
From satellite transmission, radio and television broadcasting to the now ubiquitous
mobile telephone, wireless communications has revolutionized the way societies
function [26]. It has many advantages over the earlier successful wired
communication: These are its portability, flexibility and coverage.
Portability implies the freedom a hand-held device like a cell phone offers the
user. Flexibility implies the ability to add/remove devices into existing networks

3
without any changes in hardware. Technologies such as cellular radio enable users to
move over a large area providing them coverage.
1.3 WIRELESS COMMUNICATION BLOCK
Like any communication system, a wireless communication system is made up of
the three fundamental blocks:
1. Transmitter
2. Receiver
3. Channel
When two people are conversing the person who has to convey a message
(transmitter) has to turn it into words and speak. The recipient (receiver) on receiving
the speech signals decodes the words and interprets the message. It is difficult for the
recipient to guess the message when the environment (channel) is noisy. The success
rate of deciphering the message depends on loudness of the speaker, ear sensitivity of
the recipient, and his intelligence to guess it.
Similarly, in a wireless communication system, a transmitter which is actually an
electronic circuit with the aid of an antenna creates electromagnetic vibrations which
are sent through space. These waves propagate through a channel (free space,
buildings etc.). During this propagation various distortions are introduced into the
signal. The receiver receives this signal. To successfully interpret the message in it,
the receiver has to know about the nature of discrepancies introduced by the channel.
The process of evaluating the way a channel behaves to EM waves is called Channel
Estimation.
1.4 CHANNEL ESTIMATION
Channel estimation is required in wireless communication to counter the effects of
channel on the signal. A defining characteristic of the wireless channel are the
variations of the channel strength over time and over frequency. The variations can be
roughly divided into two types:
1. Large-scale fading, due to path loss of signal as a function of distance and
shadowing by large objects such as buildings and hills.

4
2. Small-scale fading, due to the constructive and destructive interference of the
multiple signal paths between the transmitter and receiver [25].
To counter these effects various techniques are adopted at the receiver side.
Mathematical models are used to predict the general behaviour of the channel in
concern. Some important channel models are:
1. Rayleigh channel: For this model to be used it is required that there be many
scatterers present, which means that Rayleigh fading can be a useful model in
heavily built-up city centers where there is no line of sight between the
transmitter and receiver and many buildings and other objects attenuate,
reflect, refract and diffract the signal.
2. Rician channel: Rician channel is a transmission channel that may have a
line-of-sight component and several scattered of multipath components.
3. Nakagami channel: The sum of multiple independent and identically
distributed Rayleigh-fading signals have Nakagami distributed signal
amplitude. This is particularly relevant to model interference from multiple
sources in a cellular system.
Some popular techniques used at the receiver to detect the symbols sent through
the channel are:
1. Detection by LSE(Least Square Error)
2. MMSE (Minimum Mean Square Error)
Channel effects on signal and ways to rectify it in a single transmitter and single
receiver systems, generally called SISO (single-input single-output) systems, has been
discussed so far.
One major drawback in any SISO system is that it is not resistant to the effect of
multipath fading. A very effective way know to come over multipath is the technique
of diversity. Diversity involves providing the receiver with multiple copies of the
same signal. It works well when each of these copies independently arrives at the
receiver, that is, each copy arrives via independent paths, experiencing independent
fades. As the probability that at-least one of these paths transmit the symbol with high
SNR (signal-to-noise ratio) is more, diversity is preferred. Diversity can be achieved
by:

5
1. Time diversity: Copies of the same signal can be repeatedly transmitted at
different times. Very suitable for fast fading channels, this technique uses lot
of resources in the system.
2. Frequency diversity: The copies of the signals are transmitted through
different frequencies at the same time. This method is suitable for frequency
selective channels.
3. Polarization Diversity: Polarization diversity implies transmitting the copies
with different polarization so that the copies will not interfere during
transmission.
4. Spatial diversity: Proving effective than the methods discussed above, this
method requires a unique arrangement of the communication system, it needs
multiple antennas at the receiver and/or transmitter side. This method leads us
to an entirely new domain with many advantages and rich opportunities.
MIMO (multiple-input multiple-output), MISO (multiple-input single-output)
and SIMO (single-input multiple-output) provides the receiver with multiple
copies of the same signal, arriving via different spatial paths, each undergoing
different levels of distortion and fading.
1.5 MIMO
MIMO technology has attracted attention in wireless communications. MIMO
systems have various advantages over SISO systems:
1. Significant increases in data transmission without additional bandwidth or
transmit power. It achieves this by higher spectral efficiency (more bits per
second per hertz of bandwidth) and link reliability or diversity (reduced
fading).
2. No need to alter the common air interface while upgrading.
3. By various coding techniques, depth and duration of fades are reduced.
These properties make MIMO a hot research area in the field of communication.
Though MIMO‟s diversity fights multipath well, it could be still more enhanced by
combining it with some special techniques: Orthogonal Frequency Division
Multiplexing (OFDM) and Wavelet Packet based Multi Carrier Modulation
(WPMCM). OFDM and WPMCM counter Inter-symbol interference (ISI) in mobile
communications.

6
1.6 OFDM AND WPMCM
OFDM is a multicarrier modulation technique in which the available channel is
split up into several sub-channels and symbols are transmitted using different
subcarriers. Here the signal processing is made digitally in the frequency domain by
using the – IFFT/FFT blocks. Guard time is added to reduce the effects caused by
multipath propagation. With a simple implementation spectral efficiency and
tolerance to ISI is achieved.
WPMCM is a novel multicarrier modulation technique and a promising
alternative to the well established OFDM. WPMCM is also a multicarrier modulation
technique in which signal processing is made digitally in the wavelet domain using –
IDWT/DWT blocks. The greatest motivation for pursuing WPMCM systems lies in
the freedom they provide to communication systems designers. Unlike the Fourier
bases which are static sines/cosines, WPMCM uses wavelets which offer flexibility
and adaptation that can be tailored to satisfy an engineering demand. [27]
1.7 ENHANCEMENTS AND CONTRIBUTION
In this project, the authors present a detailed report on the differences in the
efficiencies of MIMO based systems which uses OFDM and WPMCM. Also, a novel
technique in which the channel is equalized at the transmitter end has been proposed.

8
Chapter 2
MIMO
2.1 Introduction
The concept of MIMO is briefly explained in this chapter. A MIMO system
has two classes namely space-time coding and layered space-time coding. The layered
space-time coding is also known as spatial multiplexing. MIMO systems are generally
of the form MT×MR, where MT is the number of transmit antenna and MR is the
number of receive antenna. However, Alamouti scheme is the most basic model for a
MIMO system having a unit code-rate.
2.2 Multiple Antenna Systems
Multiple antenna systems [11] exploit the spatial dimension to increase the
capacity (thereby data rates), and also improve reliability through spatial diversity.
Capacity can be increased by using multiple transmit antenna to transmit independent
streams of unique data, that can be separated at receiver.
2.3 Advantages of multiple antenna systems
2.3.1 Array gain: Array gain is the average increase in the SNR at the receiver that
arises from coherent combining effect of Multiple Antennas. The signals arriving at
the receiver have different amplitudes and phases. The receiver can combine the
signals coherently to enhance the resultant signal. This can improve the reliability,
and hence the capacity of the system.
2.3.2 Spatial Diversity (SD) gain: Signal power will fluctuate in a wireless channel.
When signal power drops significantly the channel is said to be in fade. Diversity is
used to combat fading. Spatial diversity [15]-[17], [12]-[14] is the supply of multiple,
independent copies of a signal at the receiver. Thus, we exploit the rich scattering
nature of the channel, which implies that the probability of all copies undergoing deep
fades is very less. At least some of the copies will be available at receiver for
combining. This is achieved by making use of multiple antennas at the transmitter
(Transmit diversity) and/or at the receiver (Receive diversity).

9
2.3.3 Spatial multiplexing: This offers a linear increase in transmission rate (in the
number of transmit-receive antenna pair) for the same bandwidth without any
additional power expenditure. SM is discussed for a 2x2 system. This can however be
extended to any MIMO system. The bit stream to be transmitted is demultiplexed into
two half rate sub-streams, modulated and transmitted simultaneously from each
transmit antenna. The spatial signatures of these signals induced at the receiver
antenna are well separated. The receiver having the knowledge about the channel, can
differentiate between the co-channel signals and extract both, after this demodulation
gives the yields original sub stream which is combined to get back the original signal.
2.3.4 Interference reduction: Co-channel interference is due to frequency reuse in
wireless channels. When multiple antennas are used, the differentiation between the
spatial signatures of the desired signal and co-channel signals can be exploited to
reduce the interference.
Fig 2.1 MIMO SYSTEM
2.4 ST channels and signal models
2.4.1 SISO channel: Let h(τ,t) be the time varying channel response from the input of
the pulse shaping filter g(τ) at the transmitter, through the propagation channel p(τ,t)
to the output of receiver matched filter. We define h(τ,t) as the response at time t to
an impulse at time t- τ. The combination of impulse shaping filter and matched filter
makes h(τ,t) a narrowband channel. If a signal s(t) is transmitted, the received signal
y(t) is given by

10
∫ ( ) ( ) ( ) ( ) (2.1)
Where denotes the convolution operator and a casual channel impulse response of
duration τtotal has been assumed. The signals s(t) and y(t) are also complex envelopes
of a narrowband signal. [4]
2.4.2 SIMO channel: Consider a SIMO channel with MR receive antennas. The
SIMO channel can be decomposed into MR SISO channels. Denoting the impulse
response between the transmit antenna and the ith
(i= 1,2,…..,MR) receive antenna by
hi(τ,t) it is observed that the SIMO channel may be represented as an MR×1 vector,
h(τ,t), given by
( ) ( ) ( ) ( ) (2.2)
further, when a signal s(t) is launched from the transmit antenna, the signal received at
the ith
receive antenna, yi(t), is given by
( ) ( ) ( ) , i= 1,2,…..,M (2.3)
Denoting the signals received at the MR receive antennas by the MR×1 vector
( ) [ ( ) ( ) ( )] it is seen that the relation in above equation may
be concisely expressed as
( ) ( ) ( )
2.4.3 MISO channel: Consider a MISO system with MT transmit antennas.
Analogous to the SIMO channel it is considered to be comprising of MT SISO links.
Denoting the impulse response between the jth
(j=1,2,…..MT) transmit antenna and the
receive antenna by hj(τ,t), the MISO channel may be represented by a 1×MT vector
h(τ,t) given by
( ) [ ( ) ( ) ( )] (2.4)
assuming sj(t) is the signal transmitted from the jth
transmit antenna and y(t) is the
received signal, the input- output relation for the MISO channel is given by

11
( ) ∑ ( ) ( )
which may be alternatively be expressed in vector notation as
( ) ( ) ( ) (2.5)
Where ( ) ( ) ( ) ( ) is a MT ×1 vector.[4]
2.4.4 MIMO channel: Consider a MIMO system with MT transmit antennas and MR
receive antennas. Denoting the impulse response between the jth
(j=1,2,…. MT)
transmit antenna and the ith
(i=1,2,…..MR) receive antenna by hi,j (τ,t), the MIMO
channel is given by the MR× MT matrix H(τ,t) with,
( )
[
( ) ( )
( ) ( )
( )
( )
( ) ( ) ( )]
The vector [ ( ) ( ) ( )]T
is the spatio-temporal signature
or channel induced by the jth
transmit antenna across the receive antenna array.
Further, given that the signal ( ) is launched from the jth
transmit antenna, the signal
received at the ith
receive antenna, ( ), is given by
( ) ∑ ( ) ( ), i=1,2,.., (2.6)
The input-output relation for MIMO channel may be expressed in matrix
notation as
( ) ( ) ( ), (2.7)
where ( ) [ ( ) ( ) ( )] is an MT×1 vector and
( ) ( ) ( ) ( ) T
is a vector of dimension MR×1.[4]

13
Chapter 3
OFDM AND WPMCM
3.1. OFDM
3.1.1 INTRODUCTION
Multicarrier modulation divides the information data into many parallel sub-
channels of narrow bandwidth. The data rate of each sub-channel is much less than
the total data rate. Each sub-channel can be designed to have a bandwidth less than
the coherence bandwidth of the channel. It increases wireless capacity without
increasing bandwidth. Therefore, it can be assumed that each sub-channel experiences
flat fading and the demodulator can be implemented without an equalizer.
In a classical parallel-data system, the total signal frequency band is divided
into N non-overlapping frequency sub-channels. Each sub-channel is modulated with
a separate symbol, and then the N sub-channels are frequency multiplexed. It seems
good to avoid spectral overlap of channels to eliminate inter-channel interference.
However, this leads to inefficient use of the available spectrum. Hence, we go for
OFDM.
A multicarrier communication system with orthogonal sub-carriers is called
Orthogonal Frequency Division Multiplex (OFDM) system. The word “orthogonal”
indicates that there is a precise mathematical relationship between the frequencies of
the carriers in the system. The basic principle of OFDM is to split a high-data-rate
sequence into a number of low-rate sequences that are transmitted simultaneously
over a number of subcarriers. Because the symbol duration is increased for the low
rate parallel subcarriers, the relative amount of dispersion in time caused by multipath
delay spread is decreased. Inter-symbol interference (ISI) is eliminated almost
completely by introducing a guard interval at the start of each OFDM symbol. In the
guard interval, a OFDM symbol is cyclically extended to avoid Inter-carrier
interference (ICI). Thus, a highly frequency selective channel is transformed into a
large set of individual flat fading, non-frequency selective, narrowband channels. An
integrated circuit implementation of a discrete Fourier transform removes the need for
the entire bank of separate transmitters and receivers. The use of Fast Fourier

14
Transform (FFT) algorithms eliminates arrays of sinusoidal generators and coherent
demodulation required in parallel data systems and makes the implementation of the
technology cost effective. Therefore, both transmitter and receiver are implemented
using efficient FFT techniques that reduce the number of operations from N2
in DFT
to N log(N) in FFT[22] .
3.1.2 SYSTEM DESIGN
The modulation of the set of K OFDM subcarriers using an inverse fast
Fourier transform (IFFT) is equivalent to modulating each subcarrier individually
with a rectangular baseband pulse shaper. The receiver samples the transmitted
waveform to Obtain K samples on which a fast Fourier transform (FFT) is performed
then. The FFT modulation is equivalent to performing an integral and dump on each
subcarrier using a matched filter of the rectangular baseband waveform. OFDM
system plays prime role to transform frequency selective channel to narrow band flat
fading channel and generally OFDM make optimum use of frequency selective
channel and eliminate the need for high complexity rake receiver.
Fig 3.1: OFDM SYSTEM

15
OFDM maximizes spectral efficiency by overlapping subcarrier spectra while
maintaining orthogonality between subcarriers. This implies a spacing of unit Td
between each subcarrier frequency.
k=0,1,2,...,K-1 (3.1)
where is the subcarrier symbol duration. A basis of elementary signals to describe
the subcarrier symbols is defined as
( ) ( ) n= (3.2)
where,
( ) {
The elementary signals satisfy the orthogonality condition.
Fig 3.2: OFDM SIGNAL WITH OVER-LAPPED SPECTRA
The orthogonality between subcarriers can also be demonstrated in another
way. Each OFDM symbol contains subcarrier signals that are non-zero over a Td
interval. Hence, the spectrum of a OFDM signal is a convolution of a group of Dirac
pulses located at the subcarrier frequencies with the spectrum of a square pulse that is
one for a Td second period and zero otherwise. The amplitude spectrum of the square

16
pulse is equal to sinc(fTd), which has zeros for all frequencies f that are an integer
multiple of unit Td . The power spectrum of subcarriers is shown in figure where the
sinc spectra of individual subcarriers are overlapped. At the maximum of each
subcarrier spectrum, all other subcarrier spectra are zero. Because an OFDM receiver
essentially calculates the spectrum values at those points that correspond to the
maxima of individual subcarriers, it can demodulate each subcarrier free from any
interference from the rest subcarriers [24].
OFDM transmission system offers possibilities for alleviating many of the
problems encountered with single carrier systems. It has the advantage of spreading
out a frequency selective fade over many symbols. This effectively randomizes burst
errors caused by fading or impulse interference, so that instead of several adjacent
symbols being completely destroyed many symbols are only slightly distorted.
This allows successful reconstruction of majority of them even without
forward error correction. Because of dividing an entire signal bandwidth into many
narrow sub bands, the frequency response over individual sub bands is relatively flat
due to sub band are smaller than coherence bandwidth of the channel. Thus,
equalization is potentially simpler than in a single carrier system and even
equalization may be avoided altogether if differential encoding is implemented.
The orthogonality of sub-channels in OFDM can be maintained and individual
sub-channels can be completely separated by the FFT at the receiver when there are
no inter symbol interference (ISI) and inter-carrier interference (ICI) introduced by
the transmission channel distortion.
Since the spectra of an OFDM signal is not strictly band limited, linear
distortions such as multipath propagation causes each sub-channel to spread energy
into the adjacent channels and consequently cause ISI.
One way to prevent ISI is to create a cyclically extended guard interval, where
each OFDM symbol is preceded by a periodic extension of the signal itself. When the
guard interval is longer than the channel impulse response or multipath delay, the ISI
can be eliminated [22].
By using time and frequency diversity, OFDM provides a means to transmit
data in a frequency selective channel. However, it does not suppress fading itself.

17
Depending on their position in the frequency domain, individual sub-channels could
be affected by fading.
3.1.3 ADVANTAGES
 Favourable Properties: OFDM receiver does not need to constantly adapt
an equalizer as a single carrier system would. OFDM system shows much favourable
properties such as high spectral efficiency, robustness to channel fading, immunity to
impulse interference, capability of handling very strong echoes (multipath fading).
• Implementation Complexity: OFDM implementation complexity is
significantly lower than that of a single-carrier system with an equalizer.
• Enhanced Capacity: In relatively slow time-varying channels, it is possible
to enhance capacity significantly by adapting the data rate per SC according to the
signal-to-noise ratio (SNR) of that particular SC.
• Robust against Interference: OFDM is robust against narrowband
interference because such interference affects only a small percentage of the SCs.
• Broadcasting Applications: OFDM makes single-frequency networks
possible, which is especially attractive for broadcasting applications.
3.1.4 DRAWBACKS
 Large PAPR:
A major obstacle is that the OFDM signal exhibits a very high Peak
to Average Power Ratio (PAPR). Therefore, RF power amplifiers should be operated
in a very large linear region. Otherwise, the signal peaks get into non-linear region of
the power amplifier causing signal distortion. This signal distortion introduces
intermodulation among the subcarriers and out of band radiation. Thus, the power
amplifiers should be operated with large power back-offs. On the other hand, this
leads to very inefficient amplification and expensive transmitters. Thus, it is highly
desirable to reduce the PAPR.
 Frequency Errors: The other limitation of OFDM in many applications is
that it is very sensitive to frequency errors caused by frequency differences between
the local oscillators in the transmitter and the receiver.

18
 Carrier frequency offset: This causes a number of impairments including
attenuation and rotation of each of the subcarriers and inter-carrier interference (ICI)
between subcarriers. In the mobile radio environment, the relative movement between
transmitter and receiver causes Doppler frequency shifts; in addition, the carriers can
never be perfectly synchronized. These random frequency errors in OFDM system
distort orthogonality between subcarriers and thus inter-carrier interference (ICI)
occurs.
3.2 WPMCM
3.2.1 INTRODUCTION
Orthogonal frequency division multiplexing (OFDM) is a Multi Carrier
Modulation(MCM) scheme where the sub-carriers are orthogonal waves. The main
advantages of OFDM are robustness against multi-path fading, frequency selective
fading, narrowband interference, and efficient use of spectrum. Recently, it is proved
that MCM system optimization can be achieved by applying wavelet bases instead of
conventional Fourier bases. WPMCM systems have overall the same capabilities as
OFDM systems with some improved features.
The wavelet basis functions are localized in time (or space) and frequency,
and have different resolutions in these domains. Wavelet transforms are broadly
classified as continuous and discrete wavelet transforms. The continuous wavelet
transform (CWT) of a continuous signal x (t) is defined as the sum of all time of the
signal multiplied by scaled, shifted versions of the wavelet waveforms. Discrete
wavelet transform (DWT) analyzes the signal at different frequency bands with
different resolutions by decomposing the signal into an approximation containing
coarse and detailed information. DWT employs two sets of functions, known as
scaling and wavelet functions, which are associated with low pass and high pass
filters. The decomposition of the signal into different frequency bands is simply
obtained by successive high pass and low pass filtering of the time domain signal.
Wavelet packet transform (WPT) decomposes the high frequency bands which are
kept intact in the DWT. Hence it obtains richer resolution[18].
In WPMCM system, orthogonality is provided by orthogonal wavelet filters.
The real wavelet transform converts real numbers to real numbers, hence the
complexity of computation is reduced. Moreover, it‟s longer basis functions offers
higher degree of side lobe suppression and decreases the effects of narrowband

19
interference, ISI, and ICI. OFDM signals only overlap in the frequency domain while
the wavelet packet signals overlap in both, time and frequency. Due to time
overlapping, WPMCM systems don‟t use cyclic prefix or any kind of guard interval
that is commonly used in OFDM systems. This enhances the bandwidth efficiency
comparing to conventional OFDM systems[19].
Fig 3.3: SPECTRUM OF 8 WPMCM SUB-CARRIERS
(DAUBECHIES WAVELET, 20 COEFFICIENTS)
3.2.2 SYSTEM DESCRIPTION
The WPMCM system is same as the OFDM system except a few major
changes. Here, IDWT replaces IFFT block in transmitter side and DWT replaces FFT
in receiver side. First, the data stream is modulated and then is passed through a serial
to parallel converter. After this successive levels of IDWT are performed so that
finally we get a serial data stream. Here, we don‟t need to perform parallel-to-serial
conversion as is the case with OFDM because IDWT takes care of that. The final
serial data is then transmitted. In the channel, noise is added. In the receiver side,
DWT is performed successively, the same number of time as performed in transmitter
side. Then, parallel to serial conversion takes place. Finally, the serial data is passed
through a demodulator block. The diagram shown below will give a better picture.

20
Fig 3.4: WPMCM TRANSMITTER
Fig 3.5: WPMCM RECEIVER

21
The desirable properties of wavelet for WPMCM system would be:
 The wavelet bases must be time-limited.
 The bases must be well-confined in frequency.
 The wavelet packet bases and their duals must be perfectly orthogonal to one
another to enable perfect reconstruction.
 The bases must be orthogonal to one another in order to have unique
demodulation.
 The bases must enable the system to handle channel effects and other
distortions.
 The system must be easily realizable and must permit application of fast
algorithms.
Choosing the right wavelet:
In theory, any time and frequency limited function may be used. In practise,
the wavelet bases cannot be arbitrarily chosen and have to satisfy a number of
requirements. In general, the choices to make can be in regard to the system of
representation(continuous or discrete), properties of wavelets
desired(orthogonality/biorthogonality, regularity/smoothness, frequency selectivity),
the application in hand and the context of use. A framework that accounts for these
requirements must first be defined and the wavelet selected in a principled approach
through optimisation of the wavelet design parameters[19].
3.2.3 ADVANTAGES
 Real wavelet transform converts real number to real number, thus, reducing the
computational complexity.
 While OFDM signals overlap only in frequency domain, wavelet packet signals
overlap in both time and frequency domain.
 Due to time-overlapping, WPMCM systems don‟t use cyclic prefix or any kind of
guard interval.
 Better bandwidth efficiency compared to traditional OFDM systems.
 The iterative nature of Wavelet Transform allows for a configurable transform
size and hence a configurable number of carriers. This can be used to reconfigure
a transceiver according to a given communication protocol.
 By flexible time-frequency resolution, effect of noise and interference on the
signal can be minimised. Wavelet based systems are capable of avoiding known

22
channel disturbance at the transmitter, rather than waiting to cancel them at
receiver.
 Robustness against ISI and ICI[18,19].
3.2.4 DISADVANTAGES
 The ISI in OFDM is generated by overlapping of two successive symbols, while
in case of WPMCM, ISI is generated by overlapping of number of consecutive
symbols. Hence, WPMCM is very sensitive to even small timing difference
between transmitter and receiver.
 In an ideal scenario, filter bands used to generate wavelets have zero transition
bands B, i.e., difference between pass and stop band frequencies. However,
available wavelet families are derived from filter banks which have a wide
transition band and hence the resultant wavelet sub-carriers have a dispersed
spectrum with foot-prints spilling into neighbouring regions. This results in
difficulty in isolating the sub-carrier. This reduces the efficiency of the system.

23
Chapter 4
MIMO-OFDM AND MIMO-WPMCM

24
Chapter 4
MIMO-OFDM AND MIMO-WPMCM
4.1 MIMO-OFDM
4.1.1 INTRODUCTION
OFDM transforms a frequency selective channel into a large set of individual
frequency non-selective narrowband channels, which is suited for a MIMO structure
that requires a frequency non-selective characteristic at each channel when the
transmission rate is high enough to make the whole channel frequency selective.
Therefore, a MIMO system employing OFDM, denoted MIMO-OFDM, is able to
achieve high spectral efficiency. However, the adoption of multiple antenna elements
at the transmitter for spatial transmission results in a superposition of multiple
transmitted signals at the receiver weighted by their corresponding multipath channels
and makes the reception more difficult. This imposes a real challenge on how to
design a practical system that can offer a true spectral efficiency improvement. If the
channel is frequency selective, the received signals are distorted by ISI, which makes
the detection of transmitted signals difficult. OFDM has emerged as one of most
efficient ways to remove such ISI.
4.1.2 SYSTEM DESIGN
The system consists of N transmit antennas and M receive antennas. The
OFDM signal for each antenna is obtained by using inverse fast Fourier transform
(IFFT) and can be detected by fast Fourier transform (FFT).

25
Fig 4.1 : MIMO-OFDM BLOCK DIAGRAM
The received MIMO-OFDM symbol of the subcarrier and the OFDM
symbol of the receive antenna after FFT can be written as
∑ , i=1,2,...,M
where [n,m] is the transmitted data symbol on carrier and OFDM symbol,
[n,m] is the additive noise contribution at receive antenna for the corresponding
symbol in frequency domain and [n,m] is the channel coefficient in the frequency
domain between the transmit antenna and the receive antenna. The channel
impulse response is assumed to be static over one OFDM channel symbol duration
Tchannel=T+T‟, where T is the OFDM symbol duration and T‟ is the cyclic prefix
duration. This corresponds to a slowly varying channel where the coherence time is
longer than the channel symbol duration. This assumption prevents from experiencing
inter-carrier interference (ICI)[23].
The channel matrix H is an NxM matrix corresponding to the subcarrier
and OFDM symbol. The received data-symbols of all antennas can be expressed
in matrix form as:
R[n,m] = H[n,m] . A[n,m] + W[n,m], (4.1)
where, A[n,m] = ,

26
R[n,m] = [ and W[n,m] is the noise
added.
In MIMO systems the Alamouti scheme realizes full spatial diversity gain in
the absence of channel knowledge at the transmitter. This requires that the channel
remains constant over at least two consecutive symbol periods. In MIMO-OFDM the
coding is performed in the frequency rather than in time[23].
4.1.3 ADVANTAGES
 Less interference
 Diversity gain
 Increase data capacity
 Power efficiency
 Bandwidth gain
4.1.4 LIMITATIONS
 Antenna spacing must be appropriate depending on the type of channels
 Very complex transmitter and receiver
4.2 MIMO-WPMCM
MIMO techniques are based on the assumption of a flat fading channel. The
use of OCWDM modulation makes the flat fading hypothesis true for each OCWDM
sub-band, allowing exploitation of the MIMO approach for broadband wireless
application as well.
4.2.1 SYSTEM DESIGN
Source information bits are mapped on the symbols of the constellation
adopted for each OCWDM symbol. A serial to parallel converter for each transmit
antenna takes L of these symbols to form the input for OCWDM. The number of
transmit antennas is M. The receiver is equipped with N antennas. Each antenna
receives a different noisy superposition of fading version of the M transmitted
symbols. The channel response can be estimated at the receiver using a training
sequence embedded in each OCWDM symbol. V-BLAST algorithm is able to
detection the M transmitted signals according to the channel response. At the receiver,

27
the received symbols pass through OCWDM demodulator and then are detected by V-
BLAST processor[21].
Fig 4.2: MIMO-WPMCM TRANSMITTER
Fig 4.3: MIMO-WPMCM RECEIVER

28
4.2.2 ADVANTAGES
 The BER of this system can reduce more than 10 db compared to MIMO-OFDM
system.
 The system can be implemented by complex-wavelet filters, which are able to
lower computational complexity and increase flexibility.
 The number of decomposition levels does not impact on simulation results. When
decomposition level increases, complexity increases. So, we can choose lower
decomposition level to reduce computational complexity without affecting it‟s
performance.

29
Chapter 5
CHANNEL ESTIMATION TECHNIQUES FOR OFDM
AND MIMO-OFDM SYSTEM

30
Chapter 5
CHANNEL ESTIMATION TECHNIQUES FOR OFDM
AND MIMO-OFDM SYSTEM
A radio channel used for majority of the communication purposes is frequency
selective and time variant. For an OFDM system the channel transfer function is
different both in frequency and in time domain for different sub-carriers. The pilot
based approach is preferred to estimate the channel and equalize the channel effect to
receive the correct signal.[29] Two common pilot arrangements[30] for an OFDM
system investigated in the chapter are:
Fig 5.1: Block type pilot arrangement Fig 5.2: Comb type pilot arrangement
The first kind of pilot arrangement shown in Fig 2.1 is denoted as block-type
pilot arrangement. The pilot signal assigned to a particular OFDM block is sent
periodically in time-domain. This type of pilot arrangement is especially suitable for
slow-fading radio channels. Because the training block contains all pilots, channel
interpolation in frequency domain is not required. Therefore, this type of pilot
arrangement is relatively insensitive to frequency selectivity. The second kind of pilot
arrangement shown in Fig 2.2 is denoted as comb-type pilot arrangement. The pilot
arrangements are uniformly distributed within each OFDM block. The comb-type
pilot arrangement system provides better resistance to fast-fading channels. Since
only some sub-carriers contain the pilot signal, the channel response of non-pilot sub-
carriers will be estimated by interpolating neighbouring pilot sub-channels. Thus the
comb-type pilot arrangement is sensitive to frequency selectivity when comparing to

31
the block-type pilot arrangement system. A combination of block and comb type pilot
arrangement is used to counteract the frequency selectivity of a channel for different
periods of time.
Results of the channel estimation for OFDM system‟s is not directly
applicable to MIMO-OFDM system. In MIMO systems, the number of channel paths
increases by Nt X Nr-folds, where Nt and Nr is the number of transmit and receive
antenna, respectively. This significantly increases the number of unknowns to be
solved. Conventional estimation techniques for single input single output (SISO)
systems have to be modified to be applicable in MIMO systems
5.1 CHANNEL ESTIMATION BASED ON BLOCK-TYPE
ARRANGEMENT
In block-type pilot based channel estimation, OFDM channel estimation
symbols are transmitted periodically, in which all sub-carriers are used as pilots. If the
channel is perfectly constant during the block, there will be no channel estimation
error since the pilots are sent at all carriers. The estimation can then be performed by
using either LSE or MMSE.[31] If Inter symbol interference(ISI) is eliminated by the
guard interval, we write in matrix notation:
Y = XFh + V
= XH + V (5.1)
where Y is the received signal vector, X is a diagonal matrix of the transmitted
signal, H is the channel frequency response vector, F is the Fourier transform
operator, and V is the noise vector in the frequency domain. We consider each OFDM
block to have N sub-carriers and thus N pilot symbols for each OFDM block. Re-
writing the symbols in matrix notation we get:
X= diag {X(0),X(1),……….,X(N-1)}
Y= [Y(0),Y(1),…………..Y(N-1)]T
V= [V(0),V(1),…………..V(N-1)]T
H= [H(0),H(1),…………..H(N-1)]T
= DFT N {h}

32
F= WN
00
……………….. ……..WN
0(N-1)
WN
10
……………………….WN
1(N-1)
………………………………………
WN
(N-1)0
………………..WN
(N-1)(N-1)
WN
nk
= ( )
5.1.1 MINIMUM MEAN SQUARE ERROR (MMSE) ESTIMATION
MSE(Mean Square Error) is expressed as
J(e) = E[(H-Ĥ)2
]
= E[(H-Ĥ)H
(H-Ĥ)] (5.2)
Where Ĥ is the channel estimate(with MMSE) and X H
denotes the Hermitian
of the matrix X. Invoking the well-known orthogonality principle in order to
minimize the mean square error vector e =H- Ĥ has to be set orthogonal by the
MMSE equalizer to the estimators input vector Y.
E[((H-Ĥ)YH
)]=0
⇒ E[HYH
] – ME[YYH
]=0
⇒ E[FhYH
] – ME[YYH
]=0
Considering the time domain channel vector h to be Gaussian and to be
uncorrelated with the channel noise v we get,
RhY = E[hY H
]
= E[h(XFh+v) H
]
= RhhF H
X H
(as E[hv H
]=0) (5.3)
Now,

33
F(RhY)= Rhh X H
(as FFH
=I)
RYY = E[YY H
]
= E[(XFh+v) (XFh+v) H
]
= XFRhhF H
X H
+ σ2
IV (as σ2
is the channel noise) (5.4)
Therefore,
F(RhY) = M(RYY) where M=F RhY RYY
-1
and Ĥ= F RhY RYY
-1
Y
The time domain MMSE estimate of h is given by
ĥ= RhY RYY
-1
Y (5.5)
5.1.2 LEAST SQUARE ERROR (LSE) ESTIMATION
We have to minimize
J = (Y-XH) H
(Y-XH)
= (Y H
-H H
X H
) (Y-XH)
= Y H
Y-Y H
XH-H H
X H
Y-H H
X H
XH (5.6)
For minimization of J we have to differentiate J with respect to H
=0
Ĥ= X-1
Y (5.7)
The time domain LS estimate of h is given by
h= F H
X-1
Y (5.8)
5.2 CHANNEL ESTIMATION BASED ON COMB-TYPE
ARRANGEMENT
In comb-type based channel estimation, the Np pilot signals are uniformly
inserted into data X(k) according to following equation:
X(k) = X(mL+l)

34
={
( )
(5.9)
where L=Np/N
We define {Hp(k) k=0,1,….,Np} as the frequency response of the channel at
pilot sub-carriers. The estimate of the channel at pilot sub-carriers based on LS
estimation
is given by:
Ĥ (5.10)
Yp(k) and Xp(k) are output and input at the kth
pilot sub-carrier respectively.
Since LS estimate is susceptible to noise and ICI, MMSE is proposed while
compromising complexity as it includes the matrix inversion in each iteration.
5.3 CHANNEL ESTIMATION OF MIMO-OFDM SYSTEM
The results of a SISO system cannot be directly applied to that of a MIMO
system due to the existence of NtXNr paths between the transmitter and the
receiver.[28] Consider the following case in which the received signal at the jth
antenna for the kth
subcarrier (in MIMO-OFDM with OSTBC( transmission and 2 X 2
antenna configuration) in expanded form can be defined as:
[n] =
( )
[n] . [n] +
( )
[n] . [n] + [n] k=0 to N-1 (5.11)
The above equation is undermined as there are two unknowns namely
( )
[n] and
( )
[n]. Thus it can be concluded from equation that for Nt by Nr antenna
configuration with N subcarriers, to estimate the channels between antenna j and
transmit antenna i =1, 2 …Nt the number of channel elements or subcarrier has to be
estimated are Nt×N whereas the number of equation is N. The complexity of the
estimation problem increases significantly since the matrix size is increased by M –
folds. There are two ways to solve
 Transmitting M OFDM blocks which is practically not possible
 Reducing the no. of unknown elements by using a different
representation o of the signal called the transform domain estimator

35
TRANSFORM DOMAIN ESTIMATOR:
The commonly used transform domain estimator is the Fourier transform so as
to reduce the complexity of the N equations and NtXN variables. It is as follows:
H(j,i)
= F . h(j.i)
(5.12)
where F is given by
F is called matrix Fourier transform and of size (N×L) and h(j,i) is the (L×1) channel
impulse vector. To extend the matrix Fourier transform to multiple channels following
matrix is used
The transformation equation now looks like
[n] = . + (5.13)
= . ϕ . hj
+

36
= W . hj
+ (5.14)
LS solution for the channel can be written as follows
ĥj=(W H
. W)-1
. W H
.Y (5.15)
QR CHANNEL ESTIMATION
Direct computation of the LS solution involves a matrix inversion, which is
highly complex and undesirable for hardware implementation. Matrix decomposition-
based least square schemes such as Cholesky, lower upper (LU), SVD, and QR
decomposition (QRD) avoid explicit inversions and are more robust and well suited
for hardware implementation.
The QR decomposition is preferable because of the clever implementation of
the scheme in a highly parallel systolic array architecture QR decomposition is an
orthogonal matrix triangularization technique that reduces a full rank matrix into a
simpler form. Consider a matrix W of size MXN then the QR decomposition is
defined as
WMXN = QMXM . * +MXN (5.16)
where Q is a (M × M) unitary matrix, R is a (N × N) upper triangular matrix and 0 is a
null matrix. A unitary matrix is one that satisfies the following condition
I = Q H
.Q (5.17)
To apply QRD to the problem of channel estimation we recall the MIMO-
OFDM system model
Y= W.h + V (5.18)
To avoid the matrix inversion we can directly apply QR decomposition to the
error equation and estimate the channels by following steps:
1. Making the LS error function
ε= Y-W . ĥ and if ε=0 then Y=W . ĥ
2. Decompose W into Hermitian matrix Q and upper triangular
matrix R

37
Y= W. ĥ = QMXM . * +MXN . ĥ (5.19)
3. Second stage is multiplying Hermitian of Q to both side
* +MXN . ĥ . = . Y (5.20)
4. Solve for the channel matrix using back substitution

38
Chapter 6
A NOVEL PRE-DISTORTION TYPE ADAPTIVE
CHANNEL EQUALISATION TECHNIQUE

39
Chapter 6
A NOVEL PRE-DISTORTION TYPE ADAPTIVE
CHANNEL EQUALISATION TECHNIQUE
Practical channels lead to distortions, such as Inter-Symbol Interference (ISI)
[5][8] and require special techniques to prevent the performance of the
communication system from degrading. Channel Equalisation is one such extensively
used technique [4][6]. The aim of equalisation is to „undo‟ the effect of the channel‟s
non-ideal behaviour. The ideal channel equaliser is one which is the exact inverse of
the impulse response of the channel. Since in practice, the channel response is not
known beforehand, one has to take recourse to „approximate‟ methods of channel
equalisation. Most equalisers periodically update their parameters based on the
channel conditions through the use of „training sequences‟ sent by the transmitter
(Adaptive Equalisation) [2][3]. This helps in estimating the current channel
conditions. The pre-distortion type adaptive channel equalisation technique is based
on sending the „training sequences‟ from receiver end to transmitter end so that the
process of Adaptive Equalisation can be held at the transmitter end itself by pre-
distorting the data-signal before transmitting it to the receiver.
The technique will work efficiently only if the following constrains are met:
(a) The channel should be slow-fading
(b) The channel is said to be mirror-channel, about which we will discuss in forth-
coming sub-topic
6.1SYSTEM MODEL
A. Slow-fading ‘mirror’ Channel
In „mirror‟ channels, the channel response remains the same even after
swapping transmitter and receiver. In other words we can say, the path loss and all
other distortions including multi-path distortion observed in both the directions
(TX=>RX and RX=>TX) is the same, i.e., in Fig.4.1., G=H. In a slow-fading channel,
the channel response is assumed to be constant for a given coherence time (T0) [1][7].

40
Fig 6.1: CHANNEL PATHS
B. Equalization of Channel
An adaptation filter, f, is adapting to the channel impulse response
(considering the channel as h) at the transmitter end. f gives an approximate estimate
of channel impulse response.
Fig 6.2: ADAPTATION FILTER F
In Fig.6.2, is transmitted pilot symbols and H is channel response observed
in frequency domain. F is the adaptation filter. Once f gets adapted to h, inverse filter
is designed whose frequency response is . Now all the data-symbols which
are transmitted from transmitter are passed through the filter and then transmitted
to the receiver end through the channel. By this, the pre-distortion applied on all the
symbols by the filter nullifies the distortion seen when the symbol traverse
through the channel.

41
Fig6.3: SYSTEM MODEL AT TRANSMITTER SIDE
In Fig.6.3, X is the data-symbol to be transmitted, H is the channel frequency
response and Y is the received symbol. Receiver is installed with a minimum standard
deviation detector. The transmission of symbols is explained in Fig. 4.4.
Fig 6.4 : SYMBOL TRANSMISSION DIAGRAM
6.2 MSD ALGORITHM
Minimum Standard Deviation (MSD) Algorithm is based on adaptation done
by the help of the error observed. In each step, the weights are adapted to a desired
value for which error is minimized, in turn minimizing the standard deviation of the

42
error. The step size decides the rate of convergence of the algorithm. It is chosen as
a value between 0 and 1. For a value of nearer to 0, the algorithm will converge
slowly but accurately and for the value of near to 1, the algorithm converge at a
faster rate but with error. Hence is taken to be an optimum value between 0 and 1.
( ) ( ) ( ) ( ) (6.1)
Where,
( ) is the weight or filter coefficient of the adaptive filter in iteration,
is the step size,
( ) is the error observed in iteration,
x is the actual value of data.
6.3 THEORY
Many algorithms are available for the process of adaptation. Here MSD
algorithm is used.
(6.2)
(6.3)
( ) ( ) (6.4)
Here, (6.2) calculates the error in received symbol, (6.3) adapts the filter f and
(6.4) estimates the MSD for every transmission. By this process of adaptation, MSD
(Minimum Standard Deviation) of f is reduced, and f moves towards h with every
iteration (for every pilot symbol received f is adapted and updated newly). As slow
fading channel is considered, coherence time (Tch) is considerably large. A
transmission of 1kb for every Tch is considered. In this transmission of 1024bits, first
N bits are selected as pilot bits (Some data bits which are known on both receiver
side). These N bits are used for adapting f to h. Then the rest 1024-N bits are sent as
data after passing through the equalisation filter f-1
. Since the channel is assumed to
be symmetric or „mirror‟, the path loss and channel impulse response for TX-RX path
as well as RX-TX paths are considered to be the same. Hence, initial N pilot bits are

43
transmitted from receiver end to transmitter end. Xp after entering channel becomes
R=H Xp on reception. The error in R is used to adapt f to h. Then the equalisation
filter is designed using formula,
( ) (( ( ( )) ) (6.5)
Now the remaining 1024-N are the data bits which is transmitted from
transmitter end to receiver end after passing through the equalisation filter. By this
process, the receiver complexity is reduced to a very great extend, since a minimum
distant detector at the receiver end is sufficient to detect the message bits at the
receiver end with a very low BER.

44
Chapter 7
SIMULATION AND RESULTS

45
Chapter 7
SIMULATION AND RESULTS
7.1 CONVERGENCE OF MSD FOR THE PROPOSED
TECHNIQUE
The simulation of the proposed technique for SISO system is done and a graph
is plotted between the number of iterations, i.e, the number of bits transmitted from
the receiver to the transmitter vs MSD.
Fig 7.1 CONVERGENCE OF MSD ALGORITHM
It is observed that there is a steep decrease in MSD from 0-50 iterations after
which an oscillatory behaviour is seen. Thus, we conclude that maximum of 30-50
iterations is sufficient for the convergence of MSD algorithm in the proposed
technique.

46
7.2 BER vs SNR (4-QAM) FOR THE PROPOSED TECHNIQUE
The simulation of the proposed technique is done with 4-QAM modulation
scheme. A BER vs SNR graph is plotted for the proposed technique of channel
equalisation at the transmitter and a normal SISO system with AWGN noise added to
the transmitted signal.
Fig 7.2 SNR VS BER (4-QAM) FOR PROPOSED TECHNIQUE
It is observed that the effect of pre-distorting the input at the transmitter
almost nullifies the distortive effect of the channel and the received signal shows
similar characteristics as in the case where there is no channel distortion except
AWGN noise added to the transmitted signal.

47
7.3 COMPARISON OF BER vs SNR (2-PAM AND 4-QAM) FOR
THE PROPOSED TECHNIQUE
The simulation of the proposed technique is done for 2-PAM and 4-QAM
modulation schemes and their respective BER vs SNR graphs are plotted.
Fig 7.3 SNR VS BER(2-PAM, 4-QAM) FOR PROPOSED TECHNIQUE
As observed in case of the existing systems, the proposed technique shows an
equivalent BER vs SNR curve for the effect of AWGN noise in 2-PAM and 4-QAM
modulation schemes.

48
7.4 COMPARISION OF BER vs SNR (2-PSK) FOR A MIMO
SYSTEM WITH AND WITHOUT THE PROPOSED TECHNIQUE
The simulation of the proposed technique is done for 2-PSK MIMO system
and BER vs SNR graph is plotted along with that of an existing MIMO system.
Fig 7.4 COMPARISON OF SNR VS BER OF PROPOSED TECHNIQUE FOR MIMO SYSTEM
It is observed that pre-distortion at the transmitter provides considerable BER
vs SNR improvement for a MIMO system(BER of 10-3
is achieved at 8dB for an
ordinary MIMO system with channel equalisation at the receiver while it is achieved
at 7 dB for the MIMO system incorporated with our proposed technique)

49
7.5 COMPARISION OF BER vs SNR(2-PSK) FOR A MIMO-OFDM
SYSTEM WITH AND WITHOUT THE PROPOSED TECHNIQUE
The simulation of the proposed technique is done for 2-PSK, MIMO-OFDM
system and BER vs SNR graph is plotted along with that of an existing MIMO-
OFDM system.
Fig 7.5 COMPARISON OF MIMO-OFDM WITH AND WITHOUT PROPOSED MODEL
It is observed that BER of 10-3
is achieved at 10 dB for the proposed
technique, whereas it is achieved at 18 dB for a normal MIMO-OFDM system. Thus,
pre-distortion at the transmitter provides 8 dB SNR improvement for a MIMO-OFDM
system.

50
7.6 COMPARISON OF BER vs SNR (2-PSK) FOR AN OFDM AND
WPMCM SYSTEM
The simulation of an OFDM and WPMCM (Haar Wavelet) system is done for
1024 bits and their respective BER vs SNR curves are plotted and compared in a
single graph.
Fig 7.6 COMPARISON OF OFDM AND WPMCM SYSTEM
It is observed that BER of 10-3
is achieved at around 8 dB for WPMCM
system, whereas it is achieved at 18 dB for an OFDM system. Thus, WPMCM system
has more than twice SNR improvement.

51
7.7 COMPARISION OF BER vs SNR(2-PSK) FOR A WPMCM
SYSTEM FOR VARIOUS CHANNEL MODELS
The simulation of a WPMCM(Haar Wavelet) system is done for 1024 bits for
Rayleigh and Rician(various k-factors) fading channels. Their respective BER vs
SNR curves are plotted and compared.
Fig 7.7 WPMCM SYSTEM WITH DIFFERENT CHANNELS
It is observed that for a Rician Fading channel, as k-factor increases, there is
an improvement in BER performance. It can also be seen that Rician Fading channel
shows better BER performance compared to a Rayleigh Fading channel (BER of 10-2
at 8 dB for Rayleigh Fading channel while it is achieved for Rician Fading channel at
maximum SNR of 6 dB)

53
Chapter 8
CONCLUSION
Pre-distorting the data symbols at the transmitter end using an adaptive
equalisation filter is an effective technique proposed for communication systems. This
model ensures considerable reduction in receiver complexity. The MATLAB
simulation results show considerable improvement in BER performance for a MIMO-
OFDM system (BER of 10-3
is achieved at a SNR value of 10 dB). The receiver
detects the incoming symbols with basic minimum distance algorithm, as the channel
equalisation is carried out at transmitter end itself thereby reducing the receiver
complexity. This technique is well suited for multi-receiver communication system in
a slow-fading, „mirror‟ channel environment.
WPMCM is a relatively young and promising communication concept which
shares most of characteristics of an orthogonal multi carrier system and in addition
offers the advantage of flexibility and adaptability. These properties can make it a
suitable technology for the design and development of future wireless communication
systems. The simulation results comparing an OFDM and a WPMCM (Using Haar
Wavelet) system also testify the enormous improvement in BER performance of a
WPMCM system ( BER of 10-3
achieved at SNR of 8dB and 18dB for a WPMCM
and an OFDM system respectively).
8.1. SCOPE FOR FUTURE WORK
The pre-distortion type adaptive channel equalization technique considered
only Rayleigh fading channel and used MSD algorithm for adaptation. The
performance of this technique can be evaluated for different channel models and for
different convergence algorithms used for adaptations. Adopting a better converging
algorithm for adaptation reduces the number of pilot bits per coherence time, which
gives a considerable increase in data-rate. The technique when extended to MIMO
and MIMO-OFDM systems considered only spatial multiplexing. The performance of
this technique in MIMO and MIMO-OFDM systems can be evaluated for spatial-
diversity, time-diversity as well. Most channels are „mirror‟ type, whereas some
channels are not. Finding the correlation between the channel path and its inverse path

54
will make the model to mature to be suited for any slow fading environment. The
simulation results in WPMCM were carried out only for Haar wavelets which can be
extended to other flexible wavelets (db-4,db-8 etc). The effects of radio front end
impairments like carrier frequency offset and phase noise on a WPMCM system can
also be extensively studied.

56
Chapter 9
PUBLICATIONS
[1]Akash Mohan, Amrita Mishra, Karthik M, Padma N, Prashanth G, Deepa R, “A
Novel Pre-Distortion type Adaptive Channel Equalisation Technique for SISO”,
International Conference on Emerging Trends in Electrical and Computer
Technology (ICETECT’11), ISBN: 978-1-4244-7925-2, pp 1047-1050, March 2011.

58
Chapter 10
REFERENCES
[1] John G. Proakis, Masoud Salehi, “Communication Systems Engineering” Pearson
Education International, 2nd
Edition, 2002.
[2] Mari Kobayashi, Joseph Boutros, and Giuseppe Caire,”Successive Interference
Cancellation with SISO Decoding and EM Channel Estimation”, IEEE Journal on
selected areas in Communications, Vol. 19, No. 8, August 2001.
[3]Ramjee Y. Lee, and W.R. Wu, “Adaptive Channel aided Decision feedback
Equalisation for SISO and MIMO systems”, IEEE Proc.- Commun., Vol. 153, No.5,
October 2006.
[4] Arogyaswami Paulraj, Rohit Nabar, Dhananjay Gore, “Introduction to Space-Time
Wireless Communication”, Cambridge University Press, 1st
Edition, 2003.
[5] Dieter Schanfhuber, Gerald Matz, and Franz Hlawatsch, “Adaptive Prediction of
Time-Varying Channel For Coded OFDM Systems”, Proc. IEEE ICASSP-2002,
Orlando (FL), May 2002, pp. 2549-2552
[6] Theodore S. Rappaport, “Wireless Communications”, Prentice Hall, 1996
[7] Simon Haykin, “Communication Systems”, John Wiley and Sons, Inc., 4th
Edition,
2008.
[8] Jungsub Byun, Nirmal Pratheep Natarajan, “Adaptive Pilot Utilization for OFDM
channel Estimation in a Time Varying Channel”, Wireless and Microwave
Technology Conference, Clearwater (FL), August 2009, pp.1-5.
[9] G.J.Foshini and M.J Gans, “On the limits of wireless communications in a Fading
Environment when using Multiple Antennas”, Wireless Personal Communications,
Ver.6, no. 3,pp.311-355, March 1998.
[10] E. Telatar, “Capacity of the multi antenna Gaussian channels,” Eur. Trans.
Telecommun., Vol.10, No. 6, pp. 585-595, Nov/ Dec. 1999

59
[11] D. Gesbert et al., “From Theory to Practise: An Overview of MIMO Space-Time
Coded Wireless Systems”, IEEE Journal on Selected Areas in Communication, Vol.
21, No. 3, pp 281-302, April 2003.
[12] Schwartz, Bennett and Stein, Communication Systems and Techniques, McGraw
Hill, 1966, Chapter 10-11
[13] J.H.Winters, J.Salz, R.D.Gitlin, “The Impact of Antenna Diversity on the
Capacity of Wireless Communication Systems”, IEEE Transactions on
Communications, Vol.42, No.2, pp.1740-1751, April 1994
[14] T.Eng, N.Kong, “Comparison of Diversity Combining Techniques for Rayleigh
Fading Channel”, IEEE Transactions on Communications, Vol.44, No.9, pp. 1117-
1129, September 1996
[15] Mohinder Jankiraman, Space Time Codes and MIMO systems, Archtech House,
2004
[16] Hamid Jafarkhani, Space Time Coding – Theory and Practice, Cambridge
University Press, 2005
[17] Branka Vucetic, Jinhong Yuan, Space Time Coding, John Wiley and Sons Ltd.,
2003
[18] Haleh Hosseini, Norsheila Fisal, Sharifah K. Syed-Yusof, “Wavelet Packet
based Multicarrier Modulation for Cognitive UWB Systems”, Signal Processing – An
International Journal (SPIJ), Volume (4): Issue (2)
[19] M.K.Lakshmanan, I.Budiarjo, H.Nikookar, “Cognitive Radio Systems”, ISBN:
978-953-307-021-6, InTech, November 2009.
[20] You Wu1, Kuixi Yin1, Hua Zhao1 Xuejun, “MIMO-OCWDM system using V-
BLAST Architecture.”, 1st International Conference on Information Science and
Engineering (ICISE2009).
[21] Muhammad Yasir, M. J. Mughal, N.D. Gohar, S. A. Moiz, “Performance
Comparison of Wavelet based OFDM (WOFDM) V-BLAST MIMO System with

60
different Detection Algorithms”, 4th
International Conference On Emerging
Technologies, ICET 2008.
[22] Amrita Mishra, Anand S, Ashmita G, Padma N, Pavitra Pratim Padhi and
Jayakumar M, “Non-linear distortion analysis and computation of BER in BPSK
OFDM systems”, 2nd
National Conference On Recent Trends in Communication,
Computation and Signal Processing, 2010.
[23] Helka Määttänen, “MIMO-OFDM”, S-72.333 Postgraduate Course in Radio
Communications
[24] www.wikipedia.org
[25] D. Tse and P. Viswanath, ”Fundamentals of Wireless Communication” ,
Cambridge University Press, 2005.
[26] Joshua S. Gans, Stephen P. King and Julian Wright, “Wireless
Communications”, Handbook of Telecommunications Economics, Volume 2.
[27] D.Karamehmedović, M.K.Lakshmanan, H.Nikookar, “Performance Evaluation
of WPMCM with Carrier Frequency Offset and Phase Noise”, Journal Of
Communications, Vol. 4, No. 7, August 2009.
[28] Reza Abdolee, “Performance of MIMO space-time coded system and Training
based channel estimation for MIMO-OFDM system” ,Thesis, Nov-2006
[29] J.J. van de Beek, O. Edfors, M. Sandell, S.K. Wilson, and P.O. Borjesson, “On
channel estimation in OFDM system,” IEEE Vehicular Technology Conference 1995,
vol. 2, pp. 815-819, Sept. 1995.
[30] S.Hara and R.Prasad, Multicarrier techniques for 4G mobile communications,
Artech House, 2003

61
[31] Sarada Prasanna Dash, Bikash Kumar Dora, “Channel estimation in multicarrier
communication systems”, Thesis, May-2009

Btech report

Recommended

Recommended

More Related Content

What's hot

What's hot (20)

Viewers also liked

Viewers also liked (20)

Similar to Btech report

Similar to Btech report (20)

Btech report