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

TO OUR BELOVED PARENTS

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

3.2.1 INTRODUCTION 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

4.1.1 INTRODUCTION 24

4.1.2 SYSTEM DESIGN 24

4.1.3 ADVANTAGES 26

4.1.4 LIMITATIONS 26

4.2 MIMO-WPMCM 26

4.2.1 SYSTEM DESIGN 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

1

Chapter 1

INTRODUCTION

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.

7

Chapter 2

MIMO

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]

12

Chapter 3

OFDM AND WPMCM

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= WN00

……………….. ……..WN0(N-1)

WN10

……………………….WN1(N-1)

………………………………………

WN(N-1)0

………………..WN(N-1)(N-1)

WNnk

=

(

)

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[YY

H]=0

⇒ E[FhYH] – ME[YY

H]=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 σ

2 is the channel noise) (5.4)

Therefore,

F(RhY) = M(RYY) where M=F RhY RYY-1 and Ĥ= F RhY RYY

-1Y

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

6.1 SYSTEM 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)

52

Chapter 8

CONCLUSION

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.

55

Chapter 9

PUBLICATIONS

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.

57

Chapter 10

REFERENCES

58

Chapter 10

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