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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.


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

i


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 4.1 MIMO-OFDM

23 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 5.1.1

31

MINIMUM MEAN SQUARE ERROR(MMSE) ESTIMATION

5.1.2

32

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 ii


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 MIMOOFDM 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 8. CONCLUSION

51 52

8.1 SCOPE FOR FUTURE WORK

53

9. PUBLICATION

55

10. REFERENCES

57

iii


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.

iv


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

v


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

Figure 7.4:

47

Comparison of BER vs SNR (2-PSK) for a MIMO system with and without the proposed technique

Figure 7.5:

48

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

Figure 7.7:

50

Comparison of BER vs SNR(2-PSK) for a WPMC system for various channel models

vi

51


Chapter 1 INTRODUCTION 1


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. Electromagnetic 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

2


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. 3


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: 4


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 MIMOâ€&#x;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.

5


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.

6


Chapter 2 MIMO 7


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 MTĂ—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).

8


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

9


(

∫ Where

) (

)

(

)

( )

(2.1)

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

10


∑ (

()

)

()

which may be alternatively be expressed in vector notation as ( ) Where ( )

( ) ( )

( )

(

)

( )

(2.5)

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 ( ) where ( )

(

) ( )

( ),

(2.7)

[ ( ) ( )

( ) ( )

( )

( )] T

is

an

MT×1

is a vector of dimension MR×1.[4]

11

vector

and


Chapter 3 OFDM AND WPMCM

12


Chapter 3 OFDM AND WPMCM 3.1. OFDM 3.1.1 INTRODUCTION Multicarrier modulation divides the information data into many parallel subchannels 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 13


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

14


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 where

(3.1)

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 15


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. 16


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. 17




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, itâ€&#x;s longer basis functions offers higher degree of side lobe suppression and decreases the effects of narrowband 18


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 donâ€&#x;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 donâ€&#x;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.

19


Fig 3.4: WPMCM TRANSMITTER

Fig 3.5: WPMCM RECEIVER

20


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 21


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.

22


Chapter 4 MIMO-OFDM AND MIMO-WPMCM

23


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).

24


Fig 4.1 : MIMO-OFDM BLOCK DIAGRAM

The received MIMO-OFDM symbol of the symbol of the

subcarrier and the

receive antenna after FFT can be written as ∑

where

OFDM

,

[n,m] is the transmitted data symbol on

[n,m] is the additive noise contribution at symbol in frequency domain and domain between the

carrier and

i=1,2,...,M OFDM symbol,

receive antenna for the corresponding

[n,m] is the channel coefficient in the frequency

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 and

subcarrier

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] =

, 25


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,

26


the received symbols pass through OCWDM demodulator and then are detected by VBLAST processor[21].

Fig 4.2: MIMO-WPMCM TRANSMITTER

Fig 4.3: MIMO-WPMCM RECEIVER

27


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.

28


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


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 subcarriers will be estimated by interpolating neighbouring pilot sub-channels. Thus the comb-type pilot arrangement is sensitive to frequency selectivity when comparing to 30


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. Rewriting 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} 31


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[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)

Now,

32

(5.3)


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-1Y The time domain MMSE estimate of h is given by ĥ= RhY RYY-1Y

(5.5)

5.1.2 LEAST SQUARE ERROR (LSE) ESTIMATION We have to minimize J = (Y-XH) H (Y-XH) = (Y H -H HX 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-1Y

(5.7)

The time domain LS estimate of h is given by h= F H X-1Y

5.2

CHANNEL

(5.8)

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) 33


( )

={

(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 34


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 +

35


= 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 decompositionbased 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 MIMOOFDM 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 36


Y= W. 張 = QMXM . * +MXN . 張

(5.19)

3. Second stage is multiplying Hermitian of Q to both side * +MXN . 張 . =

.Y

4. Solve for the channel matrix using back substitution

37

(5.20)


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

38


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 predistorting 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 forthcoming 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].

39


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. 40


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 41


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 faster rate but with error. Hence ( )

( )

( )

near to 1, the algorithm converge at a

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 „mirrorâ€&#x;, 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 42


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.

43


Chapter 7 SIMULATION AND RESULTS 44


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.

45


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.

46


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.

47


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)

48


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 MIMOOFDM 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.

49


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.

50


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)

51


Chapter 8 CONCLUSION 52


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 MIMOOFDM 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 spatialdiversity, 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 53


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.

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Chapter 9 PUBLICATIONS

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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.

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Chapter 10 REFERENCES

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