AN IMPROVED INTERPOLATION METHOD FOR CHANNEL ESTIMATION IN AN ORTHOGONAL FREQUENCY DIVISION MULTIPLEXING (OFDM) SYSTEM USING PILOT SIGNALS

AN IMPROVED INTERPOLATION METHOD FOR CHANNEL ESTIMATION IN
AN ORTHOGONAL FREQUENCY DIVISION MULTIPLEXING (OFDM)
SYSTEM USING PILOT SIGNALS

AHMED NOORI HUMMADI

THESIS SUBMITTED IN FULFILMENT FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY

FACULTY OF ENGINEERING AND BUILT ENVIRONMENT
UNIVERSITI KEBANGSAAN MALAYSIA
BANGI

2011


KAEDAH INTERPOLASI DIPERBAIKI BAGI PENGANGGARAN SALURAN
DALAM SISTEM PEMULTIPLEKSAN PEMBAHAGIAN FREKUENSI
ORTOGON MENGGUNAKAN ISYARAT PEMANDU

AHMED NOORI HUMMADI

TESIS YANG DIKEMUKAKAN UNTUK MEMPEROLEH IJAZAH
DOKTOR FALSAFAH

FAKULTI KEJURUTERAAN DAN ALAM BINA
UNIVERSITI KEBANGSAAN MALAYSIA
BANGI

2011

ii

DECLARATION

I hereby declare that the work in this thesis is my own except for quotations and
summaries which have been duly acknowledged.

Date
5/10/2011

AHMED NOORI HUMMADI
P43836


iii

AKNOWLEDGMENTS
Praise is to Allah Almighty for giving me the strength, patience and ability to
complete this thesis.
I would like to thank my supervisor Professor Dr. Mahamod Ismail for his
thoughtful comments, guidance, attention and encouragement. Thank you for the
invaluable advice and assistance. My Thanks go to my co-supervisor Professor Dr.
Mohd Alauddin Mohd Ali for her support and help.
My beloved family for all support, patience, understanding and being helpful
throughout my study. I give my deepest gratitude and sincerest love to my parents for
their love and support through my entire life. Special thank to my brother Muneer for
his help to solve any problem floating on the surface with my employer.
I am grateful to all my colleagues, friends, staff, and lecturers in Faculty of
Engineering and Built Environment, Universiti Kebangsaan Malaysia and

Hadhramout University of Science and Technology for their help and support at every
step during this study.
I wish to extend my grateful appreciation to all those who have contributed
directly and indirectly to the preparation of this study. I would like to thank my best
friend Mona Alsayigh for her assistance. Not forgetting also, my examiners and all
committee members for their helpful suggestions.


iv

ABSTRACT
Orthogonal Frequency Division Multiplexing (OFDM) system can achieve high data
rates in mobile environment due to its robustness against the Inter Symbol
Interference (ISI). Likewise, development of efficient receiver with proper channel
estimation technique is crucial to ease the prediction of the received signal. Pilot
symbol assisted modulation introduced to achieve reliable channel estimation through
transmitting pilot signals along with in OFDM symbol. Moreover, interpolation
method developed to estimate the channel samples and eliminates the effect of the
fading channel from the received signals. However, most of the interpolation
techniques such as Linear, Cubic and Spline Cubic interpolation are irresistible against
the noise while the conventional interpolation is not resilience. The objective of this
work is to propose a new improved interpolation technique which is more reliable and
efficient for channel estimation in OFDM system based on pilot signal under fast
varying and noisy channels. The proposed interpolation is much simpler than other
technique, such as Linear, Second Order Modulation, Spline, Time domain, and Lowpass interpolation; where it depends on two parameters which are the mean and
variance of two adjacent pilot signals. Furthermore, this type of interpolation can be
modified to give more accurate estimation for the channel depending on two
modification factors (β and ξ). The mathematical formulations have been derived
based on linear interpolation technique and then validated using simulations. The
Mean Square Error (MSE) performance of the interpolation technique is then

compared with other five types of interpolation under Rayleigh fading channel using
comb type channel estimation. Simulations show that the proposed interpolation
technique able to estimate the channel much better than other interpolation types for
Signal to Noise Ratio (SNR) from 1 dB to 8 dB at MSE equal to 10-3 and as a result it
is much robust against noise which reduces the accuracy of the estimated channel.
Furthermore, the channel estimation is then used to examine the effect of pilot
estimation using different technique of estimation such as Least Square Error (LSE),
Minimum Mean Square Error (MMSE) and Wavelet De-noising. It is shown that pilot
estimation give superior MSE performance in channel estimation by about 20 dB at
low SNR. Simulation also shows that SNR performance improved up to 10 dB
comparing to other type of interpolation at BER equal to 10-3. Finally, the proposed
method also performed well in the estimation of the channel over different Doppler
frequencies and achieves higher OFDM system performances.


v

ABSTRAK
Sistem Pemultipleksan Pembahagian Frekuensi Ortogon (OFDM) dapat mencapai
kadar data yang tinggi dalam persekitaran bergerak kerana ketahanannya terhadap
Gangguan Antara Simbol (ISI). pembangunan penerima cekap dengan teknik
penganggaran saluran yang tepat sangat penting untuk memudahkan ramalan isyarat
yang diterima. Pemodulatan terbantu simbol pandu diperkenalkan untuk mencapai
penganggaran saluran yang bolehharap melalui penghantaran isyarat pandu bersamasama dengan simbol OFDM. Selain itu, kaedah interpolasi dibangunkan untuk
menganggarkan sampel saluran dan menghapuskan kesan pemudaran saluran daripada
isyarat yang diterima. Namun, sebahagian besar teknik interpolasi seperti interpolasi
Lelurus, Kubik dan Kubik Spline tidak berupaya menahan kesan hingar sementara
interpolasi konvensional tidak terkawal dan tidak anjal. Tujuan penyelidikan ini
adalah untuk mencadangkan suatu teknik interpolasi baru dipertingkatkan yang lebih
bolehharap dan cekap untuk penganggaran saluran dalam sistem OFDM berdasarkan

isyarat pandu dalam saluran berubah pantas dan berhingar. Interpolasi yang
dicadangkan adalah jauh lebih ringkas dari teknik yang lain, seperti interpolasi
Lelurus, Pemodulatan Tertib Kedua, Spline, domain Masa, dan Lulus rendah, yang
bergantung pada dua parameter iaitu min dan varians dari dua isyarat pandu yang
bersebelahan. Selanjutnya, jenis interpolasi ini boleh diubahsuai untuk memberikan
penganggaran yang lebih tepat untuk saluran bergantung pada dua faktor
pengubahsuaian (β dan ξ). Formulasi matematik telah diterbitkan berdasarkan teknik
interpolasi lelurus dan kemudian disahkan menggunakan simulasi. Prestasi Ralat
Ganda Dua Min (MSE) dari teknik interpolasi ini kemudian dibandingkan dengan
lima jenis interpolasi yang lain dalam saluran pemudaran Rayleigh menggunakan
penganggaran saluran jenis sikat. Simulasi menunjukkan bahawa teknik interpolasi
yang dicadangkan berupaya menganggarkan saluran jauh lebih baik berbanding jenis
interpolasi yang lain untuk Nisbah Isyarat Terhadap Hingar (SNR) dari 1 dB hingga 8
dB pada MSE sebanyak 10-3 dan sebagai hasilnya teknik ini jauh lebih tahan terhadap
hingar yang mengurangkan kejituan saluran dijangka. Selanjutnya, penganggaran
saluran ini kemudian digunakan untuk menguji kesan penganggaran pandu
menggunakan teknik penganggaran yang berbeza seperti Ralat Ganda Dua Terkecil
(LSE), Ralat Ganda Dua Min Minimum (MMSE) dan Wavelet De-noising. ini
menunjukkan bahawa penganggaran pandu memberikan prestasi MSE yang lebih
tinggi dalam penganggaran saluran sekitar 20 dB pada SNR rendah. Simulasi juga
menunjukkan bahawa prestasi SNR dipertingkatkan sehingga 10 dB berbanding
dengan jenis interpolasi lain pada BER sebanyak 10-3. Akhirnya, kaedah yang
dicadangkan juga bertindak baik dalam menganggarkan saluran bagi frekuensi
Doppler yang berbeza dan mencapai prestasi sistem OFDM yang tinggi.


vi

TABLE OF CONTENTS

Page
DECELARATION

ii

ACKNOWLEDGEMENTS

iii

ABSTRACT

iv

ABSTRAK

v

TABLE OF CONTENTS

vi

LIST OF TABLES

x

LIST OF FIGURES

xi

LIST OF SYMBOLS AND ABBREVIATIONS

xvi

CHAPTER I

INTRODUCTION

1.1

Introduction

1

1.2

OFDM System

3

1.3

Problem Statement

9

1.4

Objective and Scope

10

1.5

Methodology

11

1.6

Thesis Contribution

12

1.7

Thesis Organization

12

CHAPTER II

LITERATURE REVIEW

2.1

Introduction

14

2.2

An Overview Of The Multiple Access Scheme

15

2.3

Modulation

19

2.4

Phase Shift Keying

20

2.5

The Basics Of OFDM

23

2.6

Multi-Path Fading Channel

24

2.7

2.6.1 Binary Phase Shift Keying
2.6.2 Mobile Channel Model
OFDM Channel Estemation

25
26
29

2.7.1
2.7.2

29
31

Least Square (LS) Estimation
Minimum Mean Square Error (MMSE) Estimation


vii

2.8

Channel Equalization Using Wavelet Denoising

32

2.9

2.8.1 Discrete Wavelet Transform (DWT)

2.8.2 Wavelet Denoising
2.8.3 Wavelet Selection
2.8.4 Threshold Selection for Wavelet Denoising
2.8.4.1 VisuShrink
2.8.4.2 SureShrink
2.8.4.3 BaysShrink
2.8.5 Level of Decomposition
Introduction For Interpolation

33
34
35
36
37
37
38
38
39

2.10

Interpolation Defenition And Methods

40

2.11

2.10.1 Linear Interpolation
2.10.2 Polynomial interpolation
2.10.3 Cubic-Spline Interpolation

Error Correction Code

40
41
42
44

2.12

Trellis Coded Modulation (TCM)

45

2.13

Viterbi Algorithm

50

CHAPTER III

CHANNEL ESTIMATION USING PILOT SIGNAL

3.1

Introduction

52

3.2

OFDM system

53

3.3

Pilot Sample Arrangment

54

3.4

Alnuaimy-Mahamod Interpolation

56

3.4.1
3.4.2
3.4.3
3.4.4
3.4.5

57
58
59
64
67

Formulation

β and ξ Factors
Samples Interpolation
Alnuaimy-Mahamod Interpolation Implementation
Summary

CHAPTER IV

MODULATION BASED CHANNEL ESTIMATION

4.1

Introduction

70

4.2

OFDM System Model

71

4.2.1
4.2.2

71
72

Transmitter Structure
Receiver Structure

4.3

Channel Estimation

73

4.4

Alnuaimy-Mahamod Interpolation

76

4.5

Computer Simulation

77

4.6

Simulation

78

4.6.1

β and ξ Factor Values

78

viii

4.7

Results and Discussion

80

4.8

Coded OFDM System Model

92

4.9

COFDM Simulation

94

4.9.1

96

Simulation Results

4.10

Summary

CHAPTER V

PILOT SIGNAL CORRECTION OF ESTIMATION

5.1

Introduction

104

5.2

OFDM System Model With Channel Estimation Block

105

5.3

Channel Estimation

106

5.3.1
5.3.2
5.3.3

106
107
109

Channel Extraction
Pilot Estimation
Channel Interpolation

102

5.4

Simulation

CHAPTER VI

CONCLUSION AND FUTURE WORK

6.1

Conclusion

116

6.1.1

117

6.2

Pilot Channel Estimation

Recommendations For Future Work

REFERENCES

109

118
120

APPENDICES
A

Alnuaimy-Mahamod Interpolation Derivation

129

B

Optimum Channel Interpolation

132

C

List Of Publication

134


x

LIST OF TABLES

Table No.

Page

2.1

Main parameters of WLAN communication systems

15

2.2

The Advantages and drawbacks of different multiple access

18

schemes

3.1

RMSE for Alnuaimy-Mahamod interpolation with the original 67
point over different parameter of β and ξ factors

4.1

The OFDM system Parameter

79

4.2

The OFDM systems performance based on BPSK Modulation

81

4.3

The OFDM systems performance based on QPSK Modulation

83

4.4

The OFDM systems performance based on DBPSK Modulation

85

4.5

The OFDM systems performance based on DQPSK Modulation

87

4.6

The OFDM systems performance based on 16-QAM Modulation

90

4.7

The COFDM system Parameter

95


xi

LIST OF FIGURE

Figure No.
1.1

Page

All the shipment on the steamship versus splitting the shipment using 3
numerous smaller ships.

1.2

Frequency Division Multiplexing (FDM) carrier frequencies

4

1.3

OFDM signal spectrum

5

1.4

Simple OFDM generator

6

1.5

Simple OFDM system

7

1.6

Inter-Symbol interference in OFDM signals

8

2.1

Principle of FDMA (with six sub-channels)

16

2.2

Principle of TDMA (with five time slots)

17

2.3

Principle of CDMA (with four spreading codes)

17

2.4

Constellation diagram for BPSK

21

2.5

Constellation diagram for QPSK

21

2.6

A radio propagation effect

25

2.7

Power spectral density of the channel

27

2.8

Base band Rayleigh fading coefficients generation

27

2.9

Tapped delay line model of fading channel

28


xii

Figure No.

Page

2.10 One-dimensional DWT

35

2.11 Linear interpolation between the two points to estimate the values of x

41

and y

2.12 Trellis Code Modulation (TCM) block diagram

45

2.13 A general type of Trellis Code Modulation block diagram

48

2.14 Partitioning of 8-PSK channel signals

49

3.1

The baseband model of OFDM system

53

3.2

The effect of channel on OFDM symbols

55

3.3

Pilot arrangement

56

3.4

The effect of the β factor on the Alnuaimy-Mahamod interpolation

59

3.5

The effect of the ξ factor on the Alnuaimy-Mahamod interpolation.

60

3.6

Samples Interpolation

61

3.7

Interpolation Subdivisions

62

3.8

Non-uniform Interpolation Subdivisions

63

3.9

Interpolation distribution based on the variant values of ξ factor

64

3.10 Points of a sinc curve.

65


xiii

Figure No.

Page
rd

th

3.11 Interpolation between the 3 and 4 points of the sinc curve

66

3.12 A complete interpolation for the whole points of the sinc curve

66

3.13 The fixed value of β and the different values of ξ for the Alnuaimy-

68

Mahamod Interpolation.
3.14 The fixed value of ξ and the different values of β for the Alnuaimy-

69

Mahamod interpolation

4.1

The baseband model of the OFDM system with pilot-based signal

73

correction

4.2

Time domain Interpolation (DFT/IDFT interpolation) block diagram

76

4.3

The Alnuaimy-Mahamod interpolation block diagram

76

4.4

Interpolation subdivision

77

4.5

MSE for the estimation of the ATTC channel based on different values of

80

β and ξ factors

4.6

The OFDM system performance based on BPSK modulation with

82

Rayleigh fading channel and AWGN

4.7

The OFDM system performance based on QPSK modulation with

84

Rayleigh fading channel and AWGN

4.8

The OFDM system performance based on DBPSK modulation with
Rayleigh fading channel and AWGN

86


xiv

Figure No.
4.9

The OFDM system performance based on DQPSK modulation with

Page
88

Rayleigh fading channel and AWGN

4.10 The OFDM system performance based on 16-QAM modulation with

91

Rayleigh fading channel and AWGN

4.11 Baseband model of the OFDM system with pilot-based signal correction

93

4.12 Signal constellation of 8-PSK

95

4.13 Rate (2/3) Trellis Code Modulations

95

4.14 Trellis diagram for (2/3) rate TCM model

96

4.15 COFDM system with uncoded OFDM system modulation over AWGN

97

channel.

4.16 Constellation plot for the received OFDM signals over AWGN channel 98
(SNR=10dB)

4.17 COFDM with uncoded OFDM system based on QPSK and 8-PSK 99
modulation over AWGN and ATTC Rayleigh fading channel

4.18 Polar plot for the received OFDM signals over AWGN and ATTC 100
Rayleigh fading channel (SNR=20dB)

4.19 COFDM system with uncoded OFDM system over AWGN and ATTC 101
Rayleigh fading channel using Alnuaimy-Mahamod interpolation for
channel estimation.

4.20 COFDM system based different type of interpolation technique for the 102
channel estimation of the system based on pilot signals.


xv

Figure No.
5.1

Page

Baseband model of the OFDM system based on pilot signal for channel 106
estimation

5.2

MMSE technique versus LS technique for pilot estimation in OFDM 107
signals

5.3

The performance comparison of LS pilot estimation with and without 108
wavelet denoising

5.4

The performance comparison of MMSE pilot estimation with and without 109
wavelet denoising

5.5

OFDM system performance based Alnuaimy-Mahamod interpolation for 110
the channel estimation using different techniques of pilot estimation.

5.6

MSE performance for channel estimation based Alnuaimy-Mahamod 112
interpolation using different techniques of pilot estimation with and
without wavelet denoising.

5.7

MSE performance for channel estimation based different interpolation 113
technique using LS technique for pilot estimation combined with wavelet
denoising

5.8

MSE performance for channel estimation based different interpolation 114
technique using MMSE for pilot estimation

5.9

MSE performance for channel estimation based different interpolation 115
technique using MMSE technique for pilot estimation combined with
wavelet denoising


xvi

LIST OF SYMBOLS AND ABBREVIATIONS

GSM

Global System for Mobile communications

3GPP-LTE

3rd Generation Partnership Project Long Term Evolution

ADSL

Asymmetric Digital Subscriber Line

AM

Amplitude Modulation

ARQ

Automatic Repeat request

ASK

Amplitude Shift Keying

ATTC

Advanced Television Technology Center

AWGN

Additive White Gaussian Noise

BCH

Bose Chaudhuri Hocquenghem

BER

Bit Error Rate

BPSK

Binary Phase Shift Keying

BS

Base Station

BWA

Broadband Wireless Access

CDMA

Code Division Multiple Access

COFDM

Coded Orthogonal Frequency Division Multiplexing

CPE

Customer-premises equipment

d2(y,z)

squared Euclidean distance

DAB

Digital Audio Broadcasting

DAMPS

Digital Advanced Mobile Phone Service

dB

decibel

DBPSK

Differential Binary Phase Shift Keying

DFT

Discrete Fourier Transform

DPSK

Differential Phase Shift Keying


xvii

DQPSK

Differential Quadrate Phase Shift Keying

DVB

Digital Video Broadcasting

DWT

Discrete Wavelet Transform

Eb

energy per bit

EDGE

Enhanced Data rate for GSM Evolution

Es

energy per symbol

ETSI

European Telecommunication Standard Institute

fc

frequency carrier

FDM

Frequency Division Multiplexing

FDMA

Frequency Division Multiple Access

Fd

Doppler Frequency

FEC

Forward Error Correction

FFT

Fast Fourier Transform

FIR

Finite Impulse Response

FM

Frequency Modulation

G

Generation

GPRS

General Packet Radio Services

h(.)

Instantaneous ISI of the channel

H(f)

Transfer function of the filter

h(τ, t)

channel impulse response at delay τ and time instant t

HARQ

Hybrid ARQ

HSCSD

High Speed Circuit Switched Data

HSDPA

High Speed Downlink Packet Access

HSPA

High Speed Packet Access

HSUPA

High Speed Uplink Packet Access


xviii

Hz

Hertz

ICI

Inter Channel Interference

IDFT

Inverse Discrete Fourier Transform

IFFT

Inverse Fast Fourier Transform

Ii

k-tuple of the input digits

Ij(D)

input associated

IMS

IP Multimedia Service

IMT
Advanced

International Mobile Telecommunications Advanced

IP

Internet Protocol

IPTV

Internet Protocol television

IS-95

Interim Standard-95

ISI

Inter Symbol Interference

Kbps

Kilobits

LAN

Local Area Networks

LS

Least Squares

MANs

Metropolitan Area wireless Networks

MatLab

Matrix Laboratory

Mbit

Megabit

MC-CDMA

Multi Carrier- Code Division Multiple Access

MC-DSCDMA

Multi-Carrier Direct Sequence Code Division Multiple Access

MC-SS

Multi-Carrier Spread Spectrum

MHz

Megahertz

MIPS

Microprocessor without Interlocked Pipeline Stages


xix

ML

Maximum Likelihood

MMSE
MSE

Minimum Mean Square Error
Mean Square Error

MUX

Multiplex

n

additive white Gaussian noise

NLOS

Non Line Of Sight

Nw

number of vanishing moments

OFDM

Orthogonal Frequency Division Multiplexing

PDC

Personal Digital Cellular

PM

Phase Modulation

PSAM

Pilot Symbol Assisted Modulation

PSK

Phase Shift Keying

QAM

Quadrature Amplitude Modulation

QPSK

Quadrate Phase Shift Keying

RF

Radio Frequency

ri

ith received sample

RMSE

Root Mean Square Error

RSS

Rich Site Summary

s(t)

transmitted signa

SNR

Signal to Noise Ratio

SURE

Stein’s Unbiased Risk Estimator

T

sampling period

Tb

bit duration

TCM

Trellis Code Modulation

TDM

Time Division Multiplexing


xx

TDMA

Time Division Multiple Access

TH

hard-thresholding

~
H p (k )

coefficient of the channel

TIA

Telecommunication Industry Association

tj

threshold value

TS

Time Slots

Ts

symbol duration

UHF

Ultra High Frequency

UMTS
(FOMA)

Universal Mobile Telecommunications System(Freedom of Mobile
Multimedia Access)

VA

Viterbi Algorithm

VHF

Very High Frequency

vn

high pass wavelet coefficients

VoIP

Voice over Internet Protocol

WCDMA

Wideband Code Division Multiple Access

WiBro

Wireless Broadband

Wi-Fi

Wireless Fidelity

WiMAX

Worldwide Interoperability for Microwave Access

WLAN

Wireless Local Area Networks

WLL

Wireless Local Loops

xe

interpolated values

xp(k)

pilot sample

β

modification factors

λji

jth digit in the k-tuple

ξ

modification factors