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DESIGN AND EVALUATION OF MULTIDIMENSIONAL TURBO PRODUCT
CODED MIMO-OFDM SYSTEM
MULADI
A thesis submitted in fulfilment of the
requirements for the award of the degree of
Doctor of Philosophy
Faculty of Electrical Engineering
Universiti Teknologi Malaysia
JANUARY 2007
v
ABSTRACT
Multiple inputs multiple outputs (MIMO) realized through employing
multiple antennas at both transmitter and receiver provides low bit error rate and high
transmission rate as required by future digital wireless communication systems.
Space time coding and spatial multiplexing are the two approaches in exploiting
MIMO channel. This project proposes a new multiple inputs multiple output-
orthogonal frequency division multiplexing (MIMO-OFDM) system employing
single parity check multidimensional turbo product codes (MDTPC) that will provide
high bit rate transmission with low bit error rate over correlated frequency selective
fading channels. The initial work is developing the dimensional-based reading order
(DBRO) algorithm for generating the MDTPC codeword sequences. The MDTPC
codeword sequence is then applied to MIMO-OFDM system that exploits space,
time, and frequency diversity and provides full-rate transmission. The system
provides diversity gain of 2.5 dB in signal to noise ratio (SNR) and coding gain of 3
dB. Spatial multiplexing space-time coded MDTPC-MIMO-OFDM system with
antennas grouping (AG-SMST-SPC-MDTPC-MIMO-OFDM) is then developed to
increase the transmission rate. The result shows that the system provides a high
transmission rate of 8 bps/Hz at SNR of 10 dB using two groups of four transmit
antennas. The final task is designing the accurate channel estimation for the AG-
SMST-MDTPC-MIMO-OFDM system employing pilot symbol assistance and least
square estimation using mean-square error criterion. The channel estimator achieves
mean-square error of 7x10-4 which is highly accurate. The proposed system provides
high transmission bit rate of 120 Mbps with bit error rate of 10-5 at SNR of 18 dB for
two groups of four transmit antennas. It can be implemented in wireless local area
network (WLAN) and can also be deployed in any broadband wireless system.
vi
ABSTRAK
Masukan berganda keluaran berganda (MIMO) wujud dengan penggunaan
antena berganda pada kedua-dua pemancar dan penerima bagi menyediakan kadar
ralat bit rendah dan kadar penghantaran tinggi sebagaimana yang diperlukan oleh
sistem-sistem perhubungan digital wayarles masa hadapan. Pengekodan ruang masa
dan gandaan mengikut ruang adalah dua pendekatan penggunaan saluran MIMO.
Projek ini mencadangkan sebuah sistem masukan berganda keluaran berganda-
pemultiplek pembahagi frekuensi ortogonal (MIMO-OFDM) yang baru bagi
menjalankan pemeriksaan persamaan tunggal pengekodan sejajar turbo dimensi
rantaian (MDTPC) yang akan menyediakan kadar penghantaran bit tinggi dengan
kadar ralat bit rendah sepanjang saluran berpudar berkaitan frekuensi terpilih. Kerja
awal adalah membangunkan algoritma berdasar dimensi pembacaan urutan (DBRO)
untuk menjana urutan-urutan kod MDTPC. Urutan-urutan kod MDTPC kemudian
digunakan kepada sistem MIMO-OFDM yang mengeksploitasikan kepelbagian
ruang, masa, dan frekuensi dan menyediakan kadar penghantaran penuh. Sistem ini
menyediakan kepelbagian gandaan 2.5 dB dalam nisbah isyarat hingar (SNR) dan
pengekodan gandaan 3 dB. Gandaan ruang bagi ruang-masa berkod sistem MDTPC-
MIMO-OFDM dengan antena berkumpul (AG-SMST-MDTPC-MIMO-OFDM)
kemudian dibangunkan untuk meningkatkan kelajuan penghantaran. Hasil kerja
menunjukkan bahawa sistem menyediakan kadar penghantaran yang tinggi iaitu 8
bps/Hz pada SNR 10 dB dengan menggunakan dua kumpulan yang terdiri daripada
empat antena. Kerja terakhir adalah merekabentuk pengiraan saluran bagi sistem
AG-SMST-MDTPC-MIMO-OFDM dengan menggunakan pembantu simbol
berpandu dan penganggaran ganda dua terkecil menggunakan kriteria purata ralat
ganda dua. Penganggar saluran memperolehi purata ralat ganda dua 7x10-4 yang
mana adalah ketepatan yang tinggi. Sistem yang dicadangkan mencapai kadar
penghantaran 120 Mbps dengan kadar ralat bit 10-5 pada SNR 18 dB untuk dua group
dari empat antena penghantar. Ianya boleh digunakan dalam aplikasi rangkaian
kawasan tempatan wayarles (WLAN) dan boleh juga digunakan dalam mana-mana
sistem jalur lebar wayarles.
vii
TABLE OF CONTENTS
CHAPTER TITLE PAGE
DECLARATION ii
DEDICATION iii
ACKNOWLEDGEMENTS iv
ABSTRACT v
ABSTRAK vi
TABLE OF CONTENTS vii
LIST OF TABLES xii
LIST OF FIGURES xiv
LIST OF ABBREVIATIONS xx
LIST OF SYMBOLS xxi
LIST OF APPENDICES xxiii
1 INTRODUCTION 1
1.1 Introduction 1
1.2 Problem Statement 3
1.3 Objective of The Research 4
1.4 Scope of The Research 5
1.5 Significant of Works 7
1.6 Thesis Outline 8
2 MIMO-OFDM WIRELESS COMMUNICATIONS 10
2.1 Introduction 10
2.2 Wireless Channel Impairments 11
2.3 MIMO Wireless Communication Systems 14
viii
2.3.1 Space-Time Diversity Approach 16
2.3.1.1 Space Time Block Codes 18
2.3.1.2 Space-Time Trellis Codes 22
2.3.2 Spatial Multiplexing Approach 25
2.3.2.1 VBLAST 27
2.3.2.2 DBLAST 29
2.3.2.3 Other BLAST Architectures 30
2.4 Application of MIMO Schemes on OFDM Systems 34
2.4.1 OFDM System 36
2.4.2 Application of Space Time Coding 38
2.4.3 Application of Spatial Multiplexing Schemes 42
2.5 Error Correcting Codes for MIMO-OFDM System 42
2.5.1 Convolutional Codes 43
2.5.2 Multidimensional Turbo Product Codes 45
2.5.2.1 Component Codes of TPC 48
2.5.2.2 Symbol by Symbol Soft Iterative TPC
Decoding 49
2.5.2.3 Pairwise Error Probability of TPC 52
2.6 Channel Estimation Strategy for MIMO-OFDM
System 54
2.7 Application of MIMO-OFDM System for Wireless
LAN 57
2.8 Summary 59
3 MULTIDIMENSIONAL TURBO PRODUCT CODES 63
3.1 Introduction 63
3.2 Dimensional Based Reading Order of MDTPC
Codeword 65
3.2.1 DBRO Algorithm 66
3.2.2 DBRO Codeword Generator for 2D MDTPC 71
3.2.3 DBRO Codeword Generator for 3D MDTPC 74
3.2.4 DBRO Codeword Generator for 4D MDTPC 81
3.2.5 DBRO Codeword Generator for 5D MDTPC 84
ix
3.3 Proposed Parallel Decoder for D Dimensional
MDTPC 86
3.3.1 Decoding Complexity 89
3.4 Performance of D dimensional MDTPC 91
3.4.1 Convergence Behaviour 92
3.4.2 Bit Error Rate Performance 95
3.4.3 Performance of DBRO Codeword Sequences 99
3.5 Summary 100
4 SPACE-TIME MULTIDIMENSIONAL TURBO
PRODUCT CODED MIMO-OFDM SYSTEM 102
4.1 Introduction 102
4.2 Space-time MDTPC-MIMO System 103
4.2.1 Zero Forcing Receiver 107
4.2.2 Maximum Likelihood Receiver 111
4.3 Channel Capacity Analysis 113
4.4 ST-MDTPC-MIMO Application on OFDM System 116
4.5 Simulation Results and Discussion 118
4.5.1 ST-MDTPC-MIMO System 120
4.5.1.1 Performance Comparison of ST-
MDTPC-MIMO and STBC 122
4.5.1.2 Convergence Behaviour of MDTPC
Decoder in MIMO System 124
4.5.1.3 Bit Error Rate Performance of ST-
MDTPC-MIMO System 130
4.5.1.4 Diversity Gain and Coding Gain 133
4.5.1.5 Bit-Interleaved ST-MDTPC-MIMO
System 135
4.5.1.6 Link Level Capacity of ST-MDTPC-
MIMO System 138
4.5.2 Performance of ST-MDTPC-MIMO-OFDM
System 140
4.6 Summary 145
x
5 SPATIAL MULTIPLEXING ST-MDTPC-MIMO-
OFDM SYSTEM WITH ANTENNA GROUPING 148
5.1 Introduction 148
5.2 Spatial Multiplexing ST-MDTPC-MIMO System
with Antenna Grouping 149
5.2.1 AG-SMST-MDTPC-MIMO Schemes 149
5.2.1.1 Zero Forcing Receiver 152
5.2.1.2 ML Receiver 155
5.3 Channel Capacity Analysis 156
5.4 AG-SMST-MDTPC-MIMO Application on OFDM
System 159
5.5 Simulation Model 161
5.6 Simulation Results and Discussion 163
5.6.1 AG-SMST-MDTPC-MIMO System 163
5.6.1.1 Bit Error Rate Performance of AG-
SMST-MDTPC-MIMO System 164
5.6.1.2 The Link Level Capacity of AG-
SMST-MDTPC-MIMO System 169
5.6.2 Bit Error Rate Performance of AG-SMST-
MDTPC-MIMO-OFDM System 172
5.7 Summary 174
6 CHANNEL ESTIMATION STRATEGY FOR AG-
SMST-MDTPC-MIMO-OFDM SYSTEM 176
6.1 Introduction 176
6.2 Least Square Channel Estimation 178
6.3 Channel Estimation Analysis 181
6.3.1 Optimal Training Over One OFDM Frame 183
6.3.2 Optimal Training Over Multiple OFDM
Frames 186
6.4 Channel Estimation Enhancement 188
6.4.1 Frequency Domain Analysis of RLS Method 191
6.5 Simulation Model 192
xi
6.6 Simulation Results and Discussion 194
6.6.1 Analytical and Simulated MSE 194
6.6.2 Error Rate and MSE Performance of LS
Channel Estimation
195
6.6.3 RLS Enhancement 200
6.7 Summary 202
7 CONCLUSION AND FUTURE WORKS 204
7.1 Introduction 204
7.2 Future Works 208
REFERENCES 210-227
Appendices A-D 228-248
xii
LIST OF TABLES
TABLE NO. TITLE PAGE
2.1 Orthogonal STBC with code rate above ½ 19
2.2 Comparison of STBC and STTC 26
2.3 Layering in DBLAST 30
2.4 MIMO receivers 33
2.5 Comparison of the approaches in exploiting MIMO 34
2.6 Major parameters for OFDM PHY of 802.11a WLAN standard 59
4.1 Bit error rate of ST-MDTPC-MIMO system 129
4.2 Bit error performance of 3D, 4D, 5D ST-MDTPC-MIMO system 132
4.3 Diversity gain of 2Tx2Rx and 3Tx3Rx ST-MDTPC-MIMO systems 134
4.4 Coding gain of ST-MDTPC-MIMO system with 2Tx2Rx and 3Tx3Rx 134
4.5 Coding gain advantage of 3Tx3Rx ST-MDTPC-MIMO system 137
4.6 Coding gain advantage of 4D and 5D ST-MDTPC-MIMO over 3D ST-MDTPC-MIMO system with 4Tx4Rx antennas 138
4.7 Simulation parameters of ST-MDTPC-MIMO-OFDM system 141
5.1 Bit error rate of 1G, 2G, and 3G 2Tx2Rx using 3D and 4D MDTPC 165
5.2 Bit error rate of the 2G, 3G, 4G 4D AG-SMST-MDTPC-MIMO system at SNR 5 dB 166
xiii
5.3 Bit error rate at transmission rate of 4 bps/Hz and SNR of 10 dB 168
5.4 Bit error rate and transmission rate of the system with 1G, 2G, and 3G at channel delay spread of 100 ns 173
5.5 Effect of delay spread on AG-SMST-MDTPC-MIMO-OFDM system at bit error rate of 10-6 173
6.1 λ optimum for slow and fast fading channel 195
6.2 Bit error rate of the system at SNR of 18 dB 196
6.3 Bit error rate at SNR 18 dB for training over two and four OFDM frames 199
6.4 MSE of channel estimation over two and four OFDM frames at SNR of 18 dB 199
6.5 Bit error rate of the system employing RLS and LS channel estimation 201
6.6 MSE of the system employing RLS and LS channel estimation 202
xiv
LIST OF FIGURES
FIGURE NO. TITLE PAGE
2.1 Faded signal envelope 11
2.2 Power spectrum of the received signal after traveling the multipath channel 12
2.3 Antenna configuration in multiple antennas wireless system, Tx = transmitter, Rx = receiver 14
2.4 Exploiting MIMO channel methods 15
2.5 Space and time diversity a) receive diversity using MRRC, b) transmit diversity (Alamouti, 1998) 17
2.6 Encoder block diagram for STBC 21
2.7 A four state STTC, R = 2 bits /s/Hz using QPSK 23
2.8 Transmitter structure for BLAST (Foschini, 1996) 27
2.9 Packet structure for BLAST, NT = NR =4. 29
2.10 Block diagram of the MIMO-OFDM system with space, time, and frequency diversity 35
2.11 Block diagram of an OFDM system (Proakis, 2000) 37
2.12 General block diagram of space-time coded OFDM system 39
2.13 Convolutional encoder with memory length k = 7 44
2.14 Recursive systematic codes with parallel concatenation: turbo encoder 44
2.15 Serial concatenated encoding representation of the TPC 46
2.16 A geometrically representation of the encoding process of TPC 47
xv
2.17 Turbo product codeword, a) fully product code b) parallel concatenated code, c) shortened product code 48
2.18 Serial soft-iterative decoder for TPC 52
2.19 Pilot symbol pattern for MIMO-OFDM with 2 transmit antennas 55
2.20 Data and pit symbols arrangement in the transmitted frame 56
2.21 Transmitted and receiver block diagram for OFDM PHY 802.11a 58
2.22 Flowchart of research methodology 62
3.1 MDTPC codeword formatting process 65
3.2 DBRO algorithm for MDTPC 58
3.3 Flowchart of DBRO algorithm 59
3.4 D MDTPC encoder using DBRO bit mapper 70
3.5 The 2D MDTPC codeword, a) two dimensions codeword block, b) corresponding two possible codeword sequences 73
3.6 Encoding and possible codeword using DBRO algorithm of 2D MDTPC with MATLAB programming, a) data block, b) codeword block, c) codeword sequences 74
3.7 The equivalent algorithm for the mapping function ξ1. 76
3.8 A typical 3D MDTPC with dimension of n1 = 4, n2 = 5, and n3 =3 77
3.9 The common codeword x1 of the 3D MDTPC given in example 77
3.10 The second possible codeword of the 3D MDTPC given in example 77
3.11 The third possible codeword of the 3D MDTPC given in example 78
3.12 The forth possible codeword of the 3D MDTPC given in example 78
3.13 The fifth possible codeword of the 3D MDTPC given in example 78
xvi
3.14 The sixth possible codeword of the 3D MDTPC given in example 79
3.15 Codeword sequences of the (4x5x3) 3D MDTPC as parallel code 80
3.16 The (4x5x3) 3D MDTPC codewords, a) data block, b) codeword block, c) codeword sequences 81
3.17 Codeword block of 4D MDTPC presented in 3D MDTPC codeword blocks 82
3.18 DBRO algorithm for 4D MDTPC 83
3.19 Representation of a 5D MDTPC codeword into several 3D MDTPC codeword 84
3.20 DBRO algorithm for generating 5D MDTPC codeword sequences 86
3.21 Parallel Decoder for D-dimensional MDTPC 88
3.22 Soft input soft output decoder component 88
3.23 Flowchart of the parallel decoder 90
3.24 Simulation model for error correcting MDTPC system 92
3.25 Convergence behaviour of the 2D, 3D, 4D, and 5D MDTPC with 4QAM modulation over AWGN channel at SNR 6 dB 93
3.26 Convergence behaviour of the 4D MDTPC decoder using 16QAM modulation over fast flat Rayleigh channel 94
3.27 Bit error rate performance of 2D, 3D, 4D, and 5D MDTPC using BPSK over AWGN channel 95
3.28 Bit error rate performance of 2D, 3D, 4D, and 5D MDTPC using BPSK over flat Rayleigh fading channel at 4 iterations 96
3.29 Bit error rate performance of 2D, 3D, 4D, and 5D MDTPC with 4QAM modulation 97
3.30 Bit error rate performance of 2D, 3D, 4D, and 5D MDTPC using 16QAM over flat Rayleigh fading channel at 6 iterations 99
3.31 The performance of the MDTPC for different selected codeword using BSPK modulation over flat Rayleigh fading channel 100
xvii
4.1 ST-MDTPC-MIMO transmitter system 104
4.2 ZF ST-MDTPC-MIMO receiver 104
4.3 ML receiver for space-time product coded multiple antennas 112
4.4 OFDM transmission scheme for ST-MDTPC-MIMO system 118
4.5 Simulation model of ST- MDTPC-MIMO-OFDM system 121
4.6 Convergence behaviour of the proposed parallel decoder of 2D ST-MDTPC code applying in the various multiple antennas schemes at SNR of 6 dB 123
4.7 Performance comparisons of the ST-MDTPC and STBC-MDTPC 124
4.8 Bit error rate performance of the 2Tx2RX 2D ST-MDTPC-MIMO system for a number of decoding iterations 125
4.9 Convergence behaviour of 3D ST-MDTPC-MIMO system at SNR=3 dB 126
4.10 Bit error rate performance of the 2Tx2Rx 3D ST-MDTPC-MIMO for a number of decoding iterations 126
4.11 Convergence behaviour of 4D ST-MDTPC-MIMO system at SNR=3 dB 127
4.12 Bit error rate performance of the 2Tx2Rx 4D ST-MDTPC-MIMO system for certain number of decoding iterations 127
4.13 Convergence behaviour of 5D ST-MDTPC-MIMO system at SNR=3 dB 128
4.14 Bit error rate performance of the 2Tx2Rx 5D ST-MDTPC-MIMO system for certain number of decoding iterations 128
4.15 Bit error rate performance of the 3D ST-MDTPC-MIMO system 131
4.16 Bit error rate performance of the 4D ST-MDTPC-MIMO-system 131
4.17 Bit error rate performance of the 5D ST-MDTPC-MIMO system 132
xviii
4.18 Diversity gain and coding gain of the ST-MDTPC-MIMO system employing 2Tx2Rx and 3Tx3Rx 134
4.19 Bit error rate of the 2Tx2Rx ST-MDTPC system using BPSK, 4QAM, and 16QAM modulation 136
4.20 Bit error rate of the 3Tx3Rx ST-MDTPC-MIMO using BPSK, 4QAM and 16QAM modulation 137
4.21 Bit error rate of 4Tx4Rx ST-MDTPC system using BPSK, 4QAM, and 16QAM 138
4.22 LLC of the 2Tx2Rx schemes using HCM, BICM, and 5D ST-MDTPC-MIMO schemes 140
4.23 Bit error rate performance of the 3Tx3Rx 3D ST-MDTPC-MIMO-OFDM system using 16QAM modulation and Doppler frequency at 100 Hz 143
4.24 Bit error rate performance of the 3D ST-MDTPC-MIMO-OFDM employing 3Tx3Rx and 4Tx4Rx (τD = 50 ns) 144
5.1 Transmitter structure of the spatial multiplexing product coded MIMO system with antenna grouping 150
5.2 The ZF receiver structure of the AG-SMST-MDTPC-MIMO system 153
5.3 The ML receiver structure of spatial multiplexing product coded MIMO 156
5.4 Block diagram of AG-SMST-MDTPC-MIMO-OFDM system 160
5.5 Simulation model of AG-SMST-MDTPC-MIMO-OFDM system 162
5.6 Bit error rate performance of the AG-SMST-MDTPC-MIMO system employing 1G, 2G, and 3G 2Tx2Rx 164
5.7 Bit error rate performance of the 4D ST-MDTPC system employing 2G, 3G, and 4G with 3Tx3Rx, 4Tx4Rx, and 5Tx5Rx 166
5.8 The 4 bits/s/Hz transmission rate 3Tx3Rx 3D AG-SMST-MDTPC-MIMO system 167
5.9 The 8 bps/Hz transmission rate 4Tx4Rx 4D AG-SMST-MDTPC-MIMO system 168
xix
5.10 Link level capacity of the 2G 4Tx4Rx 4D AG-SMST-MDTPC-MIMO system using ML receiver and ZF receiver. 170
5.11 Link level capacity of the 3G 4Tx4Rx 4D AG-SMST-MDTPC-MIMO system using ML receiver and ZF receiver. 171
5.12 Bit error rate performance of 3D AG-SMST-MDTPC-MIMO-OFDM system for 2G and 3G 3Tx3Rx 16QAM, fD = 100Hz 172
6.1 ZF receiver of the AG-SMST-MDTPC-MIMO-OFDM with channel estimator 177
6.2 Training symbol over OFDM frame, a) one frame, b) two frames 186
6.3 Simulation model of the 2G 3TxRx 3D AG-SMST-MDTPC-MIMO-OFDM system with channel estimator 193
6.4 MSE profile as a function of λ for simulation and analysis results at SNR = 20 dB (non time varying channel over an entire OFDM frame) 195
6.5 Bit error rate performance with different training sequences for channel estimation over one OFDM frame 196
6.6 MSE of channel estimation for training over one OFDM frame 197
6.7 Bit error rate performance with training for channel estimation over two and four OFDM frames 198
6.8 MSE of channel estimation for training over two and four OFDM frames 200
6.9 Bit error rate performance as SNR function with optimal tracking factor λ 201
6.10 MSE as SNR function of the 2G 3TxRx 3D AG-SMST-MDTPC-MIMO-OFDM system with optimal tracking factor λ 202
xx
LIST OF ABBREVIATIONS AWGN - Additive White Gaussian Noise
BPSK - Binary Phase Shift Keying modulation
CWEF - Conditional Weight Enumerating Function
dB - decibel
IOWEF - Input-Output Weight Enumerating Function
LLR - Log-likelihood Ratio
LOS - Line Of Sight
LS - Least Square
MDTPC - Multidimensional Turbo Product Codes
MIMO - Multiple Input Multiple Output
MISO - Multiple Input Single Output
ML - Maximum Likelihood
MSE - Mean Square Error
OFDM - Orthogonal Frequency Division Multiplexing
TPC - Turbo Product Code
PEP - Pairwise Error Probability
PSA - Pilot Symbol Assisted
QAM - Quadrature Amplitude Modulation
RLS - Recursive Least Square
SIMO - Single Input Multiple Output
SISO - Single Input Single Output
SNR - Signal to Noise Ratio
SPC - Single Parity Check code
STBC - Space Time Block Codes
STTC - Space Time Trellis Codes
ZF - Zero Forcing
xxi
LIST OF SYMBOLS
A(.) - IOWEF, input output weight enumerating function
Bh - Bit error multiplicity
b b - Information bits
C - The link level capacity, channel capacity
D - Number dimension of multi dimensional turbo product code
Es - Energy of transmitted symbol
E{.} - Expectation function, running time mean
F - Frame length of transmitted block (symbols)
H,h - Channel response
H(.) - Entropy
I - Identity matrix
I(.) - Mutual information
j - Imaginary sign of complex number
kd - Information block length, encoder input length
k - Constellation component order
M - Modulation level, number of constellation components
m, n, t - Order for transmit antenna, order for receive antenna, and order
of transmitted symbol
N - Codeword length of a product code (bits)
N0 - Power of additive noise
NT - Number of transmit antennas
NR - Number of receive antennas
NG - Number of antenna groups
nd - Codeword length of component code at dth dimension
xxii
Pe - Probability of bit error
Pr(.) - Probability of an event
p(.) - Conditional probability
s - Transmitted signal
sk - Constellation components, transmitted symbols
W,w - AWGN noise
X, X - Coded bits
Y,y - Received signal matrix
δd - Hamming distance of a codeword
- Complex number set
- Real number set
(.)ℜ Real part of complex number
Integer number set
(.)T - Matrix transpose
π - Pi = 22/7 = 3.14159
ξ - DBRO mapping function
Λ(.) - LLR = log-likelihood ratio
Λe - Extrinsic information
Λc - Soft channel output
O(.) - Computational complexity
S - Set of constellation components
C(.) - Component code of multidimensional product code
(.)H - Hermitian matrix
(.)* - Complex conjugate
(.)-1 - Matrix inverse
( )†. - Moore-Penrose pseudo-matrix inverse
xxiii
LIST OF APPENDICES
APPENDIX TITLE PAGE
A Complex orthogonal STBC with rate more than ½. 228
B Matlab source code of DBRO Algorithm for 3D MDTPC
233
C1 The codeword sequences of the 4D MDTPC 235
C2 The mapping function of the codeword sequences 237
C3 A typical 4D MDTPC with dimension 5×4×3×2 238
C4 The codeword sequences of the 4D SPC-MDTPC with dimension of 5×4×3×2
238
D Simple truncation of 3D MDTPC with C(10,9,2) to result 896 coded bits within the codeword
248
CHAPTER 1
INTRODUCTION
1.1 Introduction
Orthogonal frequency division multiplexing (OFDM) has become a popular
technique for transmission of signal over wireless channel. OFDM converts a
frequency-selective channel into a parallel collection of frequency flat channels. The
sub-carriers have the minimum frequency separation required to maintain
orthogonality of their corresponding time domain waveforms, yet the signal spectra
corresponding to different sub-carriers overlap in frequency. Based on these
advantage, OFDM has been adopted in several wireless standards such as digital
audio broadcasting (DAB), digital video broadcasting (DVB-T), the IEEE802.11a
(IEEE, 1999) local area network (LAN) standard and the IEEE 802.16a (IEEE, 2003)
metropolitan area network (MAN) standard. OFDM is also being pursued for
dedicated short-range communications (DSRC) for road side to vehicle
communications and as potential candidate for fourth-generation (4G) mobile
wireless systems.
The IEEE 802.11a LAN standard operates at raw data rates up to 54 Mbps
(channel condition permitting) with a 20 MHz channel spacing, thus yielding a
bandwidth efficiency of 2.7 bps/Hz (IEEE, 1999). The actual throughput is highly
dependent on the medium access control (MAC) protocol. Likewise, IEEE802.16a
operates in many modes depending on channel conditions with a data rate ranging
from 4.20 to 22.91 Mbps in typical bandwidth of 6 MHz, translating into bandwidth
2
efficiency of 0.7 to 3.82 bps/Hz (IEEE, 2003). Recent development of OFDM
combined with multiple input multiple output (MIMO) techniques promise a
significant performance boost. Broadband MIMO-OFDM systems with bandwidth
efficiency of the order of 10 bps/Hz are feasible for LAN/MAN environments
(Stubber et al., 2004).
MIMO system is an arrangement of multiple antennas that can be used at
transmitter and receiver. A MIMO system takes advantage of the spatial diversity
that is obtained by spatially separated antennas in a dense multi-path scattering
environment. MIMO systems may be implemented in a number of different ways to
provide a diversity gain and combat signal fading in order to obtain a capacity gain.
Generally, there are three different ways in exploiting MIMO system. The first
reason is to improve the power efficiency by maximizing spatial diversity. This
approaches provides low bit error rate at low signal to noise ratio (SNR). Such
techniques include delay diversity (Wittneben, 1993), space–time block codes
(STBC) (Alamouti, 1998; Tarokh et al., 1999) and space–time trellis codes (STTC)
(Tarokh et al., 1998). The second method uses a layered approach (spatial
multiplexing) to increase capacity. One popular example of such a system is V-
BLAST suggested by (Wolniansky et al. 1998) where full spatial diversity is usually
not achieved. Finally, the third type exploits the knowledge of channel at the
transmitter to maximize the link level capacity relate to capacity gain. It decomposes
the channel coefficient matrix using singular value decomposition (SVD) and uses
these decomposed unitary matrices as pre- and post-filters at the transmitter and the
receiver to achieve near capacity (Ha et al., 2002). This approach requires a
feedback channel from receiver to transmitter to send the channel parameters
experienced by the transmitted signals.
Spatial diversity improves the MIMO system in term of link reliability and
error-rate performance of the system (Bliss et al., 2004; Ajib and Haccoun, 2005).
STTC give high transmission rate with low error-rate at the cost of receiver
complexity that increased exponentially as the number of antenna increase. STBC
require linear decoding thus it is less complex. However, STBC does not provide
coding gain. Another disadvantage of STBC is that these code decrease the
3
transmission rate when the number of transmit antenna are more than two. Both
STTC and STBC are designed for flat fading channel and are not suitable for fast and
selective fading channel (Alamouti, 1998; Tarokh et al., 1998). On the other hand,
layered MIMO techniques are addressed to provide high transmission rate but
sacrifice the error rate performance. Since the distinct symbol streams are
transmitted from multiple transmit antennas, they will interfere each other that
introduce errors during transmission. To improve the error rate performance of the
layered MIMO, powerful coding techniques have to be used, such as turbo codes
(Jameel and Yu, 2003) and turbo product code (TPC) (Du and Chan, 2004). Turbo
code has high error correction capability among the error correcting codes. The
encoder and decoder of turbo codes are very complex since they work based on the
trellis diagram (trellis-based codes). TPC warrants less competent error correction
capability compared to turbo code with less complex encoder and decoder processing.
The existing decoder of TPC experiences the local minima in the convergence region
and converges gradually at slow rate.
1.2 Problem Statement
The existing space-time codes enhance the error rate performance of the
wireless transmission system over MIMO channels at the cost of decreasing the
transmission rate. Both STBC and STTC that employ several transmit antennas
produce maximum rate of only 3/4 symbol/s/Hz. The encoding and decoding of
STBC is simple, but STBC does not grant coding gain. On the other hand, STTC
provides coding gain but its encoding and decoding is complex. Furthermore, the
performance of these codes will degrade greatly when the fading is changing rapidly
within one transmitted symbol duration since the codes were designed for slow time
varying fading channel.
The performance of spatial multiplexing MIMO system can be enhanced
through the use of robust error correcting codes (Kothandaraman, 2002; Li et al.,
2003; Lee et al., 2003; Gidlund and Ahag, 2003; Du and Chan, 2005). The
4
performance enhancement can also be obtained by applying space-time codes onto
spatial multiplexing MIMO system (Mao and Motani, 2005; Wu et al., 2002). Other
means include developing accurate symbol detection at the receiver (Artes et al.,
2003), improving the signal shaping at the transmitter (Clerckx et al., 2004), and
grouping the transmitter antennas combined with space-time coding (Chen and
Haimovich, 2004; Xia et al., 2005). These approaches usually decrease the overall
transmission rate of the system. The usage of OFDM on spatial multiplexing MIMO
system will not only mitigate the effect of frequency-selectivity of the faded channels
but also enhance the spectrum efficiency of the channel. The OFDM signal will
divide the frequency-selective channel bandwidth into narrower flat channel
bandwidth since OFDM employs several narrowband subcarriers.
The performance of the MIMO-OFDM system is highly dependent on the
accuracy of the channel estimation schemes. The task on this issue is how to design
accurate channel estimation with low complexity and low symbol overhead on the
transmission. The most accurate channel estimation is pilot-symbol assisted (PSA)
channel estimation where the known symbol sequences at receiver are distributed
along the transmitted frame. This technique introduces high overhead when applied
to MIMO system since the pilot symbols are inserted at every transmitted frame.
Finding the optimal pilot training sequences for MIMO system is another issue that
should be explored. The optimization criteria are in terms of overhead and energy
consumption.
1.3 Objective of the Research
In order to increase the transmission rate and to improve the error rate
performance of MIMO-OFDM over wireless correlated frequency-selective fast
fading channels, the challenge is how to design the coding techniques that exploit the
space, time, and frequency diversity whilst providing full transmission rate (1
symbol/s/Hz). Another challenge is how to increase the channel capacity of the
MIMO OFDM system over time varying and frequency-selective fading channel. In
5
real system, the receiver of MIMO OFDM system requires the channel information
to perform detection and decoding, therefore the channel estimation of the full-rate
space-time coded MIMO OFDM system is another issue that should be investigated.
The objective of the research is to develop a MIMO-OFDM system design
that consist of channel coding, interleaving, space-time-frequency coding, spatial
multiplexer, and channel estimation. The design should fulfill the following features.
(i) Powerful channel code with high code rate and simple encoding and decoding
processes
(ii) Exploit space, time, and frequency diversity that will provide full rate
transmission
(iii) Employ spatial multiplexing to provide high transmission rate
(iv) Deploy low complexity MIMO detector with accurate channel estimation and
low overhead
The MIMO-OFDM system should achieve low bit error rate at low power
transmission (SNR).
1.4 Scope of the Research
The research will develop the MIMO-OFDM system that will function well
in correlated multipath frequency selective fast fading wireless channel. High rate
multidimensional turbo product code (MDTPC) will be used as error correcting code
and also for granting space, time, and frequency diversity in the system. Amplitude
modulator is used to convert the coded bit to the modulated symbols and then
transform to sub-carriers in OFDM block using inverse fast Fourier transformation.
These OFDM symbols will be transmitted trough multiple transmit antenna.
Multiple antennas are also employed at the receiver with OFDM demodulator
at each branch. Fast Fourier transformation (FFT) is used to convert the OFDM
symbols (time domain) to modulated symbols (frequency domain). These modulated
6
symbols composed of transmitted symbols from all transmit antennas and MIMO
detector will be used to separate them again. After computing the soft detected
coded bits, soft iterative decoding will be performed using parallel MDTPC decoder.
The recovery information bits will be obtained by applying hard decision. These bits
will be used for investigating the behavior and performance of the system
The development of the above system consists of several phases. The first
phase is designing high rate MDTPC. Single parity check code (SPC) has been
selected to be used as component code of MDTPC to provide high code rate. The
possible codewords are generated from MDTPC and the mapping functions are
derived. The performance of MDTPC has been improved by developing parallel
iterative MDTPC decoder with weighting feedback. Mathematical analysis and
computer simulation using MATLAB has been developed to study the performance
of MDTPC over additive white Gaussian noise channel (AWGN) and Rayleigh
fading channel.
The second phase is to provide the space, time, and frequency diversity in
MIMO OFDM system by employing the possible codeword sequences of MDTPC.
Space and time diversity has been exploited by transmitting the possible codeword
sequences through different transmit antennas. Frequency diversity is obtained by
employing OFDM modulator at the transmitter. These space-time codes ST-MDTPC
provides full transmission rate (1 symbol/s/Hz). In order to increase the transmission
rate, the spatial multiplexing with antenna grouping defined as AG-SMST-MDTPC-
MIMO-OFDM has been developed. Optimum MIMO detector has been developed
using maximum likelihood (ML) decision criteria, while, sub optimum detector was
designed using zero forcing (ZF) detection. Mathematical models and computer
simulation has been expanded to investigate the system performance in frequency
selective multipath fading channel. The channel response samples are assumed to be
perfectly estimated and available at the receiver.
The final phase of the work is developing the channel estimation for AG-
SMST-MDTPC-MIMO-OFDM system employing pilot symbol sequences. The
search of optimum pilot sequences for least square (LS) adaptation algorithm with
7
regard to mean square error (MSE) criteria has been performed. A recursive LS
(RLS) algorithm is used to enhance the performance of the overall system.
Mathematical model and simulation using MATLAB is extended to investigate the
channel estimation performance and the system performance. The channel is
assumed to be frequency selective fast fading channel and the response samples of
these channels are correlated and Rayleigh distributed random variables.
1.5 Significance of the Work
The proposed AG-SMST-MTDC-MIMO-OFDM system is a baseband
processing part of a transmission (and receiver) system that can be applied to any
existing standard such as the IEEE 802.11a WLAN Standard. The significant works
in this research is developing that can be stated as follows:
• Generating possible codeword sequences of the MDTPC codes and
developing the corresponding mapping functions.
• Developing the full rate space-time code using the possible codeword
sequences of MDTPC for any number of transmit antennas. When
combining with OFDM transmission, the frequency diversity will be
available at the system.
• Developing the spatial multiplexing with antennas grouping while providing
space, time, and frequency diversity.
• Developing the channel estimation by employing pilot symbol assisted
sequences for AG-SMST-MDTPC-MIMO-OFDM system in correlated and
frequency selective fading channel. Optimum pilot sequences criteria are
derived in terms of overhead and energy consumption. Recursive adaptation
algorithm is developed.
The proposed system will generate wireless transmission system with high
transmission rate at multiple the numbers of antenna groups. Furthermore, the system
will endure low bit error rate and require low power transmission at high
8
transmission rate. The system can be easily extended to be applicable to any wireless
communication system standards such as WLAN, DAB, DVB, and DSRC.
1.6 Thesis Outline
The thesis is organized and distributed into seven chapters. CHAPTER 1
introduces to the general idea of the research and provides an overview of the thesis
that includes the background, problem, objective, and scope of the research.
CHAPTER 2 studies and reviews the previous works related to this research. The
study covers state of the art of the developing system and also the recent related
works in references. Some important findings are presented and analyzed.
CHAPTER 3 describes the proposed MDTPC and its parallel decoder. In
this chapter, the possible codeword sequences of MDTPC are generated based on the
dimension-based reading order. The mapping functions for generating the possible
codeword from MDTPC codeword sequences are derived. Parallel MDTPC decoder
with weighting extrinsic information feedback is proposed. The performance of the
single parity check MDTPC with parallel decoder is studied through mathematical
analysis and computer simulation using MATLAB.
CHAPTER 4 designs a new space-time multidimensional product coded
(ST-MDTPC) system employing the possible codeword of MDTPC. The MIMO
receiver using ML detector and ZF detector are developed and analyzed. The
analytical link channel capacity is derived. Application of the ST-MDTPC in OFDM
system is investigated in frequency selective fading channel.
CHAPTER 5 presents the spatial multiplexing ST-MDTPC-MIMO scheme
which is an extension of the ST-MDTPC schemes (chapter three) with multiple
groups of transmit antennas (AG-SMST-MDTPC-MIMO). The analytical channel
capacity is derived. Application over OFDM channel is performed and investigated.
9
CHAPTER 6 presents the channel estimation of the AG-SMST-MDTPC-
OFDM system using adaptive LS algorithm based on MSE criteria. The optimum
pilot training criteria are derived for distinct pilot symbols types. Channel estimation
enhancement is developed using recursive LS and frequency domain analysis is
presented.
CHAPTER 7 concludes the thesis report and suggests the potential and
possible future works.
210
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