PhD thesis - Decision feedback equalization and channel estimation for SC-FDMA

Decision-Feedback Equalization and
Channel Estimation for Single-Carrier
Frequency Division Multiple Access
Gillian Huang
July 2011
A dissertation submitted to the University of Bristol in accordance with the
requirements of degree of Doctor of Philosophy in the Faculty of Engineering
Department of Electrical and Electronic Engineering

Abstract
Long-Term Evolution (LTE) is standardized by the 3rd Generation Partnership
Project (3GPP) to meet the customers’ need of high data-rate mobile communications
in the next 10 years and beyond. A popular technique, orthogonal frequency division
multiple access (OFDMA), is employed in the LTE downlink. However, the high peak-to-
average ratio (PAPR) of OFDMA transmit signals leads to low power efficiency that
is particular undesirable for power-limited mobile handsets. Single-carrier frequency
division multiple access (SC-FDMA) is employed in the LTE uplink due to its inherent
low-PAPR property, simple frequency domain equalization (FDE) and flexible resource
allocation. Working within the physical (PHY) layer, this thesis focuses on decision-feedback
equalization (DFE) and channel estimation for SC-FDMA systems.
In this thesis, DFE is investigated to improve the equalization performance of SC-FDMA.
Hybrid-DFE and iterative block decision-feedback equalization (IB-DFE) are
considered. It is shown that hybrid-DFE is liable to error propagation, especially in
channel-coded systems. IB-DFE is robust to error propagation due to the feedback (FB)
reliability information. Since the FB reliability is the key to optimize the performance of
IB-DFE, but is generally unknown at the receiver, FB reliability estimation techniques
are presented.
Furthermore, several transform-based channel estimation techniques are presented.
Various filter design algorithms for discrete Fourier transform (DFT) based channel
estimation are presented and a novel uniform-weighted filter design is derived. Also,
channel estimation techniques based on different transforms are provided and a novel
pre-interleaved DFT (PI-DFT) scheme is presented. It is shown that SC-FDMA em-ploying
the PI-DFT based channel estimator gives a close error rate performance to
the optimal linear minimum mean square error (LMMSE) channel estimator but with
a much lower complexity. In addition, a novel windowed DFT-based noise variance
estimator that remains unbiased up to an SNR of 50dB is presented.
Finally, pilot design and channel estimation schemes for uplink block-spread code
division multiple access (BS-CDMA) are presented. It is demonstrated that the recently
proposed bandwidth-efficient BS-CDMA system is a member of the SC-FDMA family.
From the viewpoint of CDMA systems, novel pilot design and placement schemes are
proposed and a channel tracking algorithm is provided. It is shown that the performance
of the proposed schemes remain robust at a Doppler frequency of 500Hz, while the pilot
block scheme specified in the LTE uplink fails to work in such a rapidly time-varying
channel.

Acknowledgements
During four years of study in the Centre for Communications Research at the Uni-versity
of Bristol, I was very fortunate to work with many distinguished researchers. I
would like to take this opportunity to sincerely thank my supervisors, Prof. Andrew
Nix and Dr. Simon Armour, for their endless enthusiasm and encouragement. Having
a meeting with them is always inspiring and enjoyable. Their confidence in me and my
ability to conduct good research is much appreciated.
I would like to thank Prof. Joe McGeehan for his support throughout my PhD study
and giving me the opportunity to work in Toshiba TRL Bristol in my fourth year of
PhD. A special thanks goes to my mentors at TRL, Dr. Justin Coon and Dr. Yue
Wang, for their kindly support and encouragement that led to the novel pilot design
schemes detailed in Chapter 6. I am thankful to many colleagues at the University of
Bristol and TRL for participating in discussions that have helped me solve the problems
and improve my work.
I would like to thank my parents and my sister for their unconditional patience and
love in all these years. Moreover, I would like to thank all my friends, who has made
my life in Bristol enjoyable and unforgettable. Finally, the completion of this thesis
would not have been possible without the merciful blessing and provision of God.
v

Author’s Declaration
I declare that the work in this dissertation was carried out in accordance with the
requirements of the University’s Regulations and Code of Practice for Research Degree
Programmes and that it has not been submitted for any other academic award. Except
where indicated by specific reference in the text, the work is the candidate’s own work.
Work done in collaboration with, or with the assistance of, others, is indicated as such.
Any views expressed in the dissertation are those of the author.
SIGNED: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . DATE: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Copyright
Attention is drawn to the fact that the copyright of this thesis rests with the author.
This copy of the thesis has been supplied on the condition that anyone who consults it
is understood to recognize that its copyright rests with its author and that no quotation
from the thesis and no information derived from it may be published without the prior
written consent of the author. This thesis may be made available for consultation
within the University Library and may be photocopied or lent to other libraries for the
purpose of consultation.
vii

Contents
List of Figures xvii
List of Tables xix
List of Abbreviations xxiv
1 Introduction 1
1.1 3GPP Long-Term Evolution (LTE) . . . . . . . . . . . . . . . . . . . . . 2
1.2 Thesis Overview and Key Contributions . . . . . . . . . . . . . . . . . . 4
1.3 Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.4 Variable Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2 Radio Channel Propagation and Broadband Wireless Communica-tions
9
2.1 Radio Channel Propagation . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.1.1 Large-Scale Fading . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.1.2 Small-Scale Fading . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.1.2.1 Rayleigh Fading and Rician Fading . . . . . . . . . . . 12
2.1.2.2 Delay-Dispersive Channel . . . . . . . . . . . . . . . . . 16
2.1.2.3 Time-Varying Channel . . . . . . . . . . . . . . . . . . 18
2.2 Mitigation and Broadband Wireless Communication Systems . . . . . . 21
2.2.1 Mitigation Techniques . . . . . . . . . . . . . . . . . . . . . . . . 21
2.2.2 Broadband Wireless Communication Systems . . . . . . . . . . . 22
2.3 Simulation Verification . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.3.1 Error Probability Derivation . . . . . . . . . . . . . . . . . . . . 25
2.3.1.1 Error Probability of BPSK in an AWGN Channel . . . 25
2.3.1.2 Error Probability of BPSK in a Flat Rayleigh Fading
Channel . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
ix

CONTENTS
2.3.2 Simulation Model Description and Verification . . . . . . . . . . 27
2.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3 Single-Carrier Frequency Division Multiple Access 31
3.1 Mathematical Description of Single-Carrier FDMA Systems . . . . . . . 32
3.2 Linear Frequency Domain Equalization . . . . . . . . . . . . . . . . . . . 36
3.2.1 Linear ZF-FDE and MMSE-FDE Design . . . . . . . . . . . . . . 37
3.2.2 Performance Comparison of IFDMA, LFDMA and OFDMA with
FDE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.3 Peak-to-Average Power Ratio . . . . . . . . . . . . . . . . . . . . . . . . 41
3.3.1 PAPR of SC-FDMA Transmit Signals . . . . . . . . . . . . . . . 42
3.3.1.1 PAPR Analysis of Multi-Carrier and SC-FDMA Signals 42
3.3.1.2 Obtaining the PAPR via Oversampling the Transmit
Signal . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
3.3.1.3 PAPR Simulation Results and Discussion . . . . . . . . 45
3.3.2 PAPR Reduction via Frequency Domain Spectrum Shaping . . . 47
3.3.2.1 Description of Frequency Domain Spectrum Shaping . . 47
3.3.2.2 PAPR Simulation Results with Raised Cosine Spectrum
Shaping . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
3.3.3 PAPR Reduction Modulation Scheme . . . . . . . . . . . . . . . 51
3.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
4 Decision Feedback Equalization for Single-Carrier FDMA 55
4.1 Matched Filter Bound . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
4.1.1 Matched Filter Bound Operation . . . . . . . . . . . . . . . . . . 57
4.1.2 Discussion on Analytical MFB performance . . . . . . . . . . . . 60
4.1.3 Performance Comparison of LE and MFB . . . . . . . . . . . . . 60
4.2 Hybrid Decision-Feedback Equalizer . . . . . . . . . . . . . . . . . . . . 62
4.2.1 Description of Hybrid Decision-Feedback Equalizer Design . . . . 62
4.2.2 Performance of SC-FDMA with Hybrid-DFE . . . . . . . . . . . 65
4.3 Iterative Block Decision-Feedback Equalizer . . . . . . . . . . . . . . . . 68
4.3.1 Description of IB-DFE Design and Operation . . . . . . . . . . . 68
4.3.2 Feedback Reliability Estimation for IB-DFE . . . . . . . . . . . . 72
4.3.2.1 Feedback Reliability Derivation for QPSK . . . . . . . . 73
4.3.2.2 Gaussian CDF Approximation for 16QAM . . . . . . . 74
4.3.2.3 Lookup Table for Systems with Channel Coding . . . . 76
x

CONTENTS
4.3.3 Performance of SC-FDMA with IB-DFE . . . . . . . . . . . . . . 77
4.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
5 Transform-Based Channel Estimation for Single-Carrier FDMA 85
5.1 LS and LMMSE Channel Estimation . . . . . . . . . . . . . . . . . . . . 86
5.1.1 LS Channel Estimator . . . . . . . . . . . . . . . . . . . . . . . . 87
5.1.2 MSE of LS Channel Estimator and Optimal Pilot Sequence . . . 88
5.1.3 LMMSE Channel Estimator . . . . . . . . . . . . . . . . . . . . . 89
5.1.4 Performance of LS and LMMSE Channel Estimator . . . . . . . 90
5.2 DFT-Based Channel Estimation . . . . . . . . . . . . . . . . . . . . . . 92
5.2.1 Generalized DFT-Based Channel Estimator . . . . . . . . . . . . 93
5.2.2 Denoise Filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
5.2.3 Uniform-Weighted Filter . . . . . . . . . . . . . . . . . . . . . . . 95
5.2.4 MMSE Filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
5.2.5 Simulation Results and Discussion . . . . . . . . . . . . . . . . . 98
5.3 Transform-Based Channel Estimation . . . . . . . . . . . . . . . . . . . 100
5.3.1 Generalized Transform-Based Channel Estimator . . . . . . . . . 100
5.3.2 Pre-Interleaved DFT-Based Channel Estimator . . . . . . . . . . 101
5.3.3 DCT-Based Channel Estimator . . . . . . . . . . . . . . . . . . . 104
5.3.4 KLT-Based Channel Estimator . . . . . . . . . . . . . . . . . . . 104
5.3.5 Derivation of Equalized SNR Gain . . . . . . . . . . . . . . . . . 105
5.4 DFT-Based Noise Variance Estimation . . . . . . . . . . . . . . . . . . . 109
5.4.1 Low-Rank DFT-Based Noise Variance Estimator . . . . . . . . . 110
5.4.2 Windowed DFT-Based Noise Variance Estimator . . . . . . . . . 110
5.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
6 Pilot Design and Channel Estimation for Uplink BS-CDMA 117
6.1 Pilot Block Based Channel Estimation for Uplink BS-CDMA . . . . . . 118
6.1.1 System Description . . . . . . . . . . . . . . . . . . . . . . . . . . 119
6.1.2 Time Domain LS Channel Estimator . . . . . . . . . . . . . . . . 122
6.1.3 MSE Derivation of Pilot Block Based Channel Estimation . . . . 123
6.1.3.1 Minimum MSE of the Time Domain LS Channel Esti-mator
and Optimal Pilot Sequence . . . . . . . . . . . . 124
xi

CONTENTS
6.1.3.2 MSE of the Pilot Block Scheme in a Time-Varying Chan-nel
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
6.2 Pilot Symbol Based Channel Estimation for Uplink BS-CDMA . . . . . 127
6.2.1 System Description . . . . . . . . . . . . . . . . . . . . . . . . . . 128
6.2.2 Time Domain LS Channel Estimation and Pilot Design Criterion 131
6.2.3 Pilot Design and Placement Schemes . . . . . . . . . . . . . . . . 133
6.2.3.1 Scheme-1: Single Pilot Symbol Placement . . . . . . . . 133
6.2.3.2 Scheme-2: Multiple Interleaved Pilot Symbol Placement 134
6.2.3.3 Scheme-3: Superimposed Pilot Placement . . . . . . . . 135
6.2.4 RLS Channel Tracking Algorithm in a Time-Varying Channel . . 135
6.2.4.1 RLS Channel Tracking Algorithm . . . . . . . . . . . . 136
6.2.4.2 Finding the Optimal RLS Forgetting Factor . . . . . . 138
6.3 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
7 Conclusions 145
7.1 Thesis Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
7.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
A Comparison of an L-tap i.i.d. Complex Gaussian Channel Model and
the 3GPP SCME 149
B Mitigating the BER Floor due to the Denoise Channel Estimator 153
C Simulation Results with Sample-Based Channel Variation 155
D List of Publications 157
Bibliography 159
xii

List of Figures
2.1 Received signal power as a function of antenna displacement based on
a free space path loss model. The transmit signal power is 1mW (i.e.
0dBm). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.2 PDF of the received signal envelope for Rayleigh and Rician fading chan-nels,
where the mean power of the NLoS multipath signal is 22 = 1. . . 15
2.3 CDF of the received signal power relative to the mean received signal
power for Rayleigh and Rician fading channels. . . . . . . . . . . . . . . 15
2.4 (a) Delay-dispersive channel (an 8-tap i.i.d. complex Gaussian channel).
(b) Corresponding frequency-selective fading channel. . . . . . . . . . . 17
2.5 Received channel power relative to the mean received channel power as
a function of d normalized to , in an one-tap channel with Jakes model. 19
2.6 (a) BPSK transmit data symbols. (b) Conditional PDFs of the received
BPSK signals in an AWGN channel. . . . . . . . . . . . . . . . . . . . . 25
2.7 Block diagram of a baseband SC simulation model with block-based
transmission/reception. . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.8 Analytic and simulated error probabilities of BPSK in AWGN and flat
Rayleigh fading channels. . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.1 Block diagram of SC-FDMA system. . . . . . . . . . . . . . . . . . . . . 32
3.2 BER comparison of IFDMA with ZF-FDE and MMSE-FDE in an 8-tap
i.i.d. complex Gaussian channel. . . . . . . . . . . . . . . . . . . . . . . 40
3.3 BER comparison of IFDMA, LFDMA and OFDMA with MMSE-FDE
in an 8-tap i.i.d. complex Gaussian channel. . . . . . . . . . . . . . . . . 40
3.4 Example of (a) IFDMA transmit signal, and (b) LFDMA transmit signal. 43
3.5 Comparison of QPSK signal amplitude. (a) Nyquist-rate QPSK symbols.
(b) Continuous SC transmit signals after oversampling the Nyquist-rate
QPSK symbols. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
xiii

LIST OF FIGURES
3.6 PAPR comparison of SC-FDMA employing interleaved, localized, and
randomized subcarrier mapping schemes (denoted as IFDMA, LFDMA
and RFDMA) with QPSK signaling. . . . . . . . . . . . . . . . . . . . . 46
3.7 PAPR comparison of IFDMA and OFDMA with QPSK and 16QAM. . 46
3.8 Block diagram of frequency domain spectrum shaping in SC-FDMA. . . 48
3.9 Equivalent RC spectrum with ro = 0.5, where K = 18, Kd = 18 and
N = 90. (a) Interleaved subcarrier mapping. (b) Localized subcarrier
mapping. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
3.10 PAPR of SC-FDMA employing RC frequency domain spectrum shaping
with QPSK signaling. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
3.11 PAPR of SC-FDMA employing RC frequency domain spectrum shaping
with 16QAM signaling. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
3.12 Constellation diagram of various baseband modulation schemes. . . . . . 52
3.13 PAPR comparison of BPSK, QPSK, /2-BPSK and /4-QPSK (with
K = 128, N = 512 and IFDMA transmission scheme). . . . . . . . . . . 53
4.1 Block diagram of block based frequency domain MFB operation for SC
systems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
4.2 BER comparison of SC-FDMA employed MMSE-LE and MFB in a 8-tap
i.i.d. complex Gaussian channel with QPSK signaling. . . . . . . . . . . 61
4.3 BER comparison of SC-FDMA employed MMSE-LE and MFB in a 8-tap
i.i.d. complex Gaussian channel with 16QAM signaling. . . . . . . . . . 61
4.4 Block diagram of Hybrid-DFE at the receiver for a SC system . . . . . . 63
4.5 BER of IFDMA employed hybrid-DFE in a 8-tap i.i.d complex Gaussian
channel. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
4.6 BER of LFDMA employed hybrid-DFE in a 8-tap i.i.d complex Gaussian
channel. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
4.7 BER of IFDMA employed hybrid DFE in a 8-tap i.i.d complex Gaussian
channel with 1/2-rate convolutional channel coding. . . . . . . . . . . . 67
4.8 Block diagram of IB-DFE reception for a SC system. . . . . . . . . . . . 69
4.9 Hard-decision error pattern for QPSK with x(s = 0) = √1 (1 + j) being
2
the transmit symbol. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
4.10 Linear regression with cj = aj + b, where a = 0.0756 and b = 0.4055. . 75
4.11 Reliability approximation for uncoded 16QAM using a Gaussian CDF
2 + 1
2erf(aj + b), where a = 0.0756 and b = 0.4055. . . 75
model, i.e. ˆj = 1
xiv

LIST OF FIGURES
4.12 Block diagram of the proposed FB reliability estimation scheme for IB-DFE
in a channel coded system. . . . . . . . . . . . . . . . . . . . . . . 76
4.13 Re-encoded reliability lookup table for QPSK and 16QAM when a 1/2-
rate convolutional encoder (133,171) and a soft-decision Viterbi decoder
are used. Simulation is performed in an AWGN channel. . . . . . . . . . 77
4.14 BER of IFDMA employing IB-DFE in a 8-tap i.i.d complex Gaussian
channel with QPSK. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
4.15 BER of IFDMA employing IB-DFE in a 8-tap i.i.d complex Gaussian
channel with 16QAM. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
4.16 Coded BER of IFDMA employing IB-DFE in a 8-tap i.i.d complex Gaus-sian
channel with QPSK, where 1/2-rate convolutional channel coding
is used. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
4.17 Coded BER of IFDMA employing IB-DFE in a 8-tap i.i.d complex Gaus-sian
channel with 16QAM, where 1/2-rate convolutional channel coding
is used. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
5.1 Slot structure specified in the LTE uplink. . . . . . . . . . . . . . . . . . 86
5.2 MSE of LS and LMMSE channel estimators for LFDMA and IFDMA in
a 8-tap i.i.d. complex Gaussian channel. . . . . . . . . . . . . . . . . . . 91
5.3 BER of LFDMA with LS and LMMSE channel estimators in a 8-tap
5.4 BER of IFDMA with LS and LMMSE channel estimators in a 8-tap i.i.d.
complex Gaussian channel. . . . . . . . . . . . . . . . . . . . . . . . . . 92
5.5 (a) Frequency domain channel response on user subcarriers. (b) Equiv-alent
time domain channel response obtained via IDFT. . . . . . . . . . 93
5.6 Block diagram of a DFT-based channel estimator. . . . . . . . . . . . . 94
5.7 MSE of different DFT-based channel estimators for LFDMA in a 8-tap
5.8 BER of LFDMA with different DFT-based channel estimators in a 8-tap
i.i.d. complex Gaussian channel, where baseband data modulation is
QPSK. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
5.9 Block diagram of a transform-based channel estimator. . . . . . . . . . . 101
5.10 Block diagram of a pre-interleaved DFT-based channel estimator. . . . . 102
5.11 Frequency domain channel response: (a) Before interleaving. (b) After
interleaving. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
xv

LIST OF FIGURES
5.12 Transform domain channel response: (a) DFT, (b) PI-DFT, (c) DCT
and (d) KLT. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
5.13 MSE comparison of the transform-based channel estimators with MMSE
scalar noise filtering in a 8-tap i.i.d. complex Gaussian channel. . . . . . 108
5.14 BER of LFDMA with different transform-based channel estimators in a
8-tap i.i.d. complex Gaussian channel. QPSK modulation is used for
data symbols. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
5.15 Equalized SNR gain at the MMSE-FDE output due to the use of the
transform-based channel estimator over the LS channel estimator. . . . 109
5.16 Block diagram of a windowed DFT-based noise variance estimator. . . . 110
5.17 The time domain window function (wn). The black solid line denotes
a rectangular window and the red dotted line denotes a window with
smooth transition. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
5.18 Frequency domain filter response of time domain rectangular and RC
window functions (where a roll-off factor is ro = 0.25). . . . . . . . . . . 112
5.19 Performance comparison of DFT-based noise variance estimators in an
8-tap i.i.d. complex Gaussian channel. . . . . . . . . . . . . . . . . . . . 114
5.20 BER comparison of four LFDMA systems (listed in Table 5.1) in an
8-tap i.i.d. complex Gaussian channel with 16QAM modulation. . . . . 114
6.1 Block diagram of BS-CDMA transceiver architecture. . . . . . . . . . . 119
6.2 MSE of the pilot block based channel estimation scheme for BS-CDMA
in a time-varying 8-tap i.i.d. complex Gaussian channel. . . . . . . . . . 126
6.3 BER of BS-CDMA employing pilot block based channel estimation in a
time-varying 8-tap i.i.d. complex Gaussian channel, where data modu-lation
is QPSK. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
6.4 Block diagram of the uplink BS-CDMA transceiver architecture with the
proposed pilot transmission. . . . . . . . . . . . . . . . . . . . . . . . . . 128
6.5 Proposed pilot design and placement schemes for uplink BS-CDMA. . . 134
6.6 PAPR of the BS-CDMA transmit signal with different transmit pilot
power in the superimposed pilot placement scheme, where K = 128
and QPSK are used. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
6.7 The heuristically-optimal RLS forgetting factor as a function of SNR
and Doppler frequency. The solid line and the dotted line represent the
transmit pilot power of = 1 and = 16 respectively. . . . . . . . . . . 139
xvi

LIST OF FIGURES
6.8 MSE of different pilot design and channel estimation schemes in a 8-tap
i.i.d. complex Gaussian channel at fd = 50Hz. . . . . . . . . . . . . . . . 141
6.9 BER of BS-CDMA employing different pilot design and channel estima-tion
schemes in a 8-tap i.i.d. complex Gaussian channel at fd = 50Hz. . 141
i.i.d. complex Gaussian channel at fd = 250Hz. . . . . . . . . . . . . . . 142
i.i.d. complex Gaussian channel at fd = 500Hz. . . . . . . . . . . . . . . 143
A.1 Channel PDPs: (a) 8-tap i.i.d complex Gaussian model. (b) 3GPP urban
macro SCME. (c) 3GPP urban micro SCME. The sample period is TS =
0.1302μs and the mean power of all the channel taps is normalized to 1. 150
A.2 BER comparison of SC-FDMA with MMSE-FDE in 8-tap i.i.d. complex
Gaussian channel model, 3GPP urban macro SCME and 3GPP urban
micro SCME. The baseband modulation scheme is QPSK. . . . . . . . . 152
C.1 BER of BS-CDMA employing the proposed pilot design and channel
estimation schemes in a 8-tap i.i.d. complex Gaussian channel with the
Jakes model at fd = 500Hz. The dashed line assumes the static channel
response within a block. The solid line with markers assumes that the
channel response varies from sample to sample within a block. . . . . . . 156
xvii

List of Tables
3.1 A complexity comparison of FDE and TDE in terms of the required
complex multipliers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3.2 Simulation parameters for IFDMA, LFDMA and OFDMA systems. . . . 39
3.3 Comparison of the PAPR and the bandwidth efficiency via RC spectrum
shaping. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
4.1 A complexity and performance comparison of MMSE-FDE (i.e. IB-DFE(
1) at the first iteration), IB-DFE(2) at the second iteration and
hybrid-DFE in the uncoded system. . . . . . . . . . . . . . . . . . . . . 80
4.2 A complexity and performance comparison of MMSE-FDE (i.e. IB-DFE(
1) at the first iteration), IB-DFE(2) at the second iteration and
hybrid-DFE in the channel coded system. . . . . . . . . . . . . . . . . . 82
5.1 Four LFDMA systems used in the simulation. . . . . . . . . . . . . . . . 113
6.1 Simulation parameters for the pilot block scheme and the proposed pilot
design schemes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
A.1 Comparison of mean excess delay ( ), RMS delay spread (RMS) and
coherence bandwidth (f0) with (a) 8-tap i.i.d complex Gaussian model,
(b) 3GPP urban macro SCME and (c) 3GPP urban micro SCME. . . . 151
xix

List of Abbreviations
1G First Generation
2D Two-Dimensional
2G Second Generation
3G Third Generation
3GPP Third Generation Partnership Project
4G Fourth Generation
AM/AM Amplitude-to-Amplitude Modulation
AM/PM Amplitude-to-Phase Modulation
AMPS Analogue Mobile Phone System
AWGN Additive White Gaussian Noise
BER Bit Error Rate
bps bits per second
BPSK Binary Phase Shift Keying
BS-CDMA Block Spread Code Division Multiple Access
CAZAC Constant Amplitude Zero Auto-Correlation
CCDF Complementary Cumulative Distribution Function
CDD Cyclic Delay Diversity
CDF Cumulative Distribution Function
CDM Code Division Multiplexing
CDMA Code Division Multiple Access
CDS Channel-Dependent Scheduling
CIBS-CDMA Chip-Interleaved Block Spread Code Division Multiple Access
CoMP Coordinated Multi-Point Transmission/Reception
CP Cyclic Prefix
DAB Digital Audio Broadcasting
DC Direct Current
DCT Discrete Cosine Transform
xxi

LIST OF ABBREVIATIONS
DFE Decision-Feedback Equalization
DFT Discrete Fourier Transform
DVB Digital Video Broadcasting
FB Feed-Back
FDE Frequency Domain Equalization
FDM Frequency Division Multiplexing
FDMA Frequency Division Multiple Access
FF Feed-Forward
FFT Fast Fourier Transform
FH Frequency Hopping
GSM Global System for Mobile Communications
HSDPA High Speed Downlink Packet Access
HSPA+ Evolved High Speed Packet Access
HSUPA High Speed Uplink Packet Access
IB-DFE Iterative Block Decision-Feedback Equalization
IBI Inter-Block Interference
ICI Inter-Carrier Interference
IDFT Inverse Discrete Fourier Transform
IEEE Institute of Electrical and Electronics Engineers
IFDMA Interleaved Frequency Division Multiple Access
i.i.d. independent and identically distributed
ISI Inter-Symbol Interference
KLT Karhunen-Lo`eve transform
LE Linear Equalization
LFDMA Localized Frequency Division Multiple Access
LMMSE Linear Minimum Mean-Square Error
LoS Light-of-Sight
LS Least Squares
LTE Long-Term Evolution
MC Multi-Carrier
MFB Matched Filter Bound
MIMO Multiple-Input Multiple-Output
MLSE Maximum Likelihood Sequence Estimation
MMSE Minimum Mean-Square Error
MRC Maximal-Ratio Combining
MSE Mean Squared Error
xxii

MUI Multi-User Interference
NLoS Non Light-of-Sight
OFDM Orthogonal Frequency Division Multiplexing
OFDMA Orthogonal Frequency Division Multiple Access
PA Power Amplifier
PAPR Peak-to-Average Power Ratio
PDF Probability Density Function
PDP Power Delay Profile
PHY Physical
PI-DFT Pre-Interleaved Discrete Fourier Transform
QAM Quadrature Amplitude Modulation
QPSK Quadrature Phase Shift Keying
RC Raised Cosine
RF Radio frequency
RFDMA Randomized Frequency Division Multiple Access
RLS Recursive Least Squares
RMS Root Mean Square
SC Single-Carrier
SCME Spatial Channel Model Extension
SCBC Space-Code Block Code
SC-FDE Single-Carrier Frequency Domain Equalization
SC-FDMA Single-Carrier Frequency Division Multiple Access
SFBC Space-Frequency Block Code
SIC Successive Interference Cancellation
SISO Single-Input Single-Output
SINR Signal-to-Interference-plus-Noise Ratio
SM Spatial Multiplexing
SNR Signal-to-Noise Ratio
STBC Space-Time Block Code
TACS Total Access Communication System
TDE Time Domain Equalization
TDM Time Division Multiplexing
TDMA Time Division Multiple Access
UMTS Universal Mobile Telecommunications System
WCDMA Wideband Code Division Multiple Access
Wi-Fi Wireless Fidelity
xxiii

WiMAX Worldwide Interoperability for Microwave Access
WLAN Wireless Local Area Network
WMAN Wireless Metropolitan Area Network
ZF Zero Forcing
xxiv

Chapter 1
Introduction
Communication over a wireless medium using electromagnetic waves is one of the great-est
scientific achievements and has become indispensable in modern life. In 1895,
Marconi built and demonstrated the first radio telegraph, and the era of wireless com-munications
thus began. From Marconi’s first telegraph, to Shannon’s communication
theory [1] and the recent capacity-approaching error-correcting codes [2], wireless com-munication
has attracted considerable research and practical interest for over a cen-tury.
Today, wireless communication systems can transmit/receive voice, image and
video data all over the globe. Moreover, wireless communication makes the demand of
accessing the Internet anytime, anywhere possible.
‘First Generation’ (1G) mobile communication systems using analogue technology
arrived in the 1980s, e.g. the Analogue Mobile Phone System (AMPS) used in America
and the Total Access Communication System (TACS) used in parts of Europe. How-ever,
the number of subscribers were limited at that time due to costly heavy handsets
and spectrally inefficient modulation. Global roaming first became possible with the
development of the digital ‘Second Generation’ (2G) Global System for Mobile Com-munications
(GSM). In the late 1990s, GSM achieved worldwide commercial success.
GSM phones were small and affordable with a long battery life.
Followed by the success of GSM, the Universal Mobile Telecommunications System
(UMTS) [3] is the ‘Third Generation’ (3G) mobile communication system developed
by the 3rd Generation Partnership Project (3GPP). UMTS employed wideband code-division
multiple access (WCDMA) technology to offer a higher data-rate for mobile
communications. Hence, the 3G handset is more than just a mobile phone. Various
applications such as video-telephony, Internet access and file transfer are supported
in 3G devices. The evolution of mobile communications continues. 3GPP has been
1

Chapter 1. Introduction
developing a beyond-3G system called Long-Term Evolution (LTE) [4] to meet the
customers’ need for the next 10 years and beyond.
The evolution of wireless communications also takes place in the Institute of Electri-cal
and Electronics Engineers (IEEE). Examples include the IEEE 802.11 [5–8], known
asWi-Fi1, and the IEEE 802.16 [9], known asWorldwide Interoperability for Microwave
Access (WiMAX). Wi-Fi networks provide high data-rate communication over a fixed
Wireless Local Area Network (WLAN). Today,WiFi networks are widely used in homes,
offices, coffee shops and hotels for wireless Internet access. To overcome the restriction
of fixed access, WiMAX aims to provide high data-rate mobile communication over a
Wireless Metropolitan Area Network (WMAN). LTE and WiMAX are emerging tech-nologies
with similar targets and transmission techniques, and both are paving the way
to the development of ‘Fourth Generation’ (4G) mobile communication systems.
The rest of this chapter is organized as follows. The features and requirements of
the 3GPP LTE standard are highlighted in Section 1.1. A thesis overview and the key
contributions of this work are given in Section 1.2. The mathematical notation and
variables used throughout this thesis are defined in Section 1.3 and Section 1.4.
1.1 3GPP Long-Term Evolution (LTE)
The 3GPP standards are structured as Releases. The first release of UMTS (Release
99 ) in theory enabled 2Mbps, but in practice gave 384kbps [3]. Several releases were
then specified as enhancements to the first release. High Speed Downlink Packet Access
(HSDPA) in Release 5 supports a data rate up to 14Mbps in the downlink and High
Speed Uplink Packet Access (HSUPA) in Release 6 supports data rates up to 5.76Mbps
in the uplink. Through the use of multiple-input multiple output (MIMO) techniques
and higher order 64 quadrature amplitude modulation (64QAM), Evolved High-Speed
Packet Access (HSPA+) in Release 7 pushes the data rate up to 56Mbps in the downlink
and 22Mbps in the uplink. The 3G operators have started rolling out HSPA+ networks
in Europe, Australia and the North America.
Since the enhancements based on WCDMA technology have become a bottleneck, a
new physical (PHY) layer design and radio network architecture are required to provide
a high data-rate, low-latency and packet-optimized service for the next 10 years and
beyond. Hence, LTE is introduced as Release 8 in the 3GPP standard, and the targets
of the LTE are [10]:
1Wi-Fi is an abbreviation of wireless fidelity.
2

1.1. 3GPP Long-Term Evolution (LTE)
• Significantly increased peak data rate, i.e. 100Mbps (downlink) and 50Mbps
(uplink) within a 20MHz spectrum allocation.
• Significantly improved spectrum efficiency, i.e. 3-4 times HSDPA for the downlink
and 2-3 times HSUPA for the uplink.
• Increased cell-edge throughput as well as average throughput (to deliver a more
uniform user experience across the cell area).
• Control plane latency (transition time to active state) less than 100ms (for idle
to active).
• Flexible and scalable bandwidth of 1.25, 2.5, 5, 10, 15 and 20MHz.
• Reasonable complexity and power consumption for the mobile terminal.
• System should be optimized at low mobile speed from 0 to 15km/hr. High mobile
speeds between 15 and 120km/hr should be supported with high performance.
Communication across the cellular network should be maintained at speeds from
120 to 350km/hr.
As mentioned previously, an evolution of the PHY layer design is required in LTE
to achieve the targeted high data-rate. As a popular choice in the emerging technolo-gies,
orthogonal frequency division multiple access (OFDMA) is employed in the LTE
donwlink and WiMAX (both downlink and uplink) due to its simple frequency do-main
equalization (FDE) and flexible resource allocation. Since the main drawback of
OFDMA is its high peak-to-average power ratio (PAPR), which results in low power
amplifier (PA) efficiency, single-carrier frequency division multiple access (SC-FDMA)
is employed in the LTE uplink due to its low-PAPR. For the power-limited mobile
handsets, the use of SC-FDMA enables power-efficient uplink transmission and thus
improves the battery life [11].
As the first release of LTE standard was completed in the end of 2008, 3GPP has be-gun
studying the further evolution based on the LTE, which is known as LTE-Advanced
(Release 10 ) [12]. The LTE-Advanced aims to fulfill the International Mobile Telecom-munications
(IMT)-Advanced 4G requirements [13], and its targeted peak data rates are
up to 1Gbps on the downlink and 500Mbps on the uplink [14]. The enhanced technolo-gies
currently being considered in the LTE-Advanced included spectrum aggregation,
multi-antenna sloutions, coordinated multi-point transmission/reception (CoMP) and
relaying [12]. Similar to the migration from the first release of UMTS to the later
3

HSPA technologies, the LTE-Advanced is developed to be backwards compatible with
the LTE (Release 8 ).
1.2 Thesis Overview and Key Contributions
As the bandwidth and data rate increases, the signal dispersion caused by a delay-dispersive
channel results in inter-symbol interference (ISI). To recover the distorted
received signal, equalization is required at the receiver for ISI mitigation [15] and the
channel response needs to be estimated for equalizer coefficient calculation. Therefore,
equalization and channel estimation are key steps in the PHY layer of all broadband
wireless communication systems.
Since SC-FDMA is a relative new transmission technique, this thesis focuses on
the investigation of SC-FDMA systems. Emphasis is placed on PAPR characteristics,
decision-feedback equalization (DFE), channel estimation, pilot design and channel
tracking algorithms in SC-FDMA. The purpose of this thesis is to:
• Stimulate interest in the field of SC-FDMA.
• Provide a clear and concise technical reference for researchers already working on
SC-FDMA and LTE uplink.
• Detail the benefits and design challenges of using SC-FDMA rather than OFDMA.
• Document original work that was conducted in the area of DFE and channel
estimation in an SC-FDMA system.
The thesis is structured as follows:
Chapter 2 : This chapter describes the characteristics of radio channel propagation and
the impact to mobile communication systems. Mitigation techniques are provided. Ex-isting
broadband wireless communication systems based on FDE are discussed, and
some of the key differences between single-carrier (SC) and multi-carrier (MC) systems
are highlighted. Simulation verification is also provided.
Chapter 3 : An overview of SC-FDMA systems is presented. A PAPR comparison
of OFDMA and SC-FDMA signals with different subcarrier mapping and modulation
schemes is presented and discussed. Also, the PAPR reduction techniques for SC-FDMA
signals are provided. The key contributions documented in this chapter are:
4

1.2. Thesis Overview and Key Contributions
• Detailed mathematical description of SC-FDMA systems.
• Detailed explanation and simulation results on the PAPR characteristics of SC-FDMA
signals (published in IEEE PIMRC’07 [16]).
Chapter 4 : This chapter investigates the DFE techniques for SC-FDMA systems. The
performance gap between the matched filter bound (MFB) and linear FDE is high-lighted.
The use of a hybrid-DFE is extended to SC-FDMA and the error propagation
phenomenon is highlighted. Feedback reliability estimation for iterative block decision-feedback
equalization (IB-DFE) is proposed to mitigate error propagation. The key
contributions documented in this chapter are:
• Extending the use of hybrid-DFE to SC-FDMA and addressing the associated
error propagation problem (published in IEEE PIMRC’08 [17]).
• Feedback reliability estimation techniques for IB-DFE (published in IEEE VTC’09-
Fall [18]).
Chapter 5 : Transform-based channel estimation techniques for SC-FDMA are inves-tigated.
Various filter design algorithms for discrete Fourier transform (DFT) based
channel estimation are presented. Furthermore, channel estimation techniques based
on different transforms are provided. Finally, DFT-based noise variance estimation
techniques are described. The novel contributions documented in this chapter are:
• Uniform-weighted filter design for DFT-based channel estimation (a UK patent
application filed in May 2009 [19]).
• Pre-interleaving scheme for DFT-based channel estimation, i.e. PI-DFT based
channel estimation.
• Derivation of the signal-to-noise ratio (SNR) gain/loss at the equalizer output
due to channel estimation error.
• Windowed DFT-based noise variance estimation technique (published in IEEE
VTC’10-Fall [20]).
Chapter 6 : This chapter focuses on pilot design and channel estimation for uplink block
spread code division multiple access (BS-CDMA). The drawback of pilot block based
channel estimation is addressed. Pilot symbol based design and placement schemes for
5

uplink BS-CDMA are proposed. A channel tracking algorithm that enhances the per-formance
in a time-varying channel is presented. The novel contributions documented
in this chapter are:
• Proposing the use of a common pilot spreading code for all users in the uplink
BS-CDMA.
• Derivation of mutually orthogonal pilot design criteria for multi-user interference
(MUI) free uplink channel estimation.
• Pilot symbol based design and placement schemes for uplink BS-CDMA (submit-ted
to IEEE Trans. Veh. Technol. [21]).
Chapter 7 : Conclusions about SC-FDMA and the novel work presented in this thesis
are drawn. Future work in the area of SC-FDMA is discussed.
1.3 Notation
The mathematical notation used throughout this work is provided as follows.
• Bold uppercase fonts are used to denote matrices, e.g. X.
• Bold lowercase fonts are used to denote column vectors, e.g. x.
• Frequency domain variables are identified with a tilde, e.g. ex.
• IN is the N × N identity matrix.
• 0N×M is the N ×M zero matrix.
• (·)∗ denotes the complex conjugate operation.
• (·)T denotes the transpose operation.
• (·)H denotes the Hermitain (conjugate transpose) operation.
• E[·] is the expectation operator.
• | · | is the absolute value operator.
• k·k is the norm operator.
• diag{·} denotes the diagonal entries of a matrix.
6

1.4. Variable Definition
• tr{·} denotes the trace of a matrix.
• ⊗ denotes the Kronecker product operator.
• ℜ[·] denotes the real part of the argument.
• X† = (XHX)−1XH denotes the pseudo inverse of a matrix X.
1.4 Variable Definition
The variables defined in this thesis are kept as consistent as possible. For ease of
reference, the global variables used throughout this work are listed here.
2n
• fc denotes the carrier frequency.
• fd denotes the Doppler frequency.
• ro denotes the roll-off factor of a raised cosine (RC) filter.
•
denotes the instantaneous SNR.
•
denotes the average SNR.
• denotes the noise variance.
• J denotes the cost function in an optimization process.
• L denotes the length of channel delay spread.
• TBLK denotes the transmission block period.
• FK denotes a size-K normalized DFT matrix, where FK(p, q) = e−j 2
K pq for
p, q = 0, . . . ,K − 1.
• Jn
K is defined as a size-K matrix which is obtained by cyclically shifting a size-K
identity matrix downward along its column by n element(s).
7

Chapter 2
Radio Channel Propagation and
Broadband Wireless
Communications
This chapter focuses on the characteristics of the mobile radio channel and the miti-gation
techniques in modern broadband wireless communications. In the application
of wireless communications, the signal propagates over a hostile radio channel, which
leads to signal fading and distortion. Moreover, the received signal is corrupted by
thermal noise generated at the receiver, which is usually modeled as additive white
Gaussian noise (AWGN). Hence, when simulating the physical layer performance of a
wireless communication system, channel distortion and thermal noise are often used as
the primary sources of performance degradation.
The rest of this chapter is organized as follows. Section 2.1 describes the radio chan-nel
propagation. In Section 2.2, the mitigation techniques for combating the channel
fading and distortion are described and the existing broadband wireless communica-tions
systems based on FDE are discussed. In Section 2.3.2, simulation verification is
provided. Section 2.4 summarizes the chapter.
2.1 Radio Channel Propagation
There are two types of mobile channel fading effects; large-scale and small-scale fading.
Large-scale fading represents the average signal power attenuation due to motion over
a large geographical area. Small-scale fading refers to the dynamic changes of signal
amplitude and phase due to a small change of the antenna displacement and orientation,
9

Chapter 2. Radio Channel Propagation and Broadband Wireless Communications
which is as small as a half-wavelength [22]. In a mobile radio channel, the received signal
experiences both large-scale fading and small scale fading.
This section is organized as follows. Section 2.1.1 describes the path loss model
for large-scale fading. Section 2.1.2 describes the statistics and two mechanisms of
small-scale fading.
2.1.1 Large-Scale Fading
The simplest model for large-scale fading is to assume the radio channel propagation
takes place over an ideal free space (i.e. no objects that might absorb or reflect the
radio frequency (RF) energy in the region between the transmit and receive antennas).
In the idealized free space model the signal attenuation as a function of the distance
between the transmit and receive antennas follows an inverse-square law. Let PT and
PR(d) denote the transmit and received signal power respectively, where d denotes the
distance between the transmit and receive antennas in meters. When the antennas are
isotropic, the signal attenuation (or free space path loss) is given by [22]
L0(d) =
PT
PR(d)
=

4d

2
=

4dfc
c
2
(2.1)
where = c
fc
is the wavelength of the propagating signal, fc is the carrier frequency in
Hz and c = 3 × 108m/s is the speed of light.
Suppose the transmit power is PT = 1mW (i.e. 0dBm). Based on the free space
path loss model in (2.1), the received signal power as a function of distance and carrier
frequency is shown in Fig. 2.1. It is shown that the received signal power decreases
as the distance between the transmit and receive antennas increases. Moreover, the
use of a higher carrier frequency gives a larger signal attenuation. Given the received
signal power threshold of -90dBm, a carrier frequency of 800MHz allows the spatial
separation of the transmit and receive antennas up to 1km, while a carrier frequency of
5GHz can only support the spatial separation of 150m. Hence, a low carrier frequency
is desirable for long-range wireless communication systems. For short-range wireless
communication systems, a high carrier frequency can be used1.
Since the wireless channel does not behave as a perfect medium and there are
normally obstacles (e.g. hills, buildings, tree, etc.) in the region of signal propagation,
the free space path loss model does not reflect the practical large-scale fading scenario.
1Nevertheless, the use of a high carrier frequency can achieve a higher capacity (by enabling a
larger number of small cells in cellular communication systems) and reduce the physical size of the
antenna [23]. In addition, from the regulation’s viewpoint, more bandwidth is available at the high
frequency spectrum.
10

2.1. Radio Channel Propagation
−30
−40
−50
−60
−70
−80
−90
−100
−110
100 101 102 103
Distance (meter)
Received signal power (dBm)
fc=800MHz
fc=2GHz
fc=5GHz
Figure 2.1: Received signal power as a function of antenna displacement based on a
free space path loss model. The transmit signal power is 1mW (i.e. 0dBm).
For mobile radio applications, the mean path loss as a function of distance between the
transmitter and the receiver can be modeled as [24]
LS ∝

d
d0
n
(2.2)
where n denotes the path loss exponent and d0 denotes a reference distance. The above
mean path loss model is often expressed in terms of dB, i.e.
LS (dB) = L0(d0) (dB) + 10n log10

d
d0

. (2.3)
In the above mean path loss model, the reference distance d0 corresponds to a point
located in the far field of the transmit antenna. The typical values of d0 are 1km
for large cells, 100m for microcells and 1m for picocells [22]. The path loss L0(d0) at
the reference distance d0 can be found using measured results [22]. The value of the
path loss exponent depends on the carrier frequency, antenna height and propagation
environment. In ideal free space, n = 2 since the signal attenuation as a function
of distance follows the inverse-square law. In the urban mircocell, n 2 due to the
presence of dense obstructions such as buildings [25].
11

The mean path loss model in (2.3) is an average of the path loss at different sites
for a given distance between the transmitter and the receiver. For different sites,
there is a variation about the mean path loss. When there are less obstacles between
the transmitter and receiver, the path loss at this site is smaller than the mean path
loss. However, for the same distance with the receiver located at a different site, the
propagation paths may be blocked by tall buildings and the path loss at this site is
higher than the mean. The measurement results in [26] show that the path loss LS(d)
can be modeled as a log-normal distributed random variable with a mean of LS in (2.3).
Therefore, the path loss model for large-scale fading can be described as [24]
LS(d) (dB) = LS + X (dB)
= L0(d0) (dB) + 10n log10

d
d0

+ X (dB) (2.4)
where X denotes a zero-mean Gaussian random variable with a standard deviation
of (the values of X and are both in dB). Since X has a normal distribution in
a log scale, X is often stated as log-normal fading [27]. The value of the standard
deviation can be found from measurement results. The typical value of is 6-10dB
or greater [22, 25]. For the path loss model used in the 3GPP spatial channel model
(SCM), = 10dB in the urban micro scenario [28]. Note that the log-normal fading is
part of large-scale fading since its variation occurs at different sites or the change over
a large geographical area. In the next section, small-scale fading will be described.
2.1.2 Small-Scale Fading
As mentioned previously, small-scale fading leads to dynamic changes in signal ampli-tude
and phase, which is caused by a small change of antenna displacement (as small as
a half-wavelength). This section describes the statistics and two mechanisms of small-scale
fading. Section 2.1.2.1 describes the statistics of small-scale fading, i.e. Rayleigh
and Rician fading. Section 2.1.2.2 describes the signal dispersion in the time-delay
domain (i.e. frequency-selective channel). Section 2.1.2.3 describes the time variation
of the channel response due to mobility (i.e. time-selective channel).
2.1.2.1 Rayleigh Fading and Rician Fading
In a wireless channel, a signal can travel from the transmitter to the receiver through
multiple reflective rays [22]. When multiple reflective rays arrive at the receiver simul-taneously,
they become unresolvable and the receiver sees it as a single path. Each
arrived ray experiences a different level of signal attenuation and phase shift due to the
12

characteristics of the wireless channel. When the arrived rays combine constructively,
the received signal envelope (or amplitude) is high. When the arrived rays combine
destructively, the received signal envelope is low. Hence, multiple simultaneous arrived
rays cause a variation in the received signal envelope, which is referred to as multipath
fading [22].
Rayleigh Fading
Suppose there is no dominant arriving ray, e.g. a non light-of-sight (NLoS) scenario.
Assuming the arriving rays are large in number and statistically independently and
identically distributed (i.i.d.). According to the central-limit theorem, the path (i.e. the
sum of the arrived rays) seen by the receiver can be modeled as a Gaussian distributed
random variable [15]. Hence, the received signal envelope (denoted as r) has a Rayleigh
probability density function (PDF) [15], i.e.
(r) =


r
2 e− r2
22 , r ≥ 0
0, r 0
(2.5)
where 22 is the pre-detection mean power of the NLoS multipath signal. In the NLoS
Rayleigh fading case, 22 = E[r2]. When the received signal envelope due to small-scale
fading follows a Rayleigh distribution, such a wireless channel is referred to as a
Rayleigh fading channel.
It is useful to derive the cumulative distribution function (CDF) of the received
signal power in a Rayleigh fading channel, since it can provide information on the
dynamic range of the received signal power variation. The CDF of the received signal
power can be defined as the probability of the received signal power (denoted as r2)
being smaller than a reference received signal power (denoted as r2
0). In a Rayleigh
fading channel, the CDF of the received signal power is described by the CDF of a
central chi-square distribution [15], i.e.
0) = pr(r2 r2
0) = 1 − e−r2
F(r2
0/22
, r, r0 ≥ 0. (2.6)
Rician Fading
In a Rayleigh fading channel, there is no dominant arrived ray. However, when there
is a dominant ray (e.g. a light-of-sight (LoS) scenario), the received signal envelope has
a Rician PDF [27], i.e.
(r) =


r
2 e−r2+A2
22 I0
rA
2

, r ≥ 0
0, r 0
(2.7)
13

where A2 is the pre-detection received signal power from the dominant ray, 22 is the
pre-detection mean power of the NLoS multipath signal, and I0(·) is the zero-th order
modified Bessel function of the first kind. When a dominant ray exists, the received
signal envelope follows a Rician PDF and such a wireless channel is referred to as a
Rician fading channel. Note that when the dominant ray disappears (i.e. A = 0), (2.7)
reduces to a Rayleigh PDF as shown in (2.5).
In the literature, a Rician fading channel is often described in terms of its K-factor.
The K-factor is defined as the ratio of the power of the dominant component to the
power of the remaining random components (often expressed in dB) [27], i.e.
K = 10 log10

A2
22

. (2.8)
In the above equation, when A = 0, K = −∞dB corresponds to a Rayleigh fading
channel. Due to the existence of the dominant component, the CDF of the received
signal power in a Rician fading channel is described by the CDF of a non-central chi-square
distribution [15], i.e.
F(r2
0) = pr(r2 r2
0) = 1 − Q1

A

,
r0

, r, r0 ≥ 0 (2.9)
where Q1(a, b) denotes the Marcum Q-function.
Comparison of Rayleigh Fading and Rician Fading
Fig. 2.2 shows the PDF of the received signal envelope for Rayleigh and Rician
fading channels, where the mean power of the NLoS multipath signal is 22 = 1.
Note that the peak of the Rayleigh PDF occurs at r = = 0.7071 [27]. When the
K-factor is large, the Rician PDF approaches a Gaussian PDF with a mean of the
dominant component amplitude A [27]. Compared to the Rayleigh fading channel, the
received signal envelope in a Rician fading channel is strengthened due to the dominant
component. As the K-factor increases, the average received signal envelope is higher
and the probability of having a deep-faded received signal envelope is lower.
Let PN denote the received signal power relative to the mean received signal power,
i.e.
PN =


r2
22 , for Rayleigh fading
r2
A2+22 , for Rician fading.
(2.10)
Based on (2.6) and (2.9), Fig. 2.3 shows the CDF of the received signal power relative
to the mean received signal for Rayleigh and Rician fading channels. It is shown that
the received signal power in a Rayleigh fading channel has a dynamic range of 27dB
14

0 1 2 3 4 5 6
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
Received signal envelope, r
½(r)
Rayleigh fading
Rician fading (K = 5 dB)
r = ¾ = 0.7071
A = 1.7783 A = 3.1623
Figure 2.2: PDF of the received signal envelope for Rayleigh and Rician fading channels,
where the mean power of the NLoS multipath signal is 22 = 1.
100
10−1
Rayleigh fading
0)
PN, PN r(P 10−2
10−3
Normalized received signal power, PN,0 (dB) −30 −25 −20 −15 −10 −5 0 5 10
Figure 2.3: CDF of the received signal power relative to the mean received signal power
for Rayleigh and Rician fading channels.
15

for 99% of the time, while the dynamic range is reduced to 10dB in a Rician fading
channel with K = 10dB. Moreover, the probabilities of the received signal power being
10dB lower than the mean received signal power are 10% and 0.5% for Rayleigh and
Rician fading (where the K-factor is K = 10dB) channels respectively.
Both Fig. 2.2 and Fig. 2.3 show that the received signal is more likely to be
faded in a Rayleigh fading channel than a Rician fading channel. Although a Rician
fading channel is a more friendly environment for wireless communications, the mobile
communication applications often take place in NLoS scenarios, where the dominant
component does not exist. Hence, Rayleigh fading is assumed as the statistics for
small-scale fading in the following sections.
2.1.2.2 Delay-Dispersive Channel
There are two mechanisms for small-scale fading. One of these is signal dispersion in
the time-delay domain, which results in a frequency-selective channel. The other one
is the time variation of a mobile channel, which results in a time-selective channel. In
this section, the signal dispersion mechanism is described.
In the previous section, a single multipath signal was used to describe Rayleigh
fading and Rician fading. However, there may be clusters of rays that arrive at the
receiver with different time delays due to different propagation distances. When the
relative time delay between the arrived clusters excesses a symbol period, there is more
than one resolvable path seen by the receiver. In other words, the received signal
becomes dispersive in the time-delay domain.
Fig. 2.4(a) shows the impulse response for a delay-dispersive channel, where the
symbol period is 0.2μs and an 8-tap i.i.d. complex Gaussian channel is assumed. For
an 8-tap i.i.d. complex Gaussian channel, there are 8 resolvable paths seen by the
receiver. Each path is modeled as an i.i.d. complex Gaussian random variable and thus
experiences Rayleigh fading individually. Since a wireless channel can be viewed as a
linear filter to the transmit signal, the received signal is the convolution of the transmit
signal and channel impulse response. Hence, a delay-dispersive channel introduces ISI
into the received signal. Note that the ISI can lead to an irreducible error floor in the
system performance, unless equalization is employed at the receiver to mitigate the ISI.
When converting a one-tap channel into the frequency domain, its frequency domain
channel response is flat. Such a channel is called a flat fading channel. However, for a
delay-dispersive channel, as shown in Fig. 2.4(a), its frequency domain channel response
becomes selective as shown in Fig. 2.4(b) (where the carrier frequency is 2GHz and
16

0 1 2 3 4 5
0.8
0.6
0.4
0.2
0
Time delay, ¿ (μs)
|h(¿ )|
(a) Delay−dispersive channel
2
1.5
1
0.5
0
1997.5 1998 1998.5 1999 1999.5 2000 2000.5 2001 2001.5 2002 2002.5
Frequency, f (MHz)
|eh(f)|
(b) Frequency−selective fading channel
Figure 2.4: (a) Delay-dispersive channel (an 8-tap i.i.d. complex Gaussian channel).
(b) Corresponding frequency-selective fading channel.
the signal bandwidth is 5MHz). Such a channel is called a frequency-selective fading
channel. Note that a frequency-selective fading channel is a dual to a delay-dispersive
channel [22] when viewing the signal distortion in the frequency domain.
The frequency selectivity of a wireless channel can be characterized by its coherence
bandwidth. The coherence bandwidth (denoted as f0) is a statistical measure of the
range of frequencies over which the channel has approximately equal gain and linear
phase [22]. Let r2
l denote the average power of the l-th channel tap at a time delay
of l. The mean excess delay (which represents the time for half the channel power to
arrive) is defined as [24]
=
P
l r2
P l l
l r2
l
(2.11)
and the root mean square (RMS) delay spread is defined as [24]
RMS =
sP
l r2
l (l − )2
P
l r2
l
. (2.12)
As a rule of thumb, a popular approximation of the coherence bandwidth with a cor-relation
of at least 0.5 is given by [24]
f0 ≈
1
5RMS
. (2.13)
17

When the transmit signal bandwidth is small compared to the coherence bandwidth
(i.e. the symbol period is long compared to the channel delay spread), the received
signal experiences a flat fading channel (i.e. an one-tap channel). In this case, channel-induced
ISI does not occur. However, when this channel tap is faded, the system
suffers from performance degradation due to low received signal-to-noise ratio (SNR).
When the transmit signal bandwidth is larger than the coherence bandwidth (i.e. the
symbol period is shorter than the channel delay spread), the received signal experiences
a frequency-selective fading channel (i.e. a delay-dispersive channel). In this case,
equalization is required at the receiver to mitigate the ISI. Since the probability of all
the channel taps being in fades at the same time is very low, there is less fluctuation
in the received SNR compared to a flat fading channel.
In the remainder of this thesis, an 8-tap i.i.d. complex Gaussian channel model that
varies independently across the transmission blocks will be assumed in the simulations
unless otherwise stated. In the next section, a time-varying channel due to small-scale
fading is described.
2.1.2.3 Time-Varying Channel
As mentioned earlier, a relative motion (as small as a half-wavelength) between the
transmitter and the receiver can cause a significant fluctuation in the received signal
power. In this section, the popular Jakes model [29] is used to describe the time
variation mechanism of a mobile channel due to small-scale fading.
In the Jakes model, it is assumed that the receiver is traveling at a constant ve-locity
of v m/s, and N equal-strength rays arrive at the receiver simultaneously (that
constitutes a single resolvable fading path2). Jakes further assumes that the azimuth
arrival angles of the rays (denoted as n) at the receiver are uniformly distributed from
0 to 2, i.e.
n =
2n
N
, n = 0, . . . ,N − 1. (2.14)
Let n denote a random initial phase of the n-th ray. Assuming the mean channel
power is normalized to 1 (i.e. E[|h(t)|2] = 1), the channel response at a time instant t
is given by [29]
h(t) =
1
√2N
NX−1
n=0
cos (2fd(cos n)t + n)+j
1
√2N
NX−1
n=0
sin (2fd(cos n)t + n) (2.15)
2The delay-dispersive channel with multiple resolvable paths can be generated using the Jakes
model. However, for brevity, a single resolvable path is used to explain the time variation mechanism
of a mobile channel.
18

0 1 2 3 4 5 6 7 8
10
5
0
−5
−10
−15
−20
−25
−30
−35
¢d/¸
Normalized received channel power (dB)
Figure 2.5: Received channel power relative to the mean received channel power as a
function of d normalized to , in an one-tap channel with Jakes model.
where fd = v
is the maximum Doppler frequency and is the propagation wave-length.
Note that when N is large, according to the central-limit theorem, h(t) is
well-approximated as a Gaussian random variable and thus leads to a flat Rayleigh
fading channel.
Since the relative motion between the transmitter and the receiver (i.e. the distance
traveled by the receiver) is given by d = vt, the channel response h(t) in (2.15) can
be written as a function of d, i.e.
h(d) =
1
√2N
NX−1
n=0
cos

2d

(cos n) + n

+j
1
√2N
NX−1
n=0
sin

2d

(cos n) + n

.
(2.16)
Based on the above equation, Fig. 2.5 shows the received channel power relative to the
mean channel power (i.e. |h(d)|2/E[|h(d)|2]) as a function of d normalized to .
It is shown that the channel power varies significantly with a small change of antenna
displacement, and the distance traveled by the receiver corresponding to two adjacent
nulls is on the order of a half-wavelength (/2) [24]. Therefore, when the carrier
frequency is fc = 2GHz and = c
fc
= 0.15m, the coherence distance of the channel is
small and the channel response can change dramatically with antenna displacements of
19

just a few centimeters. This coherence distance can be translated to the coherence time
via the traveling speed of the receiver. When the receiver is traveling at a high speed,
the coherence time of the channel becomes shorter, which leads to a fast time-varying
channel (or time-selective fading channel).
Let t denote a time difference; the space-time correlation function of the Jakes
model in (2.15) is given by [30]
R(t) = E[h∗(t)h(t + t)] = J0(2fdt) (2.17)
where J0(·) denotes the zero-th order Bessel function of the first kind. It is shown
in [31] that the coherence time of a mobile channel over which the channel response to
a sinusoid has a correlation greater than 0.5 is approximately
T0 ≈
9
16fd
. (2.18)
For a FDE system, such as orthogonal frequency division multiplexing (OFDM)
and single-carrier frequency domain equalization (SC-FDE), it is assumed that the
channel response remains highly correlated during a symbol period (or a transmission
block period). Otherwise, inter-carrier interference (ICI) occurs due to Doppler spectral
broadening [22]. In the LTE standard, the symbol period is TS = 66.67μs. In a high-speed
train scenario with v = 350km/hr, the Doppler frequency is fd = vfc
c = 648Hz
when the carrier frequency is fc = 2GHz. Based on (2.18), the channel coherence time
(T0 ≈ 276μs) is still long compared to the symbol period (i.e. TS = 66.67μs). Hence,
the Doppler spectral broadening effect may not cause severe performance degradation
in this high-mobility scenario.
From other design aspects, the high mobility still has a great impact upon the
system performance. For example, the pilot block based channel estimation is specified
in the LTE uplink [11]. In the high-mobility scenario, the channel estimate obtained
in the pilot block may become out-dated for the data blocks. The impact of mobility
on the channel estimation performance will be investigated in Chapter 6, where an
8-tap i.i.d. complex Gaussian channel following the Jakes model [29] will be assumed
to simulate a time-varying channel. Moreover, when channel-dependent scheduling
(CDS) is employed, the channel quality may become very different after the round-trip
delay [32]. Hence, the time variation of the mobile channel should be taken into account
in the system design.
20

2.2. Mitigation and Broadband Wireless Communication Systems
2.2 Mitigation and Broadband Wireless Communication
Systems
In the previous section, the characteristics of mobile radio channels were described.
To combat the channel fading and distortion, appropriate mitigation techniques and
broadband wireless communication systems are described in this section.
2.2.1 Mitigation Techniques
This section describes two categories of mitigation technique. The first one is to com-bat
the SNR loss due to signal power attenuation. The second one is to combat the
frequency-selective channel distortion.
Combating SNR Loss
The received SNR can be attenuated considerably in a wireless channel, especially
in a flat Rayleigh fading channel as shown in Fig. 2.3 and Fig. 2.5. To combat
the SNR loss, error-correcting codes can be used to lower the SNR requirement [33].
Alternatively, diversity techniques can be used to combat the SNR loss by improving
the received SNR [33].
Diversity techniques involve obtaining multiple copies of the same transmit signal
via uncorrelated channels, which can be achieved in terms of time, frequency and space.
For time diversity, the uncorrelated channels can be achieved when the separation of
transmission time slots is larger than the coherence time (i.e. T0). For frequency
diversity, the uncorrelated channels can be obtained when separation of the used car-rier
frequencies is larger than the coherence frequency (i.e. f0). Moreover, frequency
diversity is also achieved when the signal bandwidth is larger than f0 (e.g. a frequency-selective
channel as shown in Fig. 2.4(b)). This is because the channel responses at all
frequencies are unlikely to fade at the same time, and hence the fluctuation of the re-ceived
SNR is smaller. For spatial diversity, the uncorrelated channels can be obtained
through the use of multiple transmit or receive antennas with the spatial separation
larger than the coherence distance, e.g. maximal ratio combining (MRC) [34] for receive
diversity, and cyclic delay diversity (CDD) [35] and space-time block codes (STBC) [36]
for transmit diversity.
Combating Frequency-Selective Channel Distortion
When transmitting the signal over a frequency-selective fading channel, equalization
is required to mitigate the channel distortion. For SC systems, the simplest method for
21

mitigating frequency-selective channel distortion (i.e. combating ISI) is linear equal-ization.
The SC equalization algorithms are traditionally implemented in the time
domain, e.g. linear transversal equalizers. When viewing linear equalization (LE) in
the frequency domain, it is desirable that the multiplication of the equalizer response
and the frequency-selective channel response leads to (or close to) a flat spectrum with
a linear phase. Hence, the equalized channel impulse response becomes (close to) an
impulse and ISI is mitigated.
Since LE does not yield the best equalization performance due to an implicit trade-off
between noise enhancement and residual-ISI, DFE can improve the equalization
performance through the use of the previous detected symbols for feedback ISI cancel-lation.
The use of DFE for broadband SC systems will be detailed in Chapter 4. Apart
from the filter-based equalization schemes (such as LE and DFE), maximum-likelihood
sequence estimation (MLSE) is known as the optimal equalization algorithm in the
sense of minimizing the error probability [15]. However, its computational complex-ity,
which grows exponentially with channel symbol/sample memory, often makes it
prohibitive for practical use.
In contrast to SC systems, MC systems (such as OFDM) do not suffer from channel-induced
ISI in a frequency-selective channel [33]. For MC systems, the data symbols are
transmitted in parallel using multiple orthogonal subcarriers. When the symbol period
is long compared to the channel delay spread, each symbol experiences different flat
fading (according to the frequency-selectivity of the channel). As a result, a one-tap
per subcarrier FDE is sufficient to compensate the amplitude and phase distortion due
to the channel.
The FDE concept was soon extended to SC systems [37]. For SC systems, FDE
provides a computational efficient solution for LE implementation. Since FDE has
become a popular equalization technique due to its simplicity, the existing broadband
wireless communications systems based on FDE are discussed in the following section.
2.2.2 Broadband Wireless Communication Systems
High data-rate wireless communications are highly desirable nowadays to provide sat-isfactory
service (such as real-time video streaming) to the users. The simplest way
to achieve high data-rate transmission is to increase the signal bandwidth by building
a broadband wireless communication system. Hence, it becomes inevitable for broad-band
signals to experience frequency-selective fading channels. The existing broadband
transmission techniques based on FDE are discussed in the following paragraphs.
22

2.2. Mitigation and Broadband Wireless Communication Systems
Before going into the detail of FDE-based broadband wireless systems, the history
of OFDM is briefly described since SC-FDMA, SC-FDE and OFDMA are all closely
related to (or developed from) the concept of OFDM, especially in terms of efficient
FDE. The concept of using parallel data transmission and frequency division multi-plexing
(FDM) was published in the mid-1960s [38–40]. Some early development is
traced back to the 1950s [41]. In 1971, Weinstein and Ebert applied DFT to parallel
data transmission systems [42]. This leads to bandwidth-efficient data transmission in
OFDM, and the transceiver can be implemented using efficient fast Fourier transform
(FFT) techniques. Since the main drawback of OFDM is its high PAPR, Sari et. al.
proposed a SC-FDE technique [37,43] based on the concept of OFDM in 19933. As its
name implies, a low-PAPR SC signal is obtained at the transmitter for power-efficient
transmission and efficient FDE can be used at the receiver [37, 44]. With an increased
interest in optimizing the multi-user scenario, Sari et. al. proposed OFDMA [45, 46]
in 1996 by combining OFDM and FDMA, and SC-FDE was extended to SC-FDMA.
Although the concept of SC-FDMA was not completely new, interleaved frequency di-vision
multiple access (IFDMA) was proposed in 1998 [47]. To the best of author’s
knowledge, the term “SC-FDMA” first appeared in the LTE uplink standard [48] in
2006.
As mentioned previously, the key advantage of OFDM is that it does not suffer
from channel-induced ISI and a one-tap FDE is sufficient to compensate the channel
distortion. OFDM converts the ISI problem into unequal channel gains for each data
symbol since each data symbol is mapped to a corresponding subcarrier in the frequency
domian. Even when the SNR is high, deep-faded subcarriers still occur in a frequency-selective
fading channel. Hence, channel coding is necessary in practical OFDM systems
to prevent the deeply faded subcarriers from dominating the overall error performance
[49]. However, the main drawback of OFDM is the high-PAPR, which is undesirable
for power-limited devices (The PAPR issue will be detailed in Section 3.3). Hence,
OFDM is employed in the downlink, broadcast and WLAN scenarios, such as Digital
Audio Broadcasting (DAB) [50], Digital Video Broadcasting (DVB) [51] and IEEE
802.11a/g/n [5, 7, 8].
As mentioned previously, FDE can also be employed in SC systems, i.e. SC-FDE
[37, 44]. SC-FDE maintains the efficient FDE implementation while having low-PAPR
SC transmit signals. Hence, it is particularly suitable for uplink transmission, where
the mobile handset is normally power-limited [44]. Without channel coding, SC-FDE
3According to the author, the concept of SC-FDE [43] was first published in 1993 but his most
well-known SC-FDE paper [37] was published in 1995.
23

outperforms OFDM since all the SC data symbols receive the same channel power.
However, when channel coding is applied, OFDM outperforms SC-FDE [44]. This is
because OFDM does not suffer from channel-induced ISI and error-correcting codes can
yield a large performance gain. For SC-FDE, the performance is limited by residual-ISI
since a one-tap FDE is equivalent to LE for SC systems. Therefore, to improve the
performance of SC-FDE, the residual-ISI must be overcome, e.g. hybrid-DFE [44, 52]
and IB-DFE [53].
OFDMA extends the use of OFDM to a multiple-access technique [45, 46]. In
OFDMA, multiple users can access the resource simultaneously and a distinct set of
subcarriers are assigned to each user. Hence, flexible resource allocation can be achieved
in OFDMA via a scheduling algorithm. Since different users may have different service
requirements (such as data-rate and priority), an intelligent scheduler can make good
use of the available resource. Moreover, when CDS is employed to exploit multiuser
diversity, aggregated cell-throughput can be significantly enhanced [54]. OFDMA is
currently employed in the LTE downlink [4] and IEEE 802.16 [9]. As with OFDM, the
main drawback of OFDMA is the high-PAPR transmit signal.
SC-FDMA extends the use of SC-FDE to a multiple-access technique, where a dis-tinct
set of subcarriers are assigned to each user. Hence, SC-FDMA can be viewed
as SC-FDE with the flexibility of resource allocation. For SC-FDMA, interleaved and
localized subcarrier mapping schemes are referred to as IFDMA and LFDMA, respec-tively.
LFDMA with CDS can be used to exploit multiuser diversity, while IFDMA or
LFDMA with frequency hopping (FH) can be used to exploit frequency diversity [55].
Note that IFDMA and LFDMA are the only special cases for the SC-FDMA trans-mit
signals to maintain the low-PAPR property (This will be detailed in Section 3.3).
Since low-PAPR transmit signals are particularly desirable to enable power-efficient
uplink transmission, SC-FDMA is currently employed in the LTE uplink [4]. As with
SC-FDE, the performance of SC-FDMA is also limited by the residual-ISI when con-ventional
FDE is used.
SC-FDMA is a relatively new broadband transmission technique, and it has at-tracted
a lot of research interest in recent years. This thesis focuses on the equalization
and channel estimation schemes for SC-FDMA. To overcome the residual-ISI problem,
the use of DFE is investigated in the first part of the thesis. Since channel estimation
is required at the receiver to calculate the equalizer coefficients, accurate channel es-timation
plays an important role in minimizing the performance loss. Hence, channel
estimation techniques are investigated in the second part of this thesis. In the following
section, a simulation verification based on analytic results is provided.
24

2.3. Simulation Verification
Figure 2.6: (a) BPSK transmit data symbols. (b) Conditional PDFs of the received
BPSK signals in an AWGN channel.
2.3 Simulation Verification
This section provides a verification of the simulator used in the thesis. In Section 2.3.1,
the error probabilities of binary phase shift keying (BPSK) modulation in AWGN and
flat Rayleigh fading channels are derived. In Section 2.3.2, a baseband SC simulation
model is described, and verification is performed by comparing the simulated error
probability with the analytic error probability.
2.3.1 Error Probability Derivation
2.3.1.1 Error Probability of BPSK in an AWGN Channel
When BPSK modulation is used, the transmit data symbol is either x1 =
p
2x
and
x2 = −
p
2x
(where 2x
= E[|x1|2] = E[|x2|2] denotes the data symbol power), as shown
in Fig. 2.6(a). Assume x1 and x2 are equally likely to be transmitted. When x1 is
transmitted over an AWGN channel, the received data symbol is given by
y = x1 + n (2.19)
where n represents the complex white Gaussian noise component, which has a mean of
zero and a variance of 2n
= E[|n|2].
Let r = ℜ(y) denote the real part of the received symbol, since the imaginary part
of the noise does not affect the error probability of BPSK. The decision is made by
comparing r with the zero threshold. If r 0, the decision is made in favor of x1. If
r 0, the decision is made in favor of x2. Since the received signal is corrupted by
Gaussian noise, the received signal (i.e. r) has a Gaussian conditional PDF, as shown
in Fig. 2.6(b). When x1 is transmitted, the conditional PDF of r is given by [15]
(r|x1) =
1 p
2n
e−r−√2x
2
/2n
. (2.20)
25

Similarly, when x2 is transmitted, the conditional PDF of r is
(r|x1) =
1 p
2n
e−r+√2x
2
/2n
. (2.21)
Given that x1 is transmitted, the erroneous decision occurs if r 0 and the error
probability can be obtained as
P(r 0|x1) =
Z 0
−∞
(r|x1)dr
=
1 p
2n
Z 0
−∞
e−r−√2x
2
/2n
dr
| {z }
Rewrite r=√2n
/2t+√2x
and dr=√2n
/2dt
=
1
√2
Z
−√22x
/2n
−∞
e−t2/2dt
=
1
√2
Z
∞
√22x
/2n
e−t2/2dt
= Q
s
22x
2n
!
(2.22)
2n
where Q(2x
·) is the Q-function. p
Similarly, when x2 is transmitted, the error probability
is given by P(r 0|x2) = Q
2/
. Since the occurrence of x1 and x2 is equally
likely, the average error probability of BPSK in an AWGN channel is given by [15]
Pe =
1
2
P(r 0|x1) +
1
2
P(r 0|x2)
= Q
s
22x
2n
!
. (2.23)
2.3.1.2 Error Probability of BPSK in a Flat Rayleigh Fading Channel
When transmitting a BPSK symbol x1 over a flat Rayleigh fading channel, the received
symbol is given by
y = hx1 + n (2.24)
where h =

ej denotes a flat Rayleigh fading channel response (

and are the
amplitude and phase of the channel response respectively).
Let
=

2. 2x
2n
denote the instantaneous received SNR in a flat Rayleigh fading
channel. Based on the result in (2.23), the error probability of BPSK as a function of

is given by
Pe(
) = Q
p
2

. (2.25)
26

2.3. Simulation Verification
Figure 2.7: Block diagram of a baseband SC simulation model with block-based trans-mission/
reception.
Since
is random (due to random

), the error probability must be averaged over the
PDF of
(denoted as (
)). Therefore, the average error probability is given by
Pe =
Z
∞
0
Pe(
)(
)d
. (2.26)
Since

2 has a chi-square PDF with two degrees of freedom.
Hence,
also has a chi-square PDF [15], i.e.
(
) =
1

e−
/
(2.27)
where
= E[

2]. 2x
2n
denotes the average received SNR.
Substituting (2.25) and (2.27) into (2.26), (2.26) can be expressed as a double
integral, which can be solved by changing the order of integration. Therefore, the
average error probability of BPSK in a flat Rayleigh fading channel is derived as
Pe =
Z
∞
0
Pe(
)(
)d

=
1
√2
.
1

Z
∞
0
e−
/

Z
∞
√2

et2/2dtd

=
1
√2
.
1

Z
∞
0
et2/2
Z t2/2
0
e−
/
d

| {z }
=
(1−e−t2/2
)
dt
=
1
√2
Z
∞
0
e−t2/2 − e−(t2/2)(1+1/
)dt
| {z }
where R1
2√/a.
0 e−at2dt=1
=
1
√2

1
2
√2 −
1
2
s
2

+ 1
!
=
1
2

1 −
r

+ 1

. (2.28)
2.3.2 Simulation Model Description and Verification
Fig. 2.7 shows the block diagram of a baseband SC simulation model with block-based
transmission/reception. At the transmitter, the input bits are grouped and mapped to
27

a block of data symbols via a symbol mapper. Let x = [x(0), . . . , x(K−1)]T denote the
data symbol vector, where x(k) denotes the k-th (k = 0, . . . ,K−1) data symbol and K
is the number of data symbols in a transmission block. Let 2x
= E[|x(k)|2] denote the
expected data symbol power, which is normalized to 1 in the simulation, i.e. 2x
= 1.
Therefore, for BPSK modulation, when the k-th input bit is 1, x(k) =
p
2x
= 1. When
the k-th input bit is 0, x(k) = −
p
2x
= −1.
It is assumed that the channel response remains invariant within a block transmis-sion
period. For AWGN and flat fading channels (i.e. no channel delay spread), the
channel model is thus described by a K ×K diagonal-constant matrix H with h being
its diagonal entries. In the simulation, the mean channel power is normalized to 1, i.e.
E[|h|2] = 1. Hence, for an AWGN channel, h = 1. For a flat Rayleigh fading channel,
the channel tap is given by h =

and denote the amplitude and phase of
the channel tap. Based on the central-limit theorem (as mentioned in Section 2.1.2.1),
a Rayleigh fading channel tap

ej can be modeled as a complex Gaussian random
variable with a mean of zero and a variance of 1 in the simulation.
Let n = [n(0), . . . , n(K − 1)]T denote a length-K complex white Gaussian noise
vector, where each element has a mean of zero and a variance of 2n
= E[|n(k)|2]. The
received data symbol vector is thus given by
y = Hx + n. (2.29)
Since the channel power is normalized to 1, the average received SNR is
= 2x
2n
.
To compensate the channel effect, an equalizer (denoted as G) is employed to correct
the amplitude and phase of the received data symbols. Since H is a K × K diagonal-constant
matrix, G is also a K ×K diagonal-constant matrix with g being its diagonal
entries. When the minimum mean-square error (MMSE) criterion is used, the equalizer
coefficient is given by4
g =
2x
2n
h∗
|h|2 + . (2.30)
Hence, the equalized data symbol vector is obtained as
z = Gy. (2.31)
The equalized data symbols are then decoded using the zero threshold decision rule to
generate the output bits. By comparing the input bits and output bits, the simulated
error probability can be obtained.
4The design of a MMSE equalizer will be derived in Section 3.2.1.
28

2.4. Summary
0 5 10 15 20 25 30
100
10−1
10−2
10−3
10−4
10−5
SNR (dB)
BER
Analytic result
Simulation result
AWGN
channel
Flat Rayleigh
fading channel
Figure 2.8: Analytic and simulated error probabilities of BPSK in AWGN and flat
Rayleigh fading channels.
In the simulation, K = 128 is used (the choice of K does not affect the simulated
bit error rate (BER) results in this case). Ideal knowledge of the channel response and
SNR is assumed at the receiver. To produce sufficiently accurate BER curves, 200,000
independent channel realizations are generated. Fig. 2.8 shows that the simulated error
probabilities match the analytic error probabilities in both AWGN and flat Rayleigh
fading channels. The simulator is thus verified.
2.4 Summary
This chapter began with a description of the characteristics of mobile wireless channels.
It was shown that when transmitting a radio signal over a hostile wireless channel, the
received signal power could be considerably attenuated. Moreover, the received sig-nal
suffers from ISI or frequency-selective distortion in a delay-dispersive channel. To
combat the channel fading and distortion, mitigation techniques were described. Since
FDE has become a popular technique for compensating frequency-selective channel
distortion due to its simplicity, the existing broadband wireless communication sys-tems
based on FDE were discussed. Finally, a simulation verification was provided by
29

showing that the simulated error probability matched the analytic error probability in
the simple cases of AWGN and flat Rayleigh fading channels. In the next chapter, an
overview of SC-FDMA systems will be presented.
30

Chapter 3
Single-Carrier Frequency
Division Multiple Access
SC-FDMA is currently employed in the LTE uplink, while OFDMA is employed in the
downlink [4]. The main drawback of MC systems is that the transmit signals exhibit
high-PAPR [56]. Hence, the main advantage of SC-FDMA is its inherent low-PAPR
property, which enables power-efficient uplink transmission for the power-limited mo-bile
handset [11]. Furthermore, computationally efficient FDE can be supported in
SC-FDMA via the use of a CP [37]. The difference of using FDE in OFDMA and SC-FDMA
is that SC-FDMA may be liable to a performance loss due to channel-induced
ISI in a frequency-selective channel, while OFDMA sees a frequency-selective fading
channel as individual flat fading channels on its subcarriers (this will be detailed in
Chapter 4). Since the base station can usually afford higher complexity by employing
a more expensive linear PA to support OFDMA transmission, OFDMA is preferable
on the downlink to achieve higher throughput in the demanding downlink traffic. Al-though
SC-FDMA with linear FDE may suffer from some performance loss compared
to OFDMA in the channel coding case [44, 57], its low-PAPR signal advantage (which
translates to a small back-off requirement at the PA1) may outweight this performance
loss and lead to an overall performance gain over OFDMA for the low-cost, power-limited
mobile handset. Therefore, SC-FDMA is preferable for uplink transmission.
SC-FDMA is often perceived as DFT-precoded OFDMA since the data symbols
are precoded using a DFT prior to the OFDMA modulator [58,59]. Alternatively, SC-FDMA
can be viewed as SC-FDE with the flexibility of scheduling orthogonal frequency
resource to multiple users, where a low-PAPR transmit signal can be maintained via
1This will be detailed in Section 3.3.
31

Chapter 3. Single-Carrier Frequency Division Multiple Access
Figure 3.1: Block diagram of SC-FDMA system.
interleaved and localized resource allocation schemes [11]. In the reminder of the thesis,
SC-FDMA with interleaved and localized subcarrier mapping schemes are referred to
as IFDMA and LFDMA respectively [55].
The early concept of IFDMA was proposed in [47], where time domain data block
spreading was employed to achieve the interleaved subcarrier mapping in the frequency
domain. In contrast to time domain signal generation [47], frequency domain signal
generation is employed in the LTE standard as it provides better resource allocation
flexibility, and is consistent with the downlink OFDMA resource allocation scheme [11].
SC-FDMA is a relatively new transmission technique, and a comprehensive overview
of the key features of SC-FDMA is presented in this chapter.
This chapter is organized as follows. In Section 3.1, the mathematical description
of SC-FDMA systems is given and the equivalent received data symbols are derived. In
Section 3.2, linear FDE designs based on the zero-forcing (ZF) and MMSE criteria are
derived. A performance comparison of SC-FDMA with ZF-FDE and SC-FDMA with
MMSE-FDE is then presented. In Section 3.3, IFDMA and LFDMA transmit signals
are shown to be SC signals, and their PAPR is compared with OFDMA signals. PAPR
reduction techniques are then investigated via frequency domain spectrum shaping and
modified baseband modulation schemes.
3.1 Mathematical Description of Single-Carrier FDMA
Systems
Fig. 3.1 shows the block digram of an uplink SC-FDMA system. In this chapter,
the mathematical description of an uplink SC-FDMA system using a matrix form is
32

3.1. Mathematical Description of Single-Carrier FDMA Systems
extended from the mathematical description of SC-FDE and OFDM systems given
in [60,61]. At the transmitter, the μ-th user’s (μ = 1, . . . ,U) data symbols are denoted
as xμ = [xμ(0), . . . , xμ(K − 1)]T , where U is the number of users, K is the length of
the data symbol vector (or the DFT size), and xμ(k) is the k-th data symbol from the
μ-th user. Let ex
μ = [exμ(0), . . . , exμ(K − 1)]T denote the μ-th user’s frequency domain
data symbols, which can be obtained using a size-K DFT, i.e.
ex
μ = FKxμ (3.1)
where FK(p, q) = 1 √K
e−j 2
K pq (p, q = 0, . . . ,K − 1) is the normalized K × K DFT
matrix.
The μ-th user’s frequency domain symbols are then mapped to a set of user-specific
subcarriers. Interleaved and localized subcarrier mapping schemes are recommended
in uplink SC-FDMA systems [11], since they are the only special cases that maintain
the low PAPR property of the SC transmit signal. This will be further explained in
Section 3.3. The μ-th user’s subcarrier mapping block can be described as an N × K
matrix Dμ (where N is the total number of available subcarriers to be shared by all
users):
Interleaved: Dμ(n, k) =


1, n = (μ − 1) + N
Kk
0, otherwise
Localized: Dμ(n, k) =


1, n = (μ − 1)K + k
0, otherwise.
(3.2)
The above equations show that each user is given a distinct set of subcarriers (i.e. they
are orthogonal in the frequency domain), which satisfy the following criteria:
DT
mDμ =


IK, m = μ
0K×K, m6= μ.
(3.3)
where IK is the K × K identity matrix and 0K×K is a K × K zero matrix. Hence the
received signal from different users can be separated in the frequency domain at the
receiver.
After subcarrier mapping, a size-N inverse DFT (IDFT) block FHN
is used to convert
the frequency domain signal back to the time domain, where FHN
(p, q) = 1 √N
ej 2
N pq
(p, q = 0, . . . ,N − 1). Finally a cyclic prefix (CP) is added to form a SC-FDMA
transmission block. Assuming the CP length is equal to or longer than the maximum
33

channel delay spread, the CP insertion block is defined as a (L+N)×N matrix (where
L represents the maximum channel delay spread), i.e.
T =

ICP
IN
#
(3.4)
where IN is an N × N identity matrix, and ICP is a L × N matrix that copies the last
L rows of IN.
The μ-th user’s transmission block is thus given by
xBLK,μ = TFHN
Dμ(FKxμ)
= TFHN
Dμex
μ (3.5)
where xBLK,μ is a L + N column vector.
Assuming perfect uplink synchronization at the base station, the sum of the received
signals from all users is given by
r =
XU
μ=1
HμxBLK,μ + n. (3.6)
In the above equation, n = [n(0), . . . , n(L +N − 1)]T is the received noise vector; each
element is modeled as a complex, zero mean, Gaussian noise sample with a variance
of 2n
= E[|n(k)|2]. The (L + N) × (L + N) channel matrix Hμ (denoting the linear
convolution of the channel impulse response and the transmission block) is given by
Hμ =


hμ(0) 0 · · · · · · · · · 0
...
hμ(0)
. . .
...
hμ(L − 1)
...
. . .
. . .
...
0 hμ(L − 1)
. . .
. . .
...
...
. . .
. . .
. . . 0
0 · · · 0 hμ(L − 1) · · · hμ(0)


(3.7)
where hμ(l) is the l-th channel impulse response for the μ-th user.
As shown in Fig. 3.1, the inverse process is performed at the receiver (Note: the
equalization block is not shown in this figure, but the commonly used linear FDE [37]
will be derived in Section 3.2). Let 0N×L denote a N ×L zero matrix. The CP removal
block is defined as
Q =
h
0N×L IN
i
. (3.8)
After removing the CP, a size-N DFT block FN is used to convert the received time
1 e−j 2
domain signals back into the frequency domain, where FN(p, q) = √N
N pq (p, q =
34

3.1. Mathematical Description of Single-Carrier FDMA Systems
0, . . . ,N − 1). The subcarrier demapping block DT
m (see (3.2)) is then employed to
extract the m-th user’s received signal2 from the sum of the received signals. After
subcarrier demapping, the m-th user’s received data symbols in the frequency domain
are given by
ey
m = (DT
mFNQ)r
=
XU
μ=1
DT
mFN QHμT | {z }
HC,μ
FHN
Dμex
μ + DT
mFNQn | {z }
evm
(3.9)
whereev
m is the m-th user’s received noise vector in the frequency domain (each element
has a variance of 2n
, as FN is normalized), and HC,μ = QHμT is a N × N circulant
channel matrix given by
HC,μ =


hμ(0) 0 · · · 0 hμ(L − 1) · · · hμ(1)
...
hμ(0)
. . .
. . .
. . .
...
...
...
. . .
. . .
. . . hμ(L − 1)
hμ(L − 1)
...
. . .
. . . 0
0 hμ(L − 1)
. . .
. . .
...
...
. . .
. . .
. . . 0
0 · · · 0 hμ(L − 1) · · · · · · hμ(0)


.
(3.10)
The above equation shows that CP insertion at the transmitter and CP removal
at the receiver convert the linear channel matrix Hμ into a circulant channel matrix
HC,μ. Furthermore, it is well-known that a circulant matrix can be diagonalized by pre-and
post-multiplication of DFT and IDFT matrices [62]. Thus the resultant diagonal
matrix can be written as
eH
C,μ = FNHC,μFHN
= diag
n
ehμ(0), . . . , ehμ(N − 1)
o
(3.11)
where ehμ(n) is the μ-th user’s frequency domain channel response on the n-th subcarrier
(i.e. ePhμ(n) =
L−1
l=0 hμ(l)e−j 2
N nl for n = 0, . . . ,N − 1).
Based on the orthogonality criteria stated in (3.3), it follows that
DT
m
eH
C,μDμ =


e¯H
m, m = μ
0K×K, m6= μ.
(3.12)
2The reason for employing a different user index m at the receiver is to illustrate the MUI-free
reception mathematically, as shown in (3.3) and (3.12).
35

The above equation shows that MUI-free reception can be achieved since the received
signal from all the users are mutually orthogonal (providing the received signal from all
the users are synchronized to the base station). In the above equation, e¯H
m is a K ×K
diagonal channel matrix for the m-th user, which is given by
e¯H
m = diag
n
e¯h
m(0), . . . ,e¯h
m(K − 1)
o
(3.13)
where e¯h
m(k) is the channel response on the m-th user’s k-th subcarrier. Depending on
the subcarrier mapping scheme, e¯h
m(k) is given by
Interleaved: e¯h
m(k) = ehm

(m − 1) +
N
K
.k

, k = 0, . . . ,K − 1
Localized: e¯h
m(k) = ehm ((m − 1)K + k) , k = 0, . . . ,K − 1. (3.14)
Based on the above analysis, (3.9) can be rewitten and the m-th user’s received
data symbols in the frequency domain are given by
ey
m = e¯H
mex
m +ev
m. (3.15)
Since e¯H
m is a diagonal matrix, it can be written as a circulant matrix being pre- and
post-multiplied by DFT and IDFT matrices, i.e. e¯H
m = FN ¯H
mFHN
, where ¯H
m is a
K ×K circulant channel matrix with its first column given by [¯h
m(0), . . . ,¯h
m(K −1)]T
and its first row given by [¯h
m(0),¯h
m(K − 1), . . . ,¯h
m(1)]. The matrix element ¯h
m(l)
is the l-th equivalent channel impulse response that is experienced by the m-th user,
where ¯h
m(l) = 1
K
PK−1
k=0
e¯h
μ(k)ej 2
N kl (l = 0, . . . ,K − 1). Hence, when converting back
to the time domain, the time domain received data symbols can be described as
Key
ym = FH
m
KFK ¯H
= FH
Kex
mFH
Kev
| {z m}
m + FH
vm
= ¯H
mxm + vm (3.16)
where vm represents the m-th user’s equivalent received noise in the time domain.
Based on (3.15) and (3.16), it becomes clear that with MUI-free reception, any time
domain or frequency domain single-user equalization algorithm [15] can be used at the
SC-FDMA receiver to compensate for frequency-selective channel distortion.
3.2 Linear Frequency Domain Equalization
As previously mentioned, an equalizer is required to combat the multipath fading chan-nel
(i.e. ISI in a SC system). Linear FDE is widely used in practice, for example with
36

PhD thesis - Decision feedback equalization and channel estimation for SC-FDMA

PhD thesis - Decision feedback equalization and channel estimation for SC-FDMA

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