University of ConnecticutDigitalCommons@UConn

Doctoral Dissertations University of Connecticut Graduate School

6-24-2013

Communications and Networking in UnderwaterAcoustic Networked SystemsZhaohui Wangzhwang0312@gmail.com

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Recommended CitationWang, Zhaohui, "Communications and Networking in Underwater Acoustic Networked Systems" (2013). Doctoral Dissertations. 134.http://digitalcommons.uconn.edu/dissertations/134

Communications and Networking in Underwater Acoustic Networked

Systems

Zhaohui Wang, Ph.D.

University of Connecticut, 2013

The Earth is mostly a water planet, with two thirds of its surface covered

by water. Exploration of the mysterious water world has never ceased in human

history, yet at the time being, less than one percent of this environment has been

explored, since it cannot be probed through satellites nor visited by humans for

a long time. Driven by the unprecedented development of wireless communica-

tions and networking in terrestrial radio applications, underwater wireless net-

worked systems, especially underwater acoustic (UWA) networked systems, are

envisioned to revolutionize underwater exploration through providing long-term,

continuous and real-time unmanned data acquisition. Nevertheless, a plethora of

research issues associated with the UWA networked system have to be identified

and addressed before meeting its great potential. Out of a myriad of challenges,

UWA communications and networking are the most important components that

underpin the system architecture.

This thesis aims to identify and address challenges in practical acoustic net-

worked systems. Tailored to the orthogonal frequency-division multiplexing (OFDM)

modulation, three research directions are pursued:

Zhaohui Wang––University of Connecticut, 2013

• Communication techniques for UWA channels with widely separated mul-

tipath clusters: This type of channel exists in many scenarios, such as

the deep-sea horizontal communications and underwater broadcasting net-

works. Due to the extremely large delay spread and time variation of UWA

channels, both interblock and intercarrier interferences are present in the

received signal. Advanced receiver processing algorithms are investigated

to address the above interferences and recover the transmitted information.

• External interference cancellation in UWA OFDM: Despite rich interfer-

ence in UWA environments, few studies are available for interference miti-

gation in UWA communications and networking. In this vein, we propose

a parameterized interference cancellation approach to mitigate an external

interference from OFDM transmissions, which is shown applicable to other

kinds of interferences in UWA networked systems.

• Asynchronous multiuser OFDM reception: Multiuser communication is an

effective methodology to increase spectral efficiency. Due to the large

signal propagation delay in water, signals from multiple users could be

severely misaligned at receivers. By introducing the concepts of overlapped

truncation and interference aggregation, we convert the asynchronous mul-

tiuser problem to a quasi-synchronous multiuser problem with interference

contamination, which therefore can be solved through a traditional quasi-

synchronous multiuser receiver equipped with interference cancellation.

Zhaohui Wang––University of Connecticut, 2013

Proposed solutions in the above research directions are validated using both sim-

ulated and field experimental data sets.

Communications and Networking in Underwater Acoustic Networked

Systems

Zhaohui Wang

B.S., Beijing University of Chemical Technology, Beijing, China, 2006

M.S., Graduate University, Chinese Academy of Sciences, Beijing, China, 2009

A Dissertation

Submitted in Partial Fulfillment of the

Requirements for the Degree of

Doctor of Philosophy

at the

University of Connecticut

2013

Copyright by

Zhaohui Wang

2013

To my parents

iii

ACKNOWLEDGEMENTS

I would like to express my heartfelt gratitude to my major advisor, Professor

Shengli Zhou, who has been a mentor, colleague and friend. His guidance, support

and encouragement have made this a thoughtful and rewarding journey. His

sharp insight, clear mindset and down-to-earth attitude toward research have set

an example of academic perfection, from which I will continue to benefit in future.

I would like to thank Professor Peter K. Willett, Professor Yaakov Bar-

Shalom, Professor Jun-Hong Cui, Professor Krishna Pattipati, Professor Peter

Luh, Professor Bing Wang and Professor Zhijie Shi for their excellent guidance

over the years. It was my great pleasure working with such intelligent and inspi-

rational professors. I would like to thank Professor Zhengdao Wang from Iowa

State University for his valuable suggestions on my work. I would like to thank

Dr. Josko Catipovic from the Navy Undersea Warfare Center for insightful dis-

cussions on research problems and his help on collecting experimental data sets

from the AUTEC environment. I would like to thank Dr. James Preisig, Mr. Lee

Freitag and their teams from the Woods Hole Oceanographic Institution for their

help on experimental data collection. I would also like to thank Dr. Jianzhong

Huang, Dr. Jie Huang, Dr. Xiufeng Song, Dr. Ramona Georgescu, and Dr. Chris-

tian R. Berger for their help on my research.

iv

I would like to extend my gratitude to my colleagues, Lei Wan, Yi Huang,

Sora Choi, Xiaoka Xu, Hao Zhou, Patrick Carroll, Jun Liu, Yibo Zhu, Haining

Mo, Lina Pu, Yu Luo, Li Wei, Huizhong Gao, Yougan Chen, Haixin Sun, Yuzhi

Zhang, Shuo Zhang, Xin Tian, Ting Yuan, Djedjiga Belfadel, David Crouse and

Dave Zhao for their support, feedback, and friendship.

Last but not least, I give my deepest gratitude to my parents, Yongcheng

Wang and Jiuqin Sun, and my brother Lei Wang for their love, understanding,

support and encouragement, and for letting me pursue my dreams far from home.

They have been my continuous inspiration to accomplish my doctorate program.

To my family, I dedicate this dissertation.

v

TABLE OF CONTENTS

Chapter 1: Introduction 1

1.1 Motivation and Challenges . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.3 List of Publications . . . . . . . . . . . . . . . . . . . . . . . . . . 7

Chapter 2: Factor-Graph Based Joint IBI/ICI Mitigation For

OFDM in Underwater Acoustic Multipath Channels

with Widely Separated Clusters 14

2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2.1.1 Deep Water Horizontal Channels . . . . . . . . . . . . . . 16

2.1.2 Underwater Broadcasting Networks . . . . . . . . . . . . . 17

2.1.3 Our Work . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

2.2 System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

2.2.1 Modeling the Clustered Multipath Channel . . . . . . . . . 20

2.2.2 Transmitted Signal . . . . . . . . . . . . . . . . . . . . . . 22

2.2.3 Received Signal . . . . . . . . . . . . . . . . . . . . . . . . 23

2.3 Factor-Graph Based Joint IBI/ICI Equalization . . . . . . . . . . 27

2.3.1 Factor-Graph Based Joint IBI/ICI Equalization . . . . . . 29

2.3.2 Practical Issues . . . . . . . . . . . . . . . . . . . . . . . . 32

2.3.2.1 Implementation considerations . . . . . . . . . . . . . . 32

2.3.2.2 Incorporating multiple receiving elements . . . . . . . . 33

vi

2.4 The Overall Receiver Structure . . . . . . . . . . . . . . . . . . . 35

2.4.1 Sparse Channels Estimation . . . . . . . . . . . . . . . . . 38

2.4.2 Noise Variance Update and Nonbinary LDPC Decoding . . 39

2.4.3 Channel Profile Probing . . . . . . . . . . . . . . . . . . . 39

2.5 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . 40

2.6 Experiment Results in the AUTEC Environment . . . . . . . . . . 45

2.6.1 Experiment Results: AUTEC08 . . . . . . . . . . . . . . . 46

2.6.2 Experiment Results: AUTEC10 . . . . . . . . . . . . . . . 48

2.7 Emulated Experimental Results: MACE10 . . . . . . . . . . . . . 50

2.7.1 Test Case 1 . . . . . . . . . . . . . . . . . . . . . . . . . . 51

2.7.2 Test Case 2 . . . . . . . . . . . . . . . . . . . . . . . . . . 52

2.7.3 Test Case 3 . . . . . . . . . . . . . . . . . . . . . . . . . . 53

2.8 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

Chapter 3: Parameterized Cancellation of Partial-Band Partial-

Block-Duration Interference for Underwater Acoustic

OFDM 55

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

3.1.1 Impulsive Noise Suppression . . . . . . . . . . . . . . . . . 56

3.1.2 Narrowband Interference Suppression . . . . . . . . . . . . 57

3.1.3 Our Work . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

3.2 System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

vii

3.2.1 Transmitted Signal and Channel Model . . . . . . . . . . . 62

3.2.2 Received Signal without Interference . . . . . . . . . . . . 63

3.3 Interference Parameterization . . . . . . . . . . . . . . . . . . . . 65

3.4 Proposed OFDM Receiver with Interference Cancellation . . . . . 68

3.4.1 Initialization . . . . . . . . . . . . . . . . . . . . . . . . . . 70

3.4.2 Interference Detection and Estimation . . . . . . . . . . . 72

3.4.2.1 Determination of the GLRT threshold . . . . . . . . . . 74

3.4.2.2 Computational complexity reduction . . . . . . . . . . . 75

3.4.3 Channel Estimation, Equalization and Nonbinary LDPC

Decoding . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

3.4.4 Noise Variance Estimation . . . . . . . . . . . . . . . . . . 77

3.5 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . 78

3.5.1 Time-Invariant UWA Channels . . . . . . . . . . . . . . . 80

3.5.2 Time-Varying UWA Channels . . . . . . . . . . . . . . . . 81

3.5.3 Performance of the Proposed Receiver with Different SIRs 82

3.5.4 Interference Detection and Estimation . . . . . . . . . . . 83

3.6 Experimental Results: AUTEC10 . . . . . . . . . . . . . . . . . . 83

3.6.1 Test Case 1 . . . . . . . . . . . . . . . . . . . . . . . . . . 85

3.6.2 Test Case 2 . . . . . . . . . . . . . . . . . . . . . . . . . . 86

3.7 Experimental Results: SPACE08 . . . . . . . . . . . . . . . . . . 87

3.8 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90

viii

Chapter 4: Asynchronous Multiuser Reception for OFDM in Un-

derwater Acoustic Communications 92

4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

4.1.1 Asynchronous OFDM Research in Radio Channels . . . . . 93

4.1.2 Our Work . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

4.2 The Proposed Receiver for Asynchronous OFDM Transmissions . 97

4.2.1 Overlapped Truncation . . . . . . . . . . . . . . . . . . . . 100

4.2.2 Interference Aggregation . . . . . . . . . . . . . . . . . . . 101

4.2.3 The Overall Structure of the Proposed Receiver . . . . . . 102

4.2.4 Discussions on the Proposed Receiver . . . . . . . . . . . . 105

4.3 Descriptions of Receiver Modules . . . . . . . . . . . . . . . . . . 106

4.3.1 Interference Subtraction . . . . . . . . . . . . . . . . . . . 106

4.3.2 Frequency-Domain Oversampling . . . . . . . . . . . . . . 107

4.3.3 Multiuser Channel Estimation and Data Decoding with In-

terference Cancellation . . . . . . . . . . . . . . . . . . . . 108

4.3.3.1 Parameterized residual interference estimation and sub-

traction . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

4.3.3.2 Multiuser channel estimation and data detection . . . . 111

4.3.4 Interference Reconstruction . . . . . . . . . . . . . . . . . 113

4.4 Investigation on the Time Duration of Aggregated Interference . . 113

4.5 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . 116

4.5.1 Two-User Systems with Time-Varying Channels . . . . . . 118

ix

4.5.2 Multiuser Systems with Time-Invariant Channels . . . . . 122

4.6 Emulated Experimental Results: MACE10 . . . . . . . . . . . . . 123

4.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128

Chapter 5: Conclusions 129

Appendix A: Experimental Description 131

A.1 Experimental Setting: SPACE08 . . . . . . . . . . . . . . . . . . . 131

A.2 Experimental Setting: MACE10 . . . . . . . . . . . . . . . . . . . 131

A.3 Experimental Setting: AUTEC . . . . . . . . . . . . . . . . . . . 133

A.3.1 AUTEC08 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134

A.3.2 AUTEC10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134

Bibliography 136

x

LIST OF TABLES

2.1 Sensors Groups in the AUTEC08 Experiment . . . . . . . . . . . 45

2.2 AUTEC08 Results for Sensors with Two Clusters . . . . . . . . . 47

A.1 OFDM Parameters in the SPACE08 Experiment . . . . . . . . . . 132

A.2 OFDM Parameters in the MACE10 Experiment . . . . . . . . . . 133

A.3 OFDM Parameters in the AUTEC08 Experiment . . . . . . . . . 134

A.4 OFDM Parameters in the AUTEC10 Experiment . . . . . . . . . 135

xi

LIST OF FIGURES

1.1 An illustration of the underwater acoustic networked system. The

sensing nodes anchored at the water bottom or carried by underwa-

ter vehicles can communicate using the acoustic signal, while the

buoys on the water surface can communicate with control center

using radio. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.2 The AUTEC network: A deep-water network deployed by the At-

lantic Undersea Test and Evaluation Center (AUTEC). The net-

work has 96 nodes in total, which are fiber connected and occupy

an area of size 30× 50 km2. The distance between nodes is larger

than 4 km, and depths of nodes vary from 1.5 km to 2 km. . . . . 3

2.1 Illustration of multipath clusters in deep water horizontal channels. 17

2.2 Illustration of an underwater broadcasting network with multiple

gateways. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

2.3 Illustration of channels with two clusters. ∆: an integer; Tbl :

time-duration of each transmitted block. . . . . . . . . . . . . . . 24

2.4 Illustration of the received blocks. Assume ∆ = 2 and ς > 0. . . . 26

xii

2.5 Factor-graph based joint IBI/ICI equalization, empty boxes rep-

resent the prior probability density function nodes; filled boxes

represent the likelihood function nodes; messages m1 ∼ m12 repre-

sent either the prior probability density function or the marginal

probability density function over the factor nodes. . . . . . . . . . 33

2.6 Modified factor-graph based joint IBI/ICI equalization. The like-

lihood function node is omitted. . . . . . . . . . . . . . . . . . . . 34

2.7 Flow chart of the proposed progressive/iterative receiver structure. 36

2.8 BLER performance of the factor-graph based receiver versus mul-

tiuser receiver with mild Doppler spreads σv = 0.10 m/s. ICI-

depth is fixed at D = 1. . . . . . . . . . . . . . . . . . . . . . . . 41

2.9 BLER performance of three receivers with mild Doppler spreads

σv = 0.10 m/s. SNR of the first cluster is fixed at 11 dB; ICI-depth

is fixed at D = 1. Five iterations are performed. . . . . . . . . . 43

2.10 BLER performance of the factor-graph based progressive receiver

with mild Doppler spreads σv = 0.10 m/s. . . . . . . . . . . . . . 44

2.11 LFM correlation results at two sensors in the AUTEC08 experiment. 45

2.12 IBI illustration of ZP-OFDM in the AUTEC08 experiment over a

channel with two clusters at sensor (c). . . . . . . . . . . . . . . . 46

2.13 Significant paths of the estimated channel at sensor (c) in the

AUTEC08 experiment. . . . . . . . . . . . . . . . . . . . . . . . . 46

xiii

2.14 Samples of HFM correlation results at two sensors in the AUTEC10

experiment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

2.15 Sample of channel estimation results in the AUTEC10 experiment. 48

2.16 Decoding results of QPSK symbols in the AUTEC10 experiment.

22 transmissions are involved. Imax = 2 for each value of D. . . . 49

2.17 BLER performance of three receivers, averaged over 30 transmis-

sions. Imax = 2 for each value of D. . . . . . . . . . . . . . . . . . 51

2.18 BLER performance of three receivers by adding white Gaussian

noise with different variances, averaged over 30 transmissions. Two

phones are combined. Imax = 2 for each value of D. . . . . . . . . 52

2.19 BLER performance of three receivers with different power ratios

between two clusters, averaged over 30 transmissions. Two phones

are combined. Three curves for each receiver correspond to D =

0, 1, 2, respectively, and Imax = 2 for each value of D. . . . . . . . 53

3.1 Samples of the time domain waveform and the time-frequency

spectrum of the received signal at one hydrophone after bandpass

filtering. The transmitted signal consists of a hyperbolic frequency

modulated (HFM) preamble followed by 10 ZP-OFDM blocks. The

circle and the square in subfigure (a) denote the locations of inter-

ference and useful signal, respectively. . . . . . . . . . . . . . . . 58

3.2 Receiver structure for interference mitigation and data detection. 71

xiv

3.3 BLER performance of several receivers in the time-invariant sce-

nario, SIR = 0 dB. . . . . . . . . . . . . . . . . . . . . . . . . . . 81

3.4 BLER performance improvement against iterations of the pro-

posed receiver in the time-invariant scenario, SIR = 0 dB. . . . . 82

3.5 BLER performance of receivers in the time-varying channels, D =

1, SIR = 0 dB. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

3.6 BLER performance of the proposed receiver at different SIR levels. 84

3.7 ROC of the GLRT interference detector. . . . . . . . . . . . . . . 85

3.8 Block error rate of 13 transmissions with/without interference can-

cellation (IC) versus different levels of added noise, Imax = 7. . . . 86

3.9 Sample of the received signals at two hydrophones after band-

pass filtering. The two data sets are added together with different

weights to generate semi-experimental data sets at different SIR

levels. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

3.10 BLER of 18 transmissions with/without interference cancellation (IC)

versus different signal to interference power ratio, Imax = 7, SNR

≈ 7.9 dB. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

3.11 BLER performance comparison of receiver with/without interfer-

ence cancellation, 16-QAM, D = 3. Marker ∗: receiver without

interference cancellation; marker o: proposed interference cancel-

lation receiver; marker +: original BLER without adding interfer-

ence; dashed line: [0 1 5 9]th iteration, solid line: 10th iteration. . 89

xv

4.1 Two examples of underwater acoustic networks. The nodes an-

chored at the water bottom in the first network are connected to

a control center via cables. The gateways in the second network

can communicate with satellites or ships using radio waves. . . . . 94

4.2 Illustration of the overlapped partition of the received signal and

the aggregated interference in an asynchronous Nu-user system. . 99

4.3 Illustration of the proposed burst-by-burst asynchronous multiuser

receiver with iterative forward/backward processing, withNbl blocks

in each burst. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

4.4 Probability density function of the maximum asynchronism on the

OFDM block level in an asynchronous multiuser system, where the

users are uniformly distributed within a circle of diameter DN. . . 115

4.5 BLER performance of four receiving configurations, σv = 0.1 m/s. 119

4.6 BLER performance of the proposed receiver in a two-user system

with different relative delays, σv = 0.1 m/s; three receiving hy-

drophones. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120

4.7 BLER performance of four receiving configurations, solid lines:

σv = 0.3 m/s; dashed lines: σv = 0.5 m/s. . . . . . . . . . . . . . 121

4.8 BLER performance of two receiving configurations with and with-

out perfect channel knowledge, two receiving hydrophones are used,

and σv = 0.3 m/s. . . . . . . . . . . . . . . . . . . . . . . . . . . 122

xvi

4.9 BLER performance of the proposed receiver in a four-user system

with different relative delays, six receiving hydrophones. . . . . . 123

4.10 BLER performance of the proposed receiver with four rounds of

forward/backward processing, εmax ∼ U [0.3, 0.4]× Tbl, four users,

six receiving hydrophones. . . . . . . . . . . . . . . . . . . . . . . 124

4.11 BLER performance of four receiving configurations, MACE10 data

sets. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125

4.12 BLER performance of the proposed receiver with different relative

delays, four rounds of forward and backward processing and eight

iterations within each block processing; MACE10 data sets. . . . 126

4.13 PSR of the proposed receiver with different number of users with

and without a rate-8/10 Reed-Solomon erasure-correction code

across 10 blocks, four rounds of forward/backward processing, eight

iterations within each block processing. . . . . . . . . . . . . . . . 127

A.1 Setup of the SPACE08 experiment . . . . . . . . . . . . . . . . . 132

A.2 Significant wave height and average wind speed for selected days

in SPACE08 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133

A.3 Received signal magnitude fluctuations in MACE10 . . . . . . . . 134

A.4 Estimated relative moving speed in Tow 1 . . . . . . . . . . . . . 135

xvii

Acronyms

ARQ automatic repeat request

AUTEC Atlantic Undersea Test and Evaluation Center

CCI cochannel interference

CFO carrier frequency offset

CP-OFDM cyclic-prefix OFDM

CS compressive sensing

DFE decision-feedback based equalization

FFT fast Fourier transform

FG factor graph

GLRT generalized log-likelihood test

GMP Gaussian message passing

HFM hyperbolic-frequency modulation

IBI interblock interference

ICI intercarrier interference

ISI intersymbol interference

xviii

xix

LFM linear-frequency modulation

LLR log-likelihood ratio

LMMSE linear minimum mean-square error

LPF low bandpass filtering

LS least squares

MACE10 mobile acoustic communication experiment in 2010

MAP maximum the a posteriori probability

MIMO multi-input multi-output

ML maximum likelihood

MSE mean-square error

MMSE minimum mean-square error

MRC multi-access control

OFDM orthogonal frequency-division multiplexing

SNR signal-to-noise ratio

SIMO single-input multi-output

SIR signal-to-interference ratio

SINR signal-to-interference-and-noise ratio

SPA sum product algorithm

SPACE08 surface processes and acoustic communication experiment in 2008

UWA underwater acoustic

ZP-OFDM zero-padded OFDM

Notations

a scaler

a a vector

A a matrix

∝ equality of functions up to a scaling factor

[a]m the mth entry of vector a

{aℓ}jℓ=i a set formed by elements {[a]i, [a]i+1, · · · , [a]j}

[A]m,k the (m, k)th entry of matrix A

AT transpose of matrix A

AH complex conjugate transpose of matrix A

A† pseudo-inverse of matrix A

R(a) real part of complex number a

E(X) expectation of random variable X

E(x) expectation of random vector x

tr(A) trace of matrix A

|S| cardinality of set S

xx

Chapter 1

Introduction

1.1 Motivation and Challenges

The Earth is mostly a water covered planet. More than seventy percent of its

surface is covered by water. The water environment supports the largest ecosys-

tem on the planet, and drives a wide range of natural phenomena, including

climate, which impacts human daily activities. Despite the fact that exploration

of this environment has never ceased in human history, less than 1% of it has

ever been explored, primarily because it cannot be visited by humans for long

nor probed through satellites. Driven by the tremendous progress of wireless

communications and networking in the terrestrial radio environment, underwa-

ter wireless networked systems, especially underwater acoustic (UWA) network

systems, are envisioned to revolutionize the underwater exploration.

The underwater acoustic networked system, as depicted in Fig. 1.1, has many

appealing features. It can achieve unmanned underwater exploration by the

1

2

surface

bottom

vehicle

buoy

radio

radiocontrol

center

acoustic

comm.

sensor

Figure 1.1: An illustration of the underwater acoustic networked system. Thesensing nodes anchored at the water bottom or carried by underwater vehiclescan communicate using the acoustic signal, while the buoys on the water surfacecan communicate with control center using radio.

sensing nodes which are anchored at water bottom or carried by underwater ve-

hicles. Since the sensors can stay in water for a long time, an underwater acoustic

networked system can achieve long-term, continuous and real time underwater

observation. Moreover, UWA communications enable high motion agility and

flexibility of the nodes, and allow interactive system query and instantaneous

system response. One example of underwater acoustic networked systems is a

deep-sea network deployed by the Atlantic Undersea Test and Evaluation Center

(AUTEC) around Andros Island near the Tongue of the Ocean, Bahamas, as

shown in Fig. 1.2. The network has 96 nodes in total, which are fiber connected

and occupy an area of size 30 × 50 km2. The distance between nodes is larger

than 4 km, and depths of nodes vary from 1.5 km to 2 km [24, 96]. In this net-

work, acoustic communications are in extensive daily use between mobile users

and fixed network nodes.

3

Tongue of the Ocean

Andros Island,

Bahamas

AUTECFlorida

(a) The AUTEC network

0 5 10 15 20 25 300

10

20

30

40

50

60

1 23 4 5

6 7

8 910 11 12

13 14

15 161718 19 2021 22 23 2425 26 27 28 29 3031 32 33 34

35 36 37 38 39 40 4142 43 44 45 4649 50 51 52 53

56 57 58 59 6061

64 65 66 67 6869

72 73 74 75 76 77 7880 81 82 83 84 85

88 89 90 9192 93

X [km]

Y [k

m]

(b) Distribution of network nodes

Figure 1.2: The AUTEC network: A deep-water network deployed by the AtlanticUndersea Test and Evaluation Center (AUTEC). The network has 96 nodes intotal, which are fiber connected and occupy an area of size 30 × 50 km2. Thedistance between nodes is larger than 4 km, and depths of nodes vary from 1.5km to 2 km.

To make the underwater acoustic networked system function well in water,

smart technologies from multiple disciplines are required, such as acoustic com-

munication technologies, sensing technologies, platforms to carry the sensing

nodes (e.g., the autonomous underwater vehicles), power supplies, and cyber-

control to coordinate the whole system. Among the above areas, acoustic com-

munications and networking are the most important components that underpin

the system architecture.

The UWA environment is commonly viewed as one of the most challenging

environments for wireless communications and networking. It differs from the

terrestrial radio environment in many different aspects. Three prominent features

are the following:

4

• Low propagation speed of acoustic waves in water. With a typical sound

speed of 1500 m/s, the propagation delay of signal in water is about five

orders of magnitude larger than its radio counterpart, thus incurring very

large delay spreads of communication channels and considerable latency for

transmission coordination among multiple system users.

• Low communication bandwidth. Compared to the radio channels where the

available bandwidth can be up to several GHz, the available bandwidth in

water is limited to tens of kHz. Efficient utilization of the limited bandwidth

is critical for high-rate underwater networking applications.

• Rich in interferences. The underwater environment is often plagued with

various kinds of interferences, such as from marine animals, human activ-

ities, and concurrent acoustic operations. Mitigation of interferences in

underwater acoustic networked systems is vital for communication reliabil-

ity.

In short, the water medium poses many unique challenges to acoustic net-

worked systems, which could be very diverse depending on applications. Given

that we are at the early stage of doing investigations on underwater acoustic

networked systems, numerous challenges have to be identified and addressed.

5

1.2 Overview

The thesis aims to identify and address research challenges encountered in

practical UWA networked systems. Tailored to the orthogonal frequency-division

multiplexing (OFDM) modulation, three major research directions are pursued

in Chapters 2 ∼ 4, respectively.

In Chapter 2, we investigate a transceiver design for OFDM in multipath

UWA channels with widely separated clusters. These channels show up in cer-

tain practical scenarios, such as in the deep water horizontal transmissions and

in underwater broadcasting networks, and introduce both interblock interfer-

ence and intercarrier interference (IBI/ICI) in the received signal. For joint IBI

and ICI mitigation, we propose a factor-graph based equalization method, in

which estimation of information symbols is performed via messages passing over

a well-designed graph. We also present a sparse channel estimator by treating

the two clusters of the long channel as two virtual quasi-synchronous channels.

Both channel estimation and equalization are integrated into an iterative receiver

framework.

Despite that UWA channels are well known to contain various interferences,

research on interference mitigation in UWA communications has been very scarce.

In Chapter 3, we deal with a wideband OFDM transmission in the presence

of an external interference which occupies partially the signal band and whose

time duration is shorter than the OFDM block. We parameterize the unknown

6

interference waveform by a number of parameters assuming prior knowledge of

the frequency band and time duration of the interference, and develop an iterative

receiver, which couples interference detection via a generalized likelihood-ratio-

test (GLRT), interference reconstruction and cancellation, channel estimation,

and data detection.

Multiuser communication is an effective methodology to increase the spectral

efficiency in UWA environments. Due to the large signal propagation delay in

water, signals from multiple users are usually severely misaligned at receivers.

In Chapter 4, we study a time-asynchronous multiuser reception approach for

OFDM transmissions in UWA channels. The received data burst is segmented

and apportioned to multiple processing units in an overlapped fashion, where

the length of the processing unit depends on the maximum asynchronism among

users on the OFDM block level. Interference cancellation is adopted to reduce

the interblock interference between overlapped processing units. Within each

processing unit, the residual interblock interference from multiple users is aggre-

gated as one external interference which can be parameterized. Multiuser channel

estimation, data detection, and interference mitigation are then carried out in an

iterative fashion.

Contributions of the dissertation are summarized in Chapter 5.

7

1.3 List of Publications

During the course of the Ph.D. program the following articles have been pub-

lished or submitted for publication. The body of this thesis corresponds largely

to the work in articles J5, J7 and J10.

Book

B1. S. Zhou, and Z.-H. Wang, “OFDM for Underwater Acoustic Communi-

cations,” John Wiley & Sons, scheduled to appear on market in 2013.

Journals

J15. H. Sun, Z.-H. Wang, and S. Zhou, “Joint Carrier Frequency Offset and

Impulse Noise Estimation for Underwater Acoustic OFDM with Null Sub-

carriers,” IEEE Journal of Oceanic Engineering, to be submitted Jul. 2013.

J14. Y. Chen, Z.-H. Wang, L. Wan, H. Zhou, S. Zhou, and X. Xu, “OFDM

Modulated Dynamic Coded Cooperation in Underwater Acoustic Chan-

nels,” IEEE Journal of Oceanic Engineering, submitted Nov. 2012.

J13. Z.-H. Wang, S. Zhou, Z. Wang, B. Wang, and P. Willett, “Dynamic Block-

Cycling Over A Linear Network in Underwater Acoustic Channels,” IEEE

Transactions on Wireless Communications, submitted Jul. 2012; revised

Dec. 2012.

8

J12. J. Liu, Z.-H. Wang, M. Zuba, Z. Peng, J.-H. Cui, and S. Zhou, “A Joint

Time Synchronization and Localization Design for Mobile Underwater Sen-

sor Networks,” IEEE/ACM Transactions on Networking, submitted May

2013.

J11. J. Liu, Z.-H. Wang, M. Zuba, Z. Peng, J.-H. Cui, and S. Zhou, “DA-Sync:

A Doppler Assisted Time Synchronization Scheme for Mobile Underwater

Sensor Networks,”IEEE Transactions on Mobile Computing, 2013 (to ap-

pear).

J10. J.-H. Huang, S. Zhou, Z.-H. Wang, “Performance Results of Two Itera-

tive Receivers for Distributed MIMO-OFDM in Underwater Acoustic Chan-

nels,” IEEE Journal of Oceanic Engineering, vol. 38, no. 2, pp. 347 - 357,

Apr. 2013.

J9. Z.-H. Wang, S. Zhou, J. Catipovic, and P. Willett, “Asynchronous Mul-

tiuser Reception for OFDM in Underwater Acoustic Communications,”

IEEE Transactions on Wireless Communications, vol. 12, no. 3, pp. 1050-

1061, Mar. 2013.

J8. Z.-H. Wang, J. Huang, S. Zhou, and Z. Wang, “Iterative Receiver Process-

ing for OFDM Modulated Physical-Layer Network Coding in Underwater

Acoustic Channels,” IEEE Transactions on Communications, vol. 61, no.

2, pp. 541 - 553, Feb. 2013.

9

J7. Z.-H. Wang, S. Zhou, J. Catipovic, and J. Huang, “Factor-Graph Based

Joint IBI/ICI Mitigation For OFDM in Underwater Acoustic Multipath

Channels with Long-Separated Clusters,” Journal of Oceanic Engineering,

vol. 37, no. 4, pp. 680-694, Oct. 2012.

J6. Z.-H. Wang, S. Zhou, J. Preisig, K. R. Pattipati, and P. Willett, “Clus-

tered Adaptation for Estimation of Time-Varying Underwater Acoustic

Channels” IEEE Transactions on Signal Processing, vol. 60, no. 6, pp.

3079-3091, Jun. 2012.

J5. X. Xu, Z.-H. Wang, S. Zhou, and L. Wan, “Parameterizing both path am-

plitude and delay variations of underwater acoustic channels for block de-

coding of orthogonal frequency division multiplexing,”Journal of the Acous-

tical Society of America, vol. 131, no. 6, pp. 4672- 4679, Jun. 2012.

J4. L. Wan, Z.-H. Wang, S. Zhou, T. C. Yang and Z. Shi, “Performance

Comparison of Doppler Scale Estimation Methods for Underwater Acoustic

OFDM,” Journal of Electrical and Computer Engineering, Special Issue on

Underwater Communications and Networks, 2012.

J3. Z.-H. Wang, S. Zhou, J. Catipovic, and P. Willett, “Parameterized can-

cellation of partial-band partial-block-duration interference for underwater

acoustic OFDM,” IEEE Transactions on Signal Processing, vol. 60, no. 4,

pp. 1782-1795, Apr. 2012.

10

J2. Z.-H. Wang, S. Zhou, G. B. Giannakis, C. R. Berger, and J. Huang,

“Frequency-Domain Oversampling for Zero-Padded OFDM in Underwater

Acoustic Communications,”IEEE Journal of Oceanic Engineering, vol. 37,

no. 1, pp. 14 - 24, Jan. 2012.

J1. C. R. Berger, Z.-H. Wang, J.-Z. Huang, and S. Zhou, “Application of

Compressive Sensing to Sparse Channel Estimation,” IEEE Communica-

tions Magazine, vol. 48, no. 11, pp. 164-174, Nov. 2010 (invited).

Proceedings

C18. S. Lu, Z. Wang, Z.-H. Wang, and S. Zhou, “Underwater Acoustic Net-

work with Random Access: A Physical Layer Perspective,” submitted to

the Global Communications Conference, Atlanta, GA, Dec. 9-13, 2013.

C17. Z.-H. Wang, S. Zhou, Z. Wang, J. Catipovic, and P. Willett, “Outage

Performance of a Multiuser Distributed Antenna System in Underwater

Acoustic Channels,” Proc. of the Asilomar Conference on Signals, Systems

and Computers, Pacific Grove, California, Nov. 4-7, 2012 (invited).

C16. Z.-H. Wang, S. Zhou, Z. Wang, B. Wang, and P. Willett, “Dynamic Block-

Cycling Over a Linear Network in Underwater Acoustic Channels,” Proc.

of the ACM International Workshop on Underwater Networks (WUWNet),

Los Angeles, California, Nov. 5-6, 2012.

11

C15. L. Wan, S. Hurst, Z.-H. Wang, S. Zhou, Z. Shi, and S. Roy, “Joint Linear

Precoding and Nonbinary LDPC Coding for Underwater Acoustic OFDM,”

Proc. of MTS/IEEE OCEANS Conference, Virginia, USA, Oct. 14-19,

2012.

C14. H. Sun, W. Shen, Z.-H. Wang, S. Zhou, X. Xu, and Y. Chen, “Joint

Carrier Frequency Offset and Impulse Noise Estimation for Underwater

Acoustic OFDM with Null Subcarriers,” Proc. of MTS/IEEE OCEANS

Conference, Virginia, USA, Oct. 14-19, 2012.

C13. Y. Chen, H. Sun, L. Wan, Z.-H. Wang, S. Zhou, and X. Xu, “Dynamic

Network Coded Cooperative OFDM for Underwater Data Collection,” Proc.

of MTS/IEEE OCEANS Conference, Virginia, USA, Oct. 14-19, 2012.

C12. J. Liu, Z.-H. Wang, Z. Peng, M. Zuba, J.-H. Cui, and S. Zhou, “JSL: Joint

Time Synchronization and Localization Design with Stratification Compen-

sation in Mobile Underwater Sensor Networks,” Proc. of IEEE SECON

Conference, Seoul, Korea, Jun. 18-21, 2012.

C11. Z.-H. Wang, S. Zhou, J. Catipovic, and P. Willett, “Asynchronous Mul-

tiuser Reception for OFDM in Underwater Acoustic Communications,”

Proc. of MTS/IEEE OCEANS Conference, Yeosu, Korea, May 21-24, 2012.

12

C10. Z.-H. Wang, S. Zhou, J. Catipovic, and P. Willett, “Parameterized Can-

cellation of Partial-Band Partial-Block-Duration Interference for Underwa-

ter Acoustic OFDM,” Proc. of the ACM International Workshop on Un-

derwater Networks (WUWNet), Seattle, Washington, Dec. 1-2, 2011.

C9. J. Liu, Z.-H. Wang, Z. Peng, M. Zuba, J.-H. Cui, and S. Zhou, “TSMU:

A Time Synchronization Scheme for Mobile Underwater Sensor Networks,”

Proc. of Global Communications Conference, Houston, TX, Dec. 5-9, 2011.

C8. J.-Z. Huang, S. Zhou, and Z.-H. Wang, “Robust Initialization with Re-

duced Pilot Overhead for Progressive Underwater Acoustic OFDM Re-

ceivers,” Proc. of MILCOM Conference, Baltimore, Maryland, Nov. 7-10,

2011.

C7. W. Zhou, Z.-H. Wang, J. Huang, and S. Zhou, “Blind CFO Estimation

for Zero-Padded OFDM over Underwater Acoustic Channels,” Proc. of

MTS/IEEE OCEANS Conference, KONA, Hawaii, Sep. 19-22, 2011.

C6. Z.-H. Wang, S. Zhou, J. Preisig, K. Pattipati, and P. Willett, “Per-

Cluster-Prediction Based Sparse Channel Estimation for Multicarrier Un-

derwater Acoustic Communications,” Proc. of IEEE International Confer-

ence on Signal Processing, Communications and Computing, Xi’an, China,

Sep. 14-16, 2011.

13

C5. J. Huang, Z.-H. Wang, S. Zhou, and Z. Wang, “Turbo Equalization for

OFDM Modulated Physical Layer Network Coding,” Proc. of the Twelfth

IEEE International Workshop on Signal Processing Advances in Wireless

Communications (SPAWC), San Francisco, Jun. 26-29, 2011.

C4. Z.-H. Wang, S. Zhou, G. B. Giannakis, C. R. Berger, and J. Huang,

“Frequency-Domain Oversampling for Zero-Padded OFDM in Underwater

Acoustic Communications,” Proc. of Global Communications Conference,

Miami, Florida, Dec. 6-10, 2010.

C3. Z.-H. Wang, S. Zhou, J. Catipovic, and J. Huang, “OFDM in Deep Water

Acoustic Channels with Extremely Long Delay Spread,” Proc. of the ACM

International Workshop on Underwater Networks (WUWNet), Woods Hole,

Massachusetts, Sep. 31, 2010.

C2. Z.-H. Wang, S. Zhou, J. Catipovic, and J. Huang, “A Factor-Graph

based ZP-OFDM Receiver for Deep Water Acoustic Channels,” Proc. of

MTS/IEEE OCEANS Conference, Seattle, Washington, Sep. 20-23, 2010.

C1. W. Chen, J. Huang, Z.-H. Wang, and S. Zhou, “Blind Channel Shorten-

ing for Zero-Padded OFDM,” Proc. of MTS/IEEE OCEANS Conference,

Seattle, Washington, Sep. 20-23, 2010.

Chapter 2

Factor-Graph Based Joint IBI/ICI Mitigation

For OFDM in Underwater Acoustic Multipath

Channels with Widely Separated Clusters

2.1 Introduction

Multicarrier modulation has been under extensive study for UWA commu-

nications in recent years. Many challenges unique to UWA channels have been

identified and partially addressed; see e.g., [?, 6, 11, 38, 39, 43–45, 69, 71, 79] and

references therein, where various receiver designs have been proposed and verified

with experimental results. These works mainly focus on the channel with a de-

lay spread relatively shorter than the symbol time duration, hence the interblock

interference (IBI) is usually avoided by inserting a guard interval between consec-

utive transmitted symbols without a considerable data rate reduction. However,

14

15

under certain scenarios, the underwater acoustic channel could have a very large

delay spread, e.g., on the order of several symbol-lengths. Relying only on insert-

ing the guard interval to avoid IBI is thus not desirable.

In this chapter, we consider the underwater acoustic channel with widely

separated clusters, particularly the channel with two or three clusters and the

intra-cluster delay spread could be around one second. Rather than inserting a

guard interval on the order of the channel delay spread to avoid IBI, we allow

IBI in the received signal by using a relatively short guard interval so as to avoid

a significant data rate reduction.

Our work is motivated by the strong need of forming acoustic local area

networks (ALAN) in deep oceans. One example is the AUTEC network; see

Fig. 1.2, where improving the communication performance has been identified as

an important task for the network development.

Our experimental data collected in the AUTEC environment reveal that the

deep water horizontal channel could frequently contain two widely separated clus-

ters. In addition to the deep water applications, a shallow water network with

multiple collaborating broadcasters can also have a long channel with large sep-

aration between clusters. We next provide more details.

16

2.1.1 Deep Water Horizontal Channels

Sharing many common characteristics of shallow water channels, such as mul-

tipath propagation and fast variations, deep water horizontal acoustic channels

exhibit additional unique features.

• Extremely long delay spread. As an example, consider a transmitter and

a receiver placed with a distance of d = 5 km and a depth of h = 2 km.

The delay difference of the direct path and the path bounced once from the

surface is about (√4h2 + d2 − d)/c = 930 ms. In contrast, typical shallow

water acoustic channels have delay spreads about 15 to 30 ms.

• Clustered arrivals. According to the sound ray-tracing theory, propaga-

tion paths of acoustic signals can be characterized by several eigenpaths

randomly surrounded by a number of sub-eigenpaths [19]. For deep water

horizontal channels, typical eigenpaths are formed by direct transmissions,

surface and bottom reflections. The eigenpaths are well separated due to

the large difference in the distances traveled. Hence, multiple arrivals tend

to form several distinct clusters.

Fig. 2.1 illustrates a multiple-cluster channel structure in the scenario where

the transmitter and receiver are several kilometers apart and both are anchored

close to the sea floor. The first cluster as shown consists of both direct transmis-

sions and paths arising from bottom reflections. Given the short distance of both

transmitter and receiver to the sea floor, the first cluster has a very small delay

17

transmiter receiver

surface

bottom

h

d

2nd cluster

1st cluster

Figure 2.1: Illustration of multipath clusters in deep water horizontal channels.

spread. The paths associated with the first surface reflection and possible bottom

refections constitute the second cluster, which has a relatively large delay spread

and a severe Doppler spread due to the dispersion caused by reflections. The

third cluster and beyond are formed by the paths with more than one surface

reflections. The energy of the third cluster and beyond is often much smaller

than the first two clusters, and can be neglected.

2.1.2 Underwater Broadcasting Networks

Similar channel characteristics show up in the underwater communication

networks [3, 60, 65]. One example is the underwater broadcasting network as

shown in Fig. 2.2, in which the gateways communicate with a control center

using radio links, and then broadcast the same information they received from

the control center to underwater sensors via the acoustic link. Related research on

this broadcasting network with multiple gateways can be found, e.g., [13,32,33].

Notice that signals from different gateways will reach one particular sensor with

relative delays. The IBI will occur in the received signal at each sensor. To

recover the broadcast information, one can regard that the signal received at

18

surface

bottom

control centergateway

sensor

acoustic

radio

Figure 2.2: Illustration of an underwater broadcasting network with multiplegateways.

each sensor is from a single source but passing through a channel with widely

separated multipath clusters. For example, if the distances between the sensor

to the two transmitters differ by 450 meters, the relative delay is about 300 ms,

which is much larger than the typical block duration.

The broadcasting network illustrated in Fig. 2.2 falls into a large category

called single frequency networks (SFNs). The concept of SFNs has been widely

used in Digital Audio Broadcasting (DAB) and Digital Video Broadcasting (DVB)

systems [49].

2.1.3 Our Work

In this chapter, we consider the zero-padded (ZP)-OFDM transmission over

a multipath channel with widely separated clusters. Compared to the cyclic-

prefix OFDM, ZP-OFDM saves the transmission power in the guard interval,

which could be considerable due to the widely separated clusters. For simplicity,

we limit our discussion to the channel with two clusters. The situation with two

19

clusters is very typical, as shown in the data collected in the AUTEC environment.

Extension of our discussions to channels with more than two clusters will not be

pursued in this chapter.

On top of the IBI, there exists intercarrier interference (ICI) due to the fast

time variation of the channel within an OFDM block. To mitigate both IBI and

ICI jointly, a factor-graph based equalization method is proposed in this chapter,

in which the information symbols are estimated according to the Gaussian mes-

sage passing principle. A sparse channel estimator is also developed by treating

the two widely separated clusters as two virtual quasi-synchronous channels. The

channel estimation and equalization modules are then integrated in a progressive

receiver framework [28], where the system performance improves as the system

model updates progressively.

Besides simulation results, two sets of experimental results are presented to

validate the performance of the proposed receiver in the deep water horizontal

channels, and one set of emulated experimental results is provided to validate the

receiver performance in a shallow water broadcasting network. Both simulation

and experimental results show that the proposed receiver outperforms the tradi-

tional receiver without IBI mitigation and a multiuser based receiver presented

in our preliminary work in [88].

The rest of the chapter is organized as follows. The system model is intro-

duced in Section 2.2. A factor-graph based joint IBI/ICI equalization method is

presented in Section 2.3. An overall receiver design is discussed in Section 2.4.

20

Simulation results are presented in Section 2.5. Experimental results are provided

in Sections 2.6 and 2.7. We draw conclusions in Section 2.8. This chapter collects

the results published in [87–89].

2.2 System Model

In this section, we present an approach to modeling the multipath channel

with widely separated clusters, and build an input-output relationship to describe

IBI and ICI at the receiver jointly.

2.2.1 Modeling the Clustered Multipath Channel

We adopt a path-based channel model. Consider a channel with Npa discrete

paths. Let Ap(t) and τp(t) denote the amplitude and delay of the pth path,

respectively. The channel impulse response is

h(t, τ) =

Npa∑

p=1

Ap(t)δ (τ − τp(t)) . (2.1)

For the multipath channel considered in this work, the channel delay spread

can be several times larger than the transmitted block length, leading to IBI

at the receiver. To model the IBI at the receiver, we reformulate the channel

impulse response as the summation of the impulse responses of paths within each

cluster. Define Tbl as the time-duration of each transmitted block. Since the

channel contains two clusters with a long delay in between, we explicitly define

21

τ12 as the intercluster delay, and decompose it to

τ12 = ∆Tbl + ς, (2.2)

where ∆ is an integer and ς is the residual within [−Tbl/2, Tbl/2]. With such

a decomposition, the two-cluster channel within the nth received block can be

represented as the sum of two channels,

h(t, τ ;n) = h(1)(t, τ ;n) + h(2)(t, τ −∆Tbl;n), (2.3)

with h(i)(t, τ ;n) denoting the channel impulse response of the ith cluster; see

Fig. 2.3 for illustration. Each cluster consists of multiple paths as

h(i)(t, τ ;n) =

N(i)pa∑

p=1

A(i)p (t;n)δ

(τ − τ (i)p (t;n)

)(2.4)

for i = 1, 2, where A(i)p (t;n) and τ

(i)p (t;n) denote the amplitude and delay of the

pth path within the ith cluster, respectively, and N(i)pa denotes the number of

paths.

Within each received OFDM block, we assume that (i) the path amplitude

does not change A(i)p (t;n) ≈ A

(i)p [n]; and (ii) the path delay can be approximated

as τ(i)p (t;n) ≈ τ

(i)p [n] − a

(i)p [n]t, where τ

(i)p [n] and a

(i)p [n] are the initial delay and

the Doppler rate of the pth path in the ith cluster, respectively. The channel

impulse response of the ith cluster can be reformulated as

h(i)(t, τ ;n) =

N(i)pa∑

p=1

A(i)p [n]δ

(τ − (τ (i)p [n]− a(i)p [n]t)

)(2.5)

for i = 1, 2.

22

Formulations in (2.3) and (2.5) allow us to view the channel with widely sepa-

rated clusters as the sum of two channels that are aligned with the OFDM block

structure. The two channels are asynchronous across blocks with one lagging

∆ blocks behind the other, but are quasi-synchronous within the OFDM block

duration. The quasi-synchronous property allows the partitioning of the received

signals into blocks, whose frequency-domain samples can be obtained for further

data processing.

2.2.2 Transmitted Signal

Let T denote the OFDM symbol duration and Tg the length of the guard

interval between consecutive OFDM blocks. The time duration of each OFDM

block is thus Tbl = T + Tg. With the subcarrier spacing of 1/T , a total of K

subcarriers are located at frequencies

fk = fc +k

T, k = −K

2, . . . ,

K

2− 1 (2.6)

where fc is the center frequency. The signal bandwidth is thus B = K/T . Let

s[k;n] denote the information symbol on the kth subcarrier of the nth block,

and define SA and SN as the non-overlapping sets of active and null subcarriers,

respectively, which satisfy SA∪SN = {−K/2, . . . , K/2−1}. The passband signal

of the nth block can be expressed as

s(t;n) = 2R

(∑

k∈SA

s[k;n]ej2πfktg(t)

)

, t ∈ [0, Tbl] (2.7)

23

where g(t) is a rectangular window with nonzero support within [0, T ],

g(t) =

1T, t ∈ [0, T ]

0, otherwise

(2.8)

which has the Fourier transform G(f) = sin(πfT )πfT

e−jπfT . For a data burst with

Nbl blocks, the transmitted signal is

x(t) =

Nbl∑

n=1

s(t− nTbl;n), t ∈ [0, NblTbl] . (2.9)

We would like to highlight one difference concerning the signal design for the

channels with widely separated clusters compared to that for traditional shallow

water channels. Shallow water acoustic channels usually have small or moderate

delay spreads, and hence the guard interval is usually larger than the maximum

channel delay spread, so that IBI is avoided at the receiver [?, 6, 39, 43, 45, 78].

For channels with widely separated clusters, the guard interval cannot be larger

than the maximum channel delay spread, as that would lead to a significant data

rate reduction. With Tg smaller than the channel delay spread, the IBI will be

addressed explicitly in this chapter. The requirement on the guard interval for

our receiver design will be specified in Section 2.2.3.

2.2.3 Received Signal

Let χi denote the delay spread of the ith cluster. Take the channel impulse

response in the nth received block as an example. When ς ≥ 0, h(2)(t, τ ;n) lags

behind h(1)(t, τ ;n) as illustrated in Fig. 2.3. The impulse responses of h(1)(t, τ ;n)

24

τ

|h(t, τ)|

χ1 χ2

τ1,2 = ∆× Tbl + ς

(a) A channel with two long separated clusters

τ

|h(1)(t, τ)|

τ

|h(2)(t, τ)|ς ∆× Tbl

(b) Two quasi-synchronous channels with smaller delay spreads

Figure 2.3: Illustration of channels with two clusters. ∆: an integer; Tbl : time-duration of each transmitted block.

and h(2)(t, τ ;n) are within the interval of [0,max{χ1, ς+χ2}]. On the other hand,

when ς < 0, h(1)(t, τ ;n) lags behind h(2)(t, τ ;n), and their impulse responses are

within the interval of[ς,max{χ1, χ2 + ς}

]. In this chapter, we assume that Tg is

large enough so that

Tg >

max{χ1, ς + χ2}, ς > 0

max{χ1 + |ς|, χ2}, ς < 0.

(2.10)

Under such an assumption, the receiver can partition the received signals into

blocks of duration Tbl, without interblock interference due to the channel spread-

ing within each cluster. With a reasonably large Tg, the condition in (2.10) can

be satisfied with large probability, as verified by the collected experimental data;

see Fig. 2.4 for an illustration.

25

After partition, the nth received block can be expressed as

y(t;n) =

N(1)pa∑

p=1

A(1)p [n]s

((1 + a(1)p [n])t− τ (1)p [n];n

)

+

N(2)pa∑

p=1

A(2)p [n]s

((1 + a(2)p [n])t− τ (2)p [n];n−∆

)+ w(t;n), (2.11)

where w(t;n) is the ambient noise.

During the preprocessing, the receiver first performs a resampling operation on

the received block to remove the dominant Doppler effect [45], leading to z(t;n) :=

y (t/(1 + a[n]);n) where (1 + a[n]) is the resampling factor. The baseband signal

z(t;n) is then obtained with a lowpass filtering operation. The residual mean

Doppler shift is compensated by multiplying the baseband signal z(t;n) with

e−j2πǫ[n]t.

The frequency observation at the mth subcarrier of the nth block can be

obtained with the integral

z[m;n] =

∫ Tbl

0

z(t;n)e−j2πǫ[n]te−j2πmTtdt. (2.12)

After some manipulations, we have

z[m;n] =

K/2−1∑

k=−K/2

H(1)[m, k;n]s[k;n] +

K/2−1∑

k=−K/2

H(2)[m, k;n]s[k;n−∆] + w[m;n],

(2.13)

where w[m;n] is the ambient noise, and the channel coefficients are formulated

as

H(i)[m, k;n] =

N(i)pa∑

p=1

ξ(i)p [n]e−j2πmTτ(i)p [n]G

(

fm + ǫ[n]

1 + b(i)p [n]

− fk

)

(2.14)

26

τ

τ

Cluster 1

Cluster 2

Block index 1 2 3 n n+∆ Nbl Nbl + 1 Nbl +∆

1 2 3 n n+∆ Nbl

1 n−∆ n Nbl Nbl + 1 Nbl +∆

Figure 2.4: Illustration of the received blocks. Assume ∆ = 2 and ς > 0.

for i = 1, 2, with

1 + b(i)p [n] =1 + a

(i)p [n]

1 + a[n], τ (i)p [n] =

τ(i)p [n]

1 + b(i)p [n]

, ξ(i)p [n] =A

(i)p [n]

1 + b(i)p [n]

e−j2πfcτ(i)p [n].

Hence, the relationship between the frequency observations and the transmitted

symbols is completely represented by (N(1)pa +N

(2)pa ) triplets {ξ(i)p [n], τ

(i)p [n], b

(i)p [n]}.

For convenience, we define two generic K ×K matrices

[Λ(τ)]m,m = e−j2πmTτ , [Γ(b, ǫ)]m,k = G

(fm + ǫ

1 + b− fk

)

where Λ(τ) is diagonal. Stacking frequency observations and transmitted sym-

bols at all subcarriers into z[n] and s[n], respectively, yields the input-output

relationship

z[n] = H(1)[n]s[n] +H(2)[n]s[n−∆] +w[n],

=

[

H(1)[n] H(2)[n]

]

︸ ︷︷ ︸

:=H[n]

s[n]

s[n−∆]

+w[n], (2.15)

where for i = 1, 2, the channel matrix is formulated as

H(i)[n] =

N(i)pa∑

p=1

ξ(i)p [n]Λ(τ (i)p [n])Γ(b(i)p [n], ǫ[n]). (2.16)

27

2.3 Factor-Graph Based Joint IBI/ICI Equalization

Due to the block-level convolution as shown in (2.15), it is necessary to re-

cover the transmitted symbols based on all the received blocks corresponding to

one data burst. In this section, we will develop an approach for joint IBI/ICI

equalization.

Notice that the channel matrix H(i)[n] usually has the energy concentrated

on the main diagonal and several off-diagonals. We adopt an assumption that

H(i)[m, k;n] ≈ 0, if |m−k| > D, by only modeling the ICI at one subcarrier from

its D-directly neighboring subcarriers, where D is termed as the ICI-depth. The

input-output relationship in (2.13) can be simplified as

z[m;n] =m+D∑

k=m−D

H(1)[m, k;n]s[k;n] +m+D∑

k=m−D

H(2)[m, k;n]s[k;n−∆] + v[m;n],

(2.17)

where v[m;n] denotes an equivalent noise consisting of ambient noise and un-

modeled ICI.

Definitions of two vectors,

hn,k :=[

H(1)[k, k−D;n], · · · , H(1)[k, k+D;n], H(2)[k, k−D;n], · · · , H(2)[k, k+D;n]]T

,

ξn,k :=

[

s[k −D;n], · · · , s[k +D;n], s[k −D;n−∆], · · · , s[k +D;n−∆]

]T

,

(2.18)

allow us to rewrite (2.17) as

zn[k] = hTn,kξn,k + vn[k], (2.19)

28

where for notation simplicity, we put the block index n as the subscript index.

We assume that (i) transmitted symbols are independent, and (ii) frequency

noise samples are independent across subcarriers. With the second assumption,

the frequency measurements can be shown independent conditional on the trans-

mitted symbols. The a priori probability density function and the likelihood

function of transmitted symbols are expressed as

f({sn}Nbln=1) =

Nbl∏

n=1

K/2−1∏

k=−K/2

f(sn[k]), (2.20)

f({zn}Nbl+∆n=1 |{sn}Nbl

b=1) =

Nbl+∆∏

n=1

K/2−1∏

k=−K/2

f(zn[k]|ξn,k), (2.21)

respectively. The a posteriori probability can be obtained according to the

Bayesian rule

f(

{sn}Nbln=1|{zn}Nbl+∆

n=1

)

=1

C

Nbl+∆∏

n=1

K/2−1∏

k=−K/2

f(zn[k]|ξn,k)

·

Nbl∏

n=1

K/2−1∏

k=−K/2

f(sn[k])

,

(2.22)

where C is a constant.

Hence, the optimal estimate of the information symbols can be obtained via

{sn}Nbln=1 = argmax f

(

{sn}Nbln=1|{zn}Nbl+∆

n=1

)

. (2.23)

Solving (2.23) requires a very high computational complexity, especially when

the number of OFDM blocks per data burst and the number of subcarriers are

large. To make the problem trackable, one can exploit the fact that each symbol

only shows up in several frequency measurements of two blocks. Following this

29

line of thought, the posterior probability of each symbol thus can be obtained by

performing the probability marginalization over a factor-graph representation of

(2.22).

2.3.1 Factor-Graph Based Joint IBI/ICI Equalization

Factor graph and related algorithms, such as the sum-product algorithm (SPA)

and the Gaussian message passing (GMP) principle, have been under extensive

investigation in recent years [41, 52, 53]. Typical applications can be found in,

e.g., [17, 22, 34, 97, 103] and references therein.

Out of the existing factor-graph based algorithms, a joint channel estimation

and co-channel interference mitigation method was proposed in [102,103], and an

iterative channel estimation and LDPC decoding approach was developed in [62];

however, both works mainly considered about the flat fading channel, while the

input-output relationship in this work is complicated by the joint existence of both

IBI and ICI. In [17,22], the factor-graph based equalization has been investigated

for single carrier transmissions to mitigate the intersymbol interference (ISI).

In this work, we extend the above works to a factor-graph based equalization

approach for joint IBI and ICI mitigation.

Taking the the symbol vector ξn,k as the variable node, the factor graph

representation of (2.22) is shown in Fig. 2.5, where the function nodes are formed

by the prior probability density function, the likelihood function, and two delta

functions δ1(ξn,k, ξn,k+1) and δ2(ξn,k, ξn+∆,k) introduced to ensure the consistency

30

of identical symbols in adjacent variables. The messages m1 ∼ m12 in the graph

represent either the prior probability density function or the marginal probability

density function related to the function nodes. The posterior probability of each

individual symbol vector ξn,k can be found by passing messages over the graph

according to the sum-product algorithm.

For the sake of computational efficiency, Gaussian approximation is adopted

for the prior probability density function and the likelihood function of transmit-

ted symbols,

f(sn[k]) ∝ exp

{

− 1

νn,k|sn[k]− sn[k]|2

}

, (2.24)

f(zn[k]|ξn,k) ∝ exp

{

− 1

σ2n,k

∣∣zn[k]− hT

n,kξn,k

∣∣2

}

, (2.25)

where f(sn[k]) represents the Gaussian approximation of f(sn[k]), with the mean

and variance denoted by sn[k] and νn,k, respectively, and f(zn[k]|ξn,k) is the

Gaussian approximation of f(zn[k]|ξn,k) where the variance of equivalent noise

vn[k] in (2.19) is denoted by σ2n,k; estimation of σ2

n,k will be discussed in the later

section.

The mean sn[k] and variance νn,k of f(sn[k]) are computed based on the

extrinsic information from a channel decoder. Define P decext (·) as the extrinsic

probability fed back from the channel decoder. We have

sn[k] =∑M

i=1 Pdecext (sn[k] = αi)αi

νn,k =∑M

i=1 Pdecext (sn[k] = αi)‖sn[k]− αi‖2

(2.26)

31

for ∀k ∈ SD, where M denotes the constellation size, with αi denoting the ith

constellation point. We set sn[k] = sn[k], νn,k = 0, for ∀k ∈ SN ∪ SP.

According to the sum-product algorithm [41] and the Gaussian message pass-

ing principle [53], the outgoing message of each variable node is the product

of incoming messages from all the other edges. Take the variable node ξn,k in

Fig. 2.5 as an example. The outgoing message m8 can be updated as

m8 = m1m2m3m5m7. (2.27)

Meanwhile, the outgoing message from the delta functions corresponds to the

extraction of the probability distribution of common symbols among consecu-

tive variable nodes from the incoming message. The posterior probability of the

variable node is obtained as

f(ξn,k|{zn}) = m1m2m3m5m7m9, (2.28)

from which the posterior probability of each individual symbol f(sn[k]|{zn}) can

be directly obtained. With the Gaussian approximation, the computation in

(2.27) and (2.28) can be simplified by operating only over the mean and covariance

matrices.

To update all the messages in the graph in Fig. 2.5, we first initialize all the

messages as one. Then the messages are passed from the left node to the right

node row by row. Once the last row has been updated, the messages are updated

in an inverse direction, i.e., from the right node to the left node, and from the

last row to the first row.

32

Notice that for the channel with either IBI or ICI, the factor graph corre-

sponding to one column or one row of the graph in Fig. 2.5 does not have cycles.

However, for the channel under consideration with both IBI and ICI, the factor-

graph as shown in Fig. 2.5 is not cycle-free. Nonetheless, message-passing algo-

rithms can achieve excellent performance over graphs with cycles, e.g., decoding

of the low-density-parity-check codes.

In particular, for the receiver with iteration between channel equalization

and decoding operations, turbo principle should be satisfied by setting the prior

mean sn[k] and variance νn,k to 0 and 1, respectively. The extrinsic probabilities

of information symbols {P equext (·)}Nbl

n=1 are then input to the decoder for information

bits recovery.

2.3.2 Practical Issues

2.3.2.1 Implementation considerations

During the implementation of GMP, the prior information need to be factor-

ized into f(sn[k]) =

(

4

√

f(sn[k])

)4

to ensure the well-conditioned property of

covariance matrices of messages in both horizontal and vertical message propa-

gation. Illustration of the modification at one typical variable node is shown in

Fig. 2.6, in which formulations of messages m12 ∼ m4

2 are provided. Both the delta

function and the factorization of the prior information are described in [17] for a

one-dimensional factor graph. The description herein extends these approaches

to a two-dimensional factor graph.

33

Block n

Block

(Nbl+ )

m3

m6 m5

m4

m7 m10

m9

)(ˆ ][knk sf

m2

Block 1k,1 12/,1 K

m8

),(1 ! ),(1 !

),(2 !

kn, 12/, Kn

2/bl , KN !"

kN ,bl !

12/,bl !" KN

)(ˆ,, knknzf

m1

),(2 !

Subcarriers

Blo

cks

2/,1 K ... ...

...

...

...

...

...

...

...

...

...

...

2/, Kn

Figure 2.5: Factor-graph based joint IBI/ICI equalization, empty boxes representthe prior probability density function nodes; filled boxes represent the likelihoodfunction nodes; messages m1 ∼ m12 represent either the prior probability densityfunction or the marginal probability density function over the factor nodes.

2.3.2.2 Incorporating multiple receiving elements

Diversity combing based on signals from multiple receivers can improve the

system performance. Note that receiver elements could be distributed in a large

area, and hence the cluster structures could be quite different on different re-

ceivers. We divide the set of receiving elements into multiple groups, where

receivers within a group share an identical ∆.

34

m3

m6 m5

m4

m7 m10

m9

4, ])[(ˆ Dksf nkn

!"!"

m24

4, ])[(ˆ Dksf nkn

m21

4, ])[(ˆ Dksf nkn ! !

4, ])[(ˆ Dksf nkn

m22

m23

m8

kn,

),(1 ! ),(1 !

),(2 !

),(2

Figure 2.6: Modified factor-graph based joint IBI/ICI equalization. The likeli-hood function node is omitted.

For receiving elements within one group, the same factor graph can be used,

and diversity combing with multiple receivers is straightforward; instead of one

observation zn[k], a vector of observations are available on each subcarrier for the

nth block.

For the joint decoding across groups, the factor graph is different from group

to group. We can do the equalization over each group individually. The posterior

probability of each transmitted symbol can be computed as the multiplication of

the posterior probability obtained within each factor graph

f(sn[k]|{zgn}Nbl,Gn=1,g=1) =

G∏

g=1

f(sn[k]|{zgn}Nbln=1), (2.29)

where zgn denotes observations on the nth block from the gth group.

Remark: For the factor-graph based equalizer in Fig. 2.5, the computational

complexity mainly comes from inversion of the covariance matrix of ξn,k, which

is O((4D + 2)3). Notice that there are 4D common entries between ξn,k and its

neighbors in the same block, and 2D + 1 common entries between ξn,k and its

neighbors across blocks. The matrix inversion can be computed recursively, so

35

that the computational complexity can be reduced to O(D2) for each estimate.

For Nbl blocks with K subcarriers in each transmission, the total complexity is

O(D2KNbl).

Different from the traditional receiver without IBI mitigation, the proposed

receiver decodes the received (Nbl+∆) blocks simultaneously, hence, the required

storage size for the baseband processing will be about (Nbl+∆) times larger than

the traditional block-by-block receiver.

2.4 The Overall Receiver Structure

With the input-output relationship in (2.15), one can see that the problem

under consideration is similar to the multiuser problem in the sense that the IBI

here is similar to the co-channel interference (CCI) in multiuser transmissions;

however in this problem, both transmitted blocks in (2.15) are from one source,

thus making the problem distinct from the traditional single-user transmissions

and multiuser transmissions.

Based on the frequency observations in (2.15), there are two sets of unknowns

at the receiver, (i) the channel matrices, i.e. the channel paths parameters, and

(ii) the information symbols. Although one can perform a joint estimation of the

36

{y(t;n)}Nbl+∆

n=1

Preprocessing;D = 0

I = 0

Quasi-synchronouschannel estimation

Noise variance estimation

Factor-graph based jointIBI & ICI equalization

{P equext (·)}

Nbl

n=1

Channel decoding

All success or I = Imax?

Yes

All success or D = Dmax?

Yes

Outputdecisions

No

{P decext (·)}

Nbl

n=1

Inner loop

I = I + 1

No

{P decext (·)}

Nbl

n=1

Outer loop

D = D + 1

Figure 2.7: Flow chart of the proposed progressive/iterative receiver structure.

two sets of unknowns using the Bayesian method,

{{s[n]}Nbln=1, {H[n]}Nbl+∆

n=1 } = arg min

f({z[n]}Nbl+∆n=1 |{s[n]}Nbl

n=1, {H[n]}Nbl+∆n=1 )f({s[n]}Nbl

n=1)f({H[n]}Nbl+∆n=1 ),

(2.30)

it is usually computational prohibitive, especially when the block size is large.

In this chapter, we separate the channel estimation and symbol detection by

37

multiplexing the information symbols in each block with certain amount of pilot

symbols known to the receiver. At the receiver side, pilot symbols and frequency

observations at pilot subcarriers are used to estimate the multipath parameters

and reconstruct the channel coefficients at all subcarriers. Then, assuming that

the channel estimation is exact, the information symbols are estimated based on

frequency observations at data subcarriers.

It is known that one can achieve an accurate channel estimation by increasing

the number of pilots, whereas has to suffer a data rate reduction. To resolve

the conflict between channel estimation accuracy and system throughput, one

effective strategy is to perform iterative channel estimation and symbol detection.

Since the estimated information symbols can be used as new pilots to refine the

channel estimate which in turn improves the information symbol estimation, the

iteration between channel estimation and symbol detection is preferable when

the the number of pilots is not sufficiently large.

Hence, in this work, we put the factor-graph based equalization and a channel

estimator to be discussed next, into a progressive receiver framework [28] as shown

in Fig. 2.7, in which after Imax iterative operations, the channel ICI-depth D is

updated to include more ICI into the system model. Once the parity check

conditions of all blocks are satisfied during the nonbinary LDPC decoding, or the

ICI-depth reaches a predetermined threshold Dmax, the progressive process stops.

38

2.4.1 Sparse Channels Estimation

Since UWA channels exhibit fast temporal variation, channel estimation herein

is performed on each received block individually, assuming that the path delays,

amplitudes, and Doppler rates are constant within a block, but could vary con-

siderably from block to block.

The input of the channel estimator at each block includes the frequency ob-

servation vector z[n], the pilot symbols and the a posteriori probabilities of in-

formation symbols P decapp(·) fed back from the decoder. In this chapter, the soft

decisions of information symbols are used for channel estimation,

sn[k] =∑M

i=1 Pdecapp(sn[k] = αi)αi

sn−∆[k] =∑M

i=1 Pdecapp(sn−∆[k] = αi)αi

(2.31)

for ∀k ∈ SD, and we set sn[k] = sn[k] and sn−∆[k] = sn−∆[k] for ∀k ∈ SN ∪ SP.

We note that the channels corresponding to H(1)[n] and H(2)[n] in (2.15) are

synchronized on the block level except with a small offset on the channel support,

as shown in Fig. 2.3. As such, estimation of a channel with two widely separated

clusters is converted to the estimation of two quasi-synchronous virtual channels.

Hence, based on the knowledge of the delay offset, the sparse channel estimation

for single user communications over shallow water acoustic channels [6] can be

easily extended to the current channel setting.

39

2.4.2 Noise Variance Update and Nonbinary LDPC Decoding

With the estimated channel matrices and the soft decisions of information

symbols, the noise variance estimate is updated as

N0[n] = Em∈SN

[∣∣zn[m]−

m+D∑

k=m−D

(H(1)[m, k;n]sn[k] + H(2)[m, k;n]sn−∆[k]

)∣∣2]

(2.32)

which is used as the estimate of {σ2n,k, ∀k} in (2.24) for the factor-graph based

channel equalization.

After inputting extrinsic probabilities of information symbols from the chan-

nel equalizer P equext (·) into the nonbinary LDPC decoder, both a posteriori proba-

bilities P decapp(·) and extrinsic probabilities of information symbols P dec

ext (·) will be

updated, these being fed back for channel estimation and equalization in the next

loop. A detailed description of the nonbinary LDPC decoder can be found in [26].

2.4.3 Channel Profile Probing

Note that the cluster structure of the channel under consideration depends on

the propagation geometry, and is unknown to the receiver. Channel probing based

on a preamble prior to data transmissions is thus necessary. Since underwater

acoustic channels usually have large Doppler distortion, a Doppler insensitive

waveform, such as a linear frequency modulated (LFM) waveform or a hyperbolic

frequency modulated (HFM) waveform can be used as the preamble [40], and the

matched filter at the receiver side provides a multipath profile of the two-cluster

40

channel. As a detection scheme for Sonar applications, the modified Page test [2]

is employed at the matched filter output to detect the rising and falling edges of

clusters; the intercluster delay τ12 and the delay spreads χ1 and χ2 thus become

available. These are used as known parameters in the proposed receiver. Detailed

description and performance analysis of the Page test can be found in [2] and

references therein.

2.5 Simulation Results

In the simulation, we assume that each cluster consists of 10 discrete paths.

Within each cluster, the inter-arrival time of paths follows an exponential distri-

bution with a mean of 1 ms. Amplitudes of paths are Rayleigh distributed with

the average power decreasing exponentially with delay, leading to a power differ-

ence at the beginning and the end of the guard time of 20 dB. The Doppler rate

of each path follows a zero mean uniform distribution with a standard deviation

σvfc/c, where σv denotes the standard deviation of the relative speed between

the transmitter and the receiver, and c is the sound speed in water being set to

1500 m/s. The maximum possible Doppler rate is thus√3σvfc/c. The inter-

arrival time of the two clusters follows a uniform distribution with ∆ ∼ U [0, 2]

and ς ∼ U [−0.2Tbl, 0.2Tbl].

The ZP-OFDM parameters are specified in Table A.1, with a subcarrier dis-

tribution identical to that in the experiment described in Section A.1. A rate-1/2

nonbinary LDPC code [26] and a 16-QAM constellation are used for information

41

7 8 9 10 11 12 13 14 15 1610

−3

10−2

10−1

100

SNR per Symbol [dB]

BLE

R

FG, I = 3 FG, I = 2

FG, I = 1

Multiuser, I = 1 FG, I = 4

Multiuser, I = 8 FG, I = 5

FG, I = 8

Figure 2.8: BLER performance of the factor-graph based receiver versus multiuserreceiver with mild Doppler spreads σv = 0.10 m/s. ICI-depth is fixed at D = 1.

bits encoding and data symbol mapping, respectively. The data rate can be

computed as in (A.1).

In the following, performance of the proposed factor-graph receiver will be

tested in three different cases. We consider a time-varying scenario by setting

the Doppler spread σv = 0.10 m/s.

Test Case 1: In this test, we compare the performance of the factor-graph

based iterative IBI/ICI-aware receiver and the iterative multiuser receiver based

on an LMMSE equalizer [88]. The average power of both clusters are simulated as

identical, and only one receiving element is used. We fix the ICI-depth a constant

value without the progressive operation. To facilitate channel estimation in the

presence of ICI, 96 data subcarriers are converted to be extra pilot subcarriers,

which are grouped with both null subcarriers and the original pilot subcarrier

42

for joint delay and Doppler estimation [6]. The effective code rate is reduced to

(336− 96)/(672− 96) ≈ 0.4, and the overall data rate is

R =336− 96

T + Tg· log2 16 = 7.4 kb/s. (2.33)

For all the simulation results, at least 100 block errors are collected for each

signal-to-noise ratio (SNR) level. Fig. 2.8 depicts the BLER performance of the

two receivers. For the factor-graph based receiver, one can observe significant

performance improvements with iterations between the equalizer and the decoder.

Moreover, relative to the multiuser receiver, the factor-graph receiver has more

than 1 dB gain when iteration times reaches three, since the latter can utilize the

decoding results of all the other blocks to facilitate the decoding of a particular

block, while only the knowledge of the previous blocks can be utilized in the

former.

Test Case 2: To get insights on how the performance of both the factor-graph

receiver and the multiuser receiver changes at different intercluster interference

levels, we fix the SNR of the signal arriving along the first cluster to be 11 dB,

and vary the power ratio of the signal arriving along the first cluster to that

arriving along the second cluster from −12 dB to 0 dB. As the same in test case

1, extra pilots are introduced to facilitate channel estimation.

Fig. 2.9 shows the performance curves of the proposed factor-graph based

IBI/ICI-aware receiver, multiuser receiver, and the conventional LMMSE receiver

43

−12 −10 −8 −6 −4 −2 010

−4

10−3

10−2

10−1

100

Power Ratio [dB]

BLE

R

Without IBI mitigation

Multiuser

Factor−Graph

Figure 2.9: BLER performance of three receivers with mild Doppler spreadsσv = 0.10 m/s. SNR of the first cluster is fixed at 11 dB; ICI-depth is fixed atD = 1. Five iterations are performed.

which views the signal from the second cluster as ambient noise, versus different

power ratios between the second and the first cluster. One can find that

• as the signal arriving along the second cluster becomes stronger, perfor-

mance of both the factor-graph based receiver and the multiuser receiver

increases, while performance of the traditional receiver without IBI miti-

gation decreases. This result shows that signal arriving along the second

cluster can be utilized by both the factor-graph based receiver and the

multiuser receiver to improve decoding performance, while the decoding

performance of the traditional receiver without IBI mitigation deteriorates

due to the intercluster interference.

44

8 9 10 11 12 13 14 1510

−4

10−3

10−2

10−1

100

SNR per Symbol [dB]

BLE

R

D=0, I=1D=1, I=1−−−, I=2−−−, I=3D=2, I=1−−−, I=2−−−, I=3D=3, I=1−−−, I=2−−−, I=3

Figure 2.10: BLER performance of the factor-graph based progressive receiverwith mild Doppler spreads σv = 0.10 m/s.

• the performance gap between the factor-graph based receiver and the mul-

tiuser receiver gets pronounced as the power of the second cluster increases.

This is due to the fact that the multiuser receiver can only partially miti-

gate the intercluster interference while the factor-graph based receiver can

fully exploit all the available information from both clusters.

Test Case 3: To reduce the pilot overhead, performance of the factor-graph

based receiver with both progressive and iterative operations is tested. Under the

same simulation setting as in test case 1, the BLER performance of the proposed

progressive receiver is shown in Fig. 2.10 without introducing extra pilots. The

data rate is thus increased to be

R =336

T + Tg· log2 16 = 10.4 kb/s. (2.34)

45

Table 2.1: Sensors Groups in the AUTEC08 Experiment

Group 1 Group 2Channel parameters (a) (b) (c) (d) (e)transmitter-to-receiver distance: d (km) 7.6 7.5 6.2 3.82 3.81inter-cluster delay: τ12 (ms) 582 581 505 707 713inter-cluster block delay: ∆ 2 2 2 3 3inter-cluster residual delay: ς (ms) 70 69 -7 -61 -55input SNR (dB) 6.9 6.5 6.3 6.7 6.4

14 14.5 15 15.5

0.1

0.2

0.3

Time [s]

Mag

nitu

de 80ms

830ms

1st cluster 2nd cluster

(a) sensor (c)

16 16.5 17

0.05

0.1

0.15

0.2

0.25

Time [s]M

agni

tude

2nd cluster

80ms

520ms

1st cluster

(b) sensor (e)

Figure 2.11: LFM correlation results at two sensors in the AUTEC08 experiment.

Fig. 2.10 shows that progressively updating the system model improves the per-

formance quickly.

2.6 Experiment Results in the AUTEC Environment

In this section, we test the performance of the proposed receiver in the deep

water horizontal channels. The experimental data was collected over the AUTEC

network; see Section 1.1 for descriptions on the AUTEC network. Two experi-

ments were carried out. One was in December 2008, and the other was in March

2010, which are termed as AUTEC08 and AUTEC10, respectively. Experimental

setups of the two experiments are specified in Section A.3. Out of 96 sensing

46

0 2 4 6 8 100

0.5

1

Time [s]A

mpl

itude

preamble of cluster 2

preamble ofcluster 1

830ms

Figure 2.12: IBI illustration of ZP-OFDM in the AUTEC08 experiment over achannel with two clusters at sensor (c).

Dop

pler

spe

ed [m

/s]

delay [ms]2 4 6 8

−0.5

0

0.5

(a) the first cluster

Dop

pler

spe

ed [m

/s]

delay [ms]10 20 30 40 50 60

−0.5

0

0.5

1

(b) the second cluster

Figure 2.13: Significant paths of the estimated channel at sensor (c) in theAUTEC08 experiment.

nodes, received signals at only several nodes are used for receiver performance

validation.

2.6.1 Experiment Results: AUTEC08

We consider five receiver in this test, which can be divided into two groups

based on their cluster structures, as shown in Table 2.1. A linear frequency

modulated (LFM) waveform was used as the preamble to probe the channel. A

matched filter is used to generate the correlation results of the received signal with

47

Table 2.2: AUTEC08 Results for Sensors with Two Clusters

Sensor LDPC Uncoded Block RateReceiver type groups rate BER errors B/(3s)Multiuser receiver {1} 1/3 0.158 0 255Factor-graph based receiver {1} 1/3 0.163 0 255Multiuser receiver {1} 1/2 0.158 10 383Factor-graph based receiver {1} 1/2 0.092 6 383Multiuser receiver {1, 2} 1/2 0.150 0 383Factor-graph based receiver {1, 2} 1/2 0.107 0 383

2.5 3 3.5 4 4.50

10

20

30

40

Time [s]

Mag

nitu

de [d

B]

771 ms

1st cluster

Test Statistics

2nd cluster

Threshold

(a) the first sensor

3 3.5 4 4.5 50

10

20

30

40

Time [s]M

agni

tude

[dB

]

672 ms

Test Statistics

2nd cluster

1st cluster

Threshold

(b) the second sensor

Figure 2.14: Samples of HFM correlation results at two sensors in the AUTEC10experiment.

an LFM local replica. Samples of the correlation results of the LFM preamble

at sensor (c) and sensor (e) are shown in Fig. 2.11. The corresponding IBI at

sensor (e) is illustrated in Fig. 2.12. One can find that the first ∆ = 3 data blocks

arriving along the first cluster have been corrupted by the preamble arriving along

the second cluster, and the last 2 data blocks along the second cluster have been

corrupted by the preamble of the second transmission along the first cluster. We

hence only decode the (Nbl−5) = 15 blocks in the middle of the first transmission,

and assume the first 3 and the last 2 data blocks have been successfully decoded.

48

Dop

pler

spe

ed [m

/s]

delay [ms]2 4 6 8 10 12

−0.5

0

0.5

(a) the first cluster

Dop

pler

spe

ed [m

/s]

delay [ms]0 10 20 30 40 50 60

−0.5

0

0.5

1

(b) the second cluster

Figure 2.15: Sample of channel estimation results in the AUTEC10 experiment.

One sample channel estimate is shown in Fig. 2.13. The traditional receiver

without IBI mitigation does not work for this data set, as the two clusters have

similar power and hence the IBI is severe. Decoding results of the multiuser

receiver and the factor-graph based receiver are summarized in Table 2.2, where

15 blocks of one packet are tested. The data rate is calculated as (A.1) with

M = 4, which is also represented as 38R Bytes/(3s) – the unit used by the current

AUTEC single carrier system with a typical packet duration of 3 s.

One can find that both receivers work well in the presence of IBI. BLER

performance of the joint-group combining is better than that of single group.

Compared with the multiuser receiver, the factor-graph based receiver has better

performance.

2.6.2 Experiment Results: AUTEC10

In this experiment, a hyperbolic frequency modulated (HFM) waveform was

used as the preamble to probe the channel. Samples of correlation results of the

49

5 10 15 200

0.5

1

1.5

2

Tranmission

Num

ber

of b

lock

s in

err

or

Without IBI mitigationMultiuserFactor−Graph

(a) Decoding results of three receivers

0 0.5 1 1.5 2

10−3

10−2

10−1

ICI−depth D

BLE

R

Without IBI mitigationMultiuserFactor−Graph

(b) BLER performance with iterations

Figure 2.16: Decoding results of QPSK symbols in the AUTEC10 experiment.22 transmissions are involved. Imax = 2 for each value of D.

received signal with an HFM local replica, and the Page-test test statistics for

channel probing at sensors with two cluster-structures are shown in Fig. 2.14.

Distances between these two sensors and the transmitter are about 3.7 km and

4.4 km, respectively. The average input SNR of received signals is about 17.9 dB

at the first sensor, and about 14.9 dB at the second sensor. We can find that

power of the signal arriving along the second cluster is about 20 dB lower relative

to that of the signal arriving along the first cluster. The intercluster delay of these

two sensors can be rounded into two OFDM blocks, with the residual term being

ς = −70 ms and ς = −169 ms, respectively.

One sample of channel estimation results at one sensor is shown in Fig. 2.15.

Again, the channel estimates agree well with the HFM correlations results in

Fig. 2.14. Combining the received signals from these two sensors, the decoding

results for 22 transmissions are shown in Fig. 2.16. We observe that:

50

• As the number of iterations increases, more and more blocks become de-

codable.

• With 5 progressive operations, out of 22 × 10 = 220 transmitted blocks,

all blocks can be decoded with the factor-graph based progressive IBI/ICI-

aware receiver, while only one block error occurs for the progressive mul-

tiuser and traditional receiver without IBI mitigation. Due to the signifi-

cant power difference between the two clusters, the advantage of the factor-

graph based receiver over the other two receivers is small, which agrees with

Fig. 2.9.

2.7 Emulated Experimental Results: MACE10

The Mobile Acoustic Communication Experiment (MACE10) was carried out

off the coast of Martha’s Vineyard, Massachusetts, June, 2010. The experimental

setting and OFDM parameters can be found in Section A.2. We consider data sets

corresponding to a rate-1/2 nonbinary LDPC code and a 16-QAM constellation,

which lead to a data rate R = 5.4 kb/s.

Notice that this experiment was carried out in shallow water with a single

source. To create a scenario in the underwater broadcasting network where mul-

tiple gateways transmit the same information to underwater sensors, we shift

the received signal of each transmission two OFDM blocks behind, and take the

shifted signal as the signal from the second source. Then, by adding up the

51

1 2 3 4 5 6

1

0.1

0.01

0.0010

number of phones

BLE

R

D = 0D = 1D = 2

Without IBI mitigation

Multiuser

Factor−Graph

Figure 2.17: BLER performance of three receivers, averaged over 30 transmis-sions. Imax = 2 for each value of D.

shifted signal with the originally received signal, we obtain a set of emulated

experimental signal which can be regarded as the received signal at one sensor in

the underwater broadcasting network with two gateways. The intercluster block

delay of the broadcasting channel is ∆ = 2, and the fractional delay ς follows a

uniform distribution ς ∼ U [−0.1Tbl, 0.1Tbl].

In the sequel, we test the decoding performance of the traditional receiver

without IBI mitigation, the multiuser receiver and the factor-graph based receiver

in three cases.

2.7.1 Test Case 1

During the preprocessing, we resample the received signal to compensate the

mobility of the source array. With five iterations, the decoding results of the

52

0 2 4 6 8 10 12

1

0.1

0.02

added noise variance (× N0) [dB]

BLE

R

D = 0D = 1D = 2

Multiuser

Without IBI mitigation

Factor−Graph

Figure 2.18: BLER performance of three receivers by adding white Gaussiannoise with different variances, averaged over 30 transmissions. Two phones arecombined. Imax = 2 for each value of D.

traditional receiver without IBI mitigation, the multiuser receiver and the factor-

graph based receiver are shown in Fig. 2.17. One can see that the traditional

receiver without IBI mitigation almost cannot work, and there is a considerable

performance gap between the multiuser receiver and the factor-graph based re-

ceiver. Meanwhile, one can find that the decoding performance converges after

three to four iterations for the multiuser receiver and the factor-graph based

receiver.

2.7.2 Test Case 2

Based on the estimated ambient noise variance N0, the white Gaussian noise

is added to the received signal to create an emulated experimental data set to test

the performance of the proposed receiver under different SNR levels. Decoding

53

−8 −6 −4 −2 0 2 4 6 8

1

0.1

0.01

0.0010

power ratio of the 2nd cluster to the 1st cluster [dB]

BLE

R

Without IBI mitigation

MultiuserFactor−Graph

Figure 2.19: BLER performance of three receivers with different power ratiosbetween two clusters, averaged over 30 transmissions. Two phones are combined.Three curves for each receiver correspond to D = 0, 1, 2, respectively, and Imax =2 for each value of D.

results of the traditional receiver without IBI mitigation, the multiuser receiver

and the factor-graph based receiver are shown in Fig. 2.18. One can see that the

decoding performance keeps decreasing as the added noise variance level increases,

and the factor-graph based receiver has the best performance.

2.7.3 Test Case 3

To test the performance of the proposed receiver with different power ratios

between the second cluster and the first cluster, we vary the weighting coefficients

when adding the delay-shifted signal with the originally received signal. Decoding

results of the traditional receiver without IBI mitigation, the multiuser receiver

and the factor-graph based receiver are shown in Fig. 2.19. One can see that

54

the multiuser receiver is sensitive to the relative power levels of the two clusters,

while the decoding performance of the factor-graph based receiver is very stable.

2.8 Summary

Unlike existing works on underwater OFDM where the IBI is absent, in this

chapter, we proposed a ZP-OFDM receiver for underwater acoustic channels with

widely separated multipath clusters. To mitigate both IBI and ICI in the received

signal, we developed a factor-graph based iterative equalizer, where data detection

is achieved by Gaussian message passing over a well-designed graph. By viewing

the clustered physical channel as two virtual quasi-synchronous channels, a quasi-

synchronous joint sparse channel estimation method was presented in the presence

of IBI. Several practical concerns about the application of the proposed receiver,

including a channel probing scheme and a progressive framework to reduce the

pilot overhead, were also discussed. Both simulation and experimental results

verified the effectiveness of the proposed receiver, which showed that the factor-

graph based receiver can effectively leverage the signals from both clusters, thus

enjoys a quite stable performance, while the multiuser receiver is sensitive to the

relative power levels of the two clusters.

Chapter 3

Parameterized Cancellation of Partial-Band

Partial-Block-Duration Interference for

Underwater Acoustic OFDM

3.1 Introduction

Interference mitigation in communication systems has been an interesting

topic since the advent of communication. As opposed to the internal interfer-

ence, such as the intersymbol interference (ISI) in single carrier transmissions,

or intercarrier interference (ICI) in multicarrier transmissions, interference from

the external environment, such as jamming and unintentional interference, could

result in significant performance degradation. The interference in UWA com-

munications includes both unintentional interference, such as interference from

sonar operations and marine mammals, and malicious jamming [10].

55

56

This work was primarily motivated by our observations in an experiment held

in March, 2010 over the AUTEC network. During the transmission of communi-

cation signals, other unknown users were transmitting multiple sonar waveforms

in the same environment. The received communication signal at certain sensors

was thus superimposed with the sonar transmissions as shown in Fig. 3.1, which

leads to significant performance degradation. Although such interference occurs

quite often during the UWA communications, limited research results for its mit-

igation are available. For example, although considerable advancements have

been made for OFDM and single-carrier transmissions with frequency domain

equalization in recent years; see e.g., [?, 6, 11, 38, 39, 43–45, 67, 68, 71, 78, 100] and

references therein, all of these are investigated in the absence of interference.

On the other hand, various methods for interference suppression have been

investigated for wireless communications in the last two decades [20,42]. Mainly,

the external interferences are divided into two categories according to the time-

frequency characteristics: (i) impulsive interference with short time duration and

large bandwidth; and (ii) narrowband interference with small bandwidth and long

time duration.

3.1.1 Impulsive Noise Suppression

For impulsive noise suppression in multicarrier transmissions, the characteris-

tics of short time duration is usually utilized. Using the time-domain clipping, an

erasure/Reed-Solomn (RS) decoding scheme for impulsive noise mitigation was

57

proposed in [104]; the proposed scheme was improved in [48] by performing joint

erasure marking and Viterbi decoding, but at the cost of high computational

complexity. An iterative interference mitigation strategy was proposed in [101],

where the frequency components of the impulsive noise and the information sym-

bols were estimated iteratively, and a threshold detector was used to reconstruct

the impulsive noise events in the time domain. The proposed receiver structure

was further developed in [57] to increase its convergence rate by employing a syn-

drome decoder. However, both approaches assume perfect channel knowledge,

which is impractical in most cases. For channel estimation in the presence of im-

pulsive noise, a support vector machine based algorithm was proposed in [18] by

introducing a ǫ-Huber cost function. An iterative channel estimator was devel-

oped in [99] by performing impulsive noise estimation/cancellation and channel

estimation iteratively.

3.1.2 Narrowband Interference Suppression

For narrowband interference suppression, the frequency characteristics of the

interference are usually required. In [61], a linear minimum mean-square-error (LMMSE)

estimate of the interference across multiple OFDM blocks is obtained based on

a few measurements near the obstructed frequency band. However, this method

requires not only the prior knowledge of the center frequency and bandwidth

of the interference, but also its power spectral density. The method in [14, 15]

performs a successive estimation of the information symbol at one subcarrier by

58

0 2 4 6 8 10−0.03

−0.02

−0.01

0

0.01

0.02

0.03

Time [s]

Pas

sban

d si

gnal

HFM Preamble

InterferenceInterference

ZP−OFDM Blocks

(a) Time domain waveform (b) Time-frequency spectrum

Figure 3.1: Samples of the time domain waveform and the time-frequency spec-trum of the received signal at one hydrophone after bandpass filtering. Thetransmitted signal consists of a hyperbolic frequency modulated (HFM) pream-ble followed by 10 ZP-OFDM blocks. The circle and the square in subfigure (a)denote the locations of interference and useful signal, respectively.

subtracting the interference component predicted from the previous subcarrier,

followed by the prediction of the interference at the next subcarrier. In [35], an

expectation-maximization (EM)-based iterative channel estimation and symbol

decoding scheme in the frequency domain was proposed for a single-user and

multi-antenna OFDM system with synchronous interferences, where both spatial

and frequency correlation of interference measurements are exploited. Another

EM-based iterative channel estimation and data decoding algorithm was proposed

in [58, 59]. By assuming that the variance of the interference follows an inverse-

Gamma distribution, the unknown variance of the interference at each subcarrier

is treated as a nuisance parameter which can be averaged out. Several other in-

terference estimation or detection schemes can be also found in, e.g. [21,47,103].

59

In [47], the code structure was exploited for interference detection in the OFDM-

based cognitive system. A compressive-sensing based interference localization

algorithm was developed in [103] by assuming perfect channel knowledge. Based

on message-passing techniques, a factor-graph based interference cancellation and

information symbol estimation framework was developed in [21].

3.1.3 Our Work

We consider interference mitigation for OFDM transmissions in underwater

acoustic channels. Relative to the large signal bandwidth (e.g. 5 ∼ 10 kHz) and

long block duration (e.g. 100 ∼ 200 ms), the interference usually occupies part

of the signal band and has shorter time duration. As such, the interference could

neither be treated as impulse noise nor narrowband interference, as illustrated in

Fig. 3.1. Conventional interference mitigation methods which exploit either short

time duration or narrowband property may not work well for this type of inter-

ference. Specifically, for the impulsive noise mitigation methods, the nonlinear

operation, such as the clipping and nulling operations, could lead to considerable

information loss when the time duration of interference is not relatively small;

for the narrowband interference mitigation methods, the assumption that inter-

ference is independent across subcarriers might not be valid, which could result

in considerable performance degradation in the low SNR scenario, especially in

a time-varying scenario where ICI exists.

60

For such a type of interference with short time duration and partial band-

width, we represent its waveform by a number of parameters by assuming prior

knowledge of the frequency band and time duration of the interference, where

the number of parameters is equal to the time-bandwidth product. After incor-

porating the interference representation into the system model [6, 45], a receiver

framework is proposed to perform interference detection, estimation and data

decoding iteratively.

The main contributions of this work are the following.

• We provide a parameterized representation of the interference explicitly

such that interference cancellation can be carried out without information

loss nor performance degradation caused by approximations.

• We develop an iterative OFDM receiver, which couples interference detec-

tion, interference reconstruction and cancellation, channel estimation, and

data detection.

• Besides extensive simulation results, we provide validation based data sets

collected in two experiments. Both time-invariant and time-varying scenar-

ios have been considered.

Remark 1: In this chapter, we propose a systematic approach to mitigating

short-time duration partial-band interference in underwater acoustic communi-

cations. Note that this approach is quite general that the interference is param-

eterized by a number of unknowns depending on the time-bandwidth product.

61

With a given time-bandwidth product, the time duration or the bandwidth of

the interference could be arbitrary. Hence, the proposed interference cancella-

tion receiver could also be applicable to the mitigation of impulsive noise and

narrowband interference; instead of only utilizing some properties of impulsive

noise and narrowband interference to suppress them, one could directly estimate

the interference through suitable parameterization and pursue joint or iterative

interference cancellation and data detection. We are currently pursuing this ap-

proach for the mitigation of impulsive noise, where comparison will be carried

out with respect to existing methods, e.g., in [4, 8, 48, 57, 64].

Remark 2: The proposed approach relies on the prior knowledge of the in-

terference frequency band and waveform duration. These parameters could be

acquired based on the received waveforms in the absence of useful signals, as in

the operation situation of the AUTEC network. The focus of this work is on un-

intentional interferences. For malicious interferences with fast-varying waveform

characteristics, further research is needed.

The rest of the chapter is organized as follows. The system model is intro-

duced in Section 3.2. The interference model is presented in Section 3.3. The

proposed interference cancellation receiver is developed in Section 3.4, with de-

tailed descriptions on several key modules. Numerical simulations are presented

in Section 3.5, and experimental results are provided in Sections 3.6 and 3.7.

We draw conclusions in Section 3.8. This chapter collects the results published

in [90, 92].

62

3.2 System Model

3.2.1 Transmitted Signal and Channel Model

Let T denote the OFDM symbol duration and Tg the length of the guard

interval between consecutive OFDM blocks, which leads to the OFDM block

duration Tbl = T+Tg. With the subcarrier spacing of 1/T , a total ofK subcarriers

are located at frequencies

fk = fc +k

T, k = −K

2, . . . ,

K

2− 1 (3.1)

where fc is the center frequency, and K is assumed even. The signal bandwidth

is thus B = K/T . Let s[k] denote the information symbol on the kth subcarrier,

and define SA and SN as the non-overlapping sets of active and null subcarriers,

respectively, which satisfy SA∪SN = {−K/2, . . . , K/2−1}. The passband signal

of one OFDM block can be expressed as

s(t) = 2R

(∑

k∈SA

s[k]ej2πfktg(t)

)

, t ∈ [0, Tbl] (3.2)

where g(t) is a pulse shaping filter defined in (2.8), with the Fourier transform

denoted by G(f).

Assume that the channel consists of Npa discrete paths. The channel impulse

response is

h(τ ; t) =

Npa∑

p=1

Ap(t)δ (τ − τp(t)) , (3.3)

where Ap(t) and τp(t) are the amplitude and delay of the pth path, respectively.

Within one OFDM block, we assume that (i) the amplitude does not change

63

Ap(t) ≈ Ap, and (ii) the path delay can be approximated as

τp(t) ≈ τp − apt,

where τp is the initial delay, and ap is the Doppler rate of the pth path, which

can be expressed as ap = vp/c with vp being the relative speed of the transmitter

and the receiver projected on the pth path, and c is the sound speed in water.

The channel impulse response can be reformulated as

h(τ ; t) =

Npa∑

p=1

Apδ (τ − (τp − apt)) . (3.4)

3.2.2 Received Signal without Interference

Using the path-based channel model, the received signal in the absence of

interference is

y(t) =

Npa∑

p=1

Aps((1 + ap)t− τp) + n(t) (3.5)

where n(t) is the additive noise.

The following processing is applied on the received signal. First, the main

Doppler effect of the received signal is removed through the resampling operation

with a resampling factor (1+a), leading to the resampled signal as z(t) = y(t/(1+

a)) [45]; second, after passband to baseband downshifting, the carrier frequency

offset ǫ caused by the residual Doppler effect is compensated through multiplying

e−j2πǫt with the baseband signal z(t). In this chapter, we use the method in [56] to

estimate a based on a cyclic-prefix (CP)-OFDM preamble; other research on the

64

resampling factor estimation can be found in, e.g. [98]. We use the null-subcarrier

based method [55] to estimate ǫ, as done in [45].

The frequency measurement at the mth subcarrier is then obtained via the

integration

z[m] =

∫ T+Tg

0

z(t)e−j2π(mT+ǫ)tdt

=

∫ T+Tg

0

z(t)e−j2π(fm+ǫ)tdt. (3.6)

Substituting (3.2) and (3.5) into (3.6) yields

z[m] =

K/2−1∑

k=−K/2

H [m, k]s[k] + w[m] (3.7)

where w[m] is the additive noise sample, and

H [m, k] =

Npa∑

p=1

A′pe

−j2π(fm+ǫ)τ ′pm,k, (3.8)

with

bp =ap − a

1 + a, A′

p =Ap

1 + bp, τ ′p =

τp1 + bp

m,k = G

(

fm − fk +ǫ− bpfm1 + bp

)

.

To reduce the computational load in data decoding, the channel matrix is usu-

ally assumed to be banded, i.e., only the main diagonal and several off-diagonals

on each side are non-zeros,

m,k =

G(

fm − fk +ǫ−bpfm1+bp

)

, |m− k| 6 D

0, otherwise

(3.9)

65

where we term D as the ICI depth of the channel matrix.

Stack transmitted symbols and frequency measurements at all subcarriers into

vectors s and z, respectively,

s =

[

s[−K/2] s[−K/2 + 1] · · · s[K/2− 1]

]T

(3.10)

z =

[

z[−K/2] z[−K/2 + 1] · · · z[K/2− 1]

]T

(3.11)

and collect channel coefficients H [m, k] into a matrix H,

H =

H [−K/2,−K/2] · · · H [−K/2, K/2− 1]

.... . .

...

H [K/2− 1,−K/2] · · · H [K/2− 1, K/2− 1]

. (3.12)

The frequency-domain measurements are then compactly expressed as

z = Hs+w, (3.13)

where w is similar defined as z.

3.3 Interference Parameterization

In conventional interference suppression methods, the interference is described

either as impulsive noise with large bandwidth or narrowband noise with long time

duration. In this section, by assuming prior knowledge of the frequency band and

time duration of the interference, we develop a parameterized interference model

to address the interference explicitly.

Denote the center frequency, bandwidth and time duration of the interference

as fIc, BI and TI, respectively. The bandwidth BI is taken as the 3-dB bandwidth

66

of the interference, however, the knowledge of BI does not need to very accurate;

a loose upperbound on BI is sufficient.

Let I(t) denote the passband waveform of the interference, and I(t) the base-

band waveform. Since I(t) is time limited, it adopts a Fourier-series representa-

tion as

I(t) =

∞∑

l=−∞

clej2π l

TIt, t ∈ [0, TI] , (3.14)

where cl is the coefficient on the basis ej2π l

TIt. Without loss of generality, as-

sume that NI = ⌈BITI⌉ is an even number. Since I(t) is bandwidth-limited to

[−BI/2, BI/2), the coefficient cl is approximately zero for l < −NI/2 or l ≥ NI/2.

Hence, we rewrite (3.14) as

I(t) ≈NI/2−1∑

l=−NI/2

clej2π l

TIt, t ∈ [0, TI] . (3.15)

The corresponding passband signal is

I(t) = 2R

NI/2−1∑

l=−NI/2

clej2πflt

, t ∈ [0, TI] (3.16)

where fl := fIc + l/TI. The Fourier transform of I(t) in the frequency band

BI := [fIc −BI/2, fIc +BI/2] can be expressed as

I(f) =NI/2−1∑

l=−NI/2

clsin(π(f − fl)TI

)

π(f − fl)e−jπ(f−fl)TI , ∀f ∈ BI. (3.17)

Note that the interference overlaps the received OFDM signal with an un-

known delay. Define τ ′I as the delay of the interference relative to the starting

point of the OFDM block in which it resides. After the preprocessing of the

67

OFDM receiver, the interference component at the mth subcarrier is

ν[m] =

∫ T+Tg

0

I

(t− τ ′I1 + a

)

e−j2π(fm+ǫ)tdt. (3.18)

Following the derivation to (3.17), we can formulate ν[m] as

ν[m] = e−j2πmTτI

NI/2−1∑

l=−NI/2

ρm,lul, (3.19)

where

ul = (1 + a)TIe−j2π(fc+ǫ)τIcl, τI =

τ ′I1 + a

,

ρm,l =sin(π((1 + a)(fm + ǫ)− fl)TI)

π((1 + a)(fm + ǫ)− fl)TI

e−jπ((1+a)(fm+ǫ)−fl)TI .

Stacking interference components at all subcarriers into a vector ν yields

ν = Λ(τI)ΓIu (3.20)

where Λ(τI) is a K × K diagonal matrix, ΓI is a K × NI matrix, and u is an

NI × 1 vector,

[Λ(τI)]m,m = e−j2πmTτI , [ΓI]m,l = ρm,l, u = [u−NI/2, . . . , uNI/2−1]

T. (3.21)

The received signal in the presence of interference is then formulated as

z = Hs+Λ(τI)ΓIu+w. (3.22)

By modeling the interference explicitly, an effective OFDM receiver will be de-

veloped in Section 3.4 through iterative estimation of the interference and infor-

mation symbols.

68

3.4 Proposed OFDM Receiver with Interference Cancellation

The received signal model in (3.22) shows that four sets of parameters: (i)

the channel mixing matrix H; (ii) the information symbol vector s; (iii) the in-

terference vector u; and (iv) the delay τI, need to be estimated from the same

measurements z. Although pilots are usually multiplexed with information sym-

bols to separate channel estimation and information symbol detection in the con-

ventional OFDM receiver [45], frequency measurements at both pilot and data

subcarriers within the interference band are contaminated. One could adopt a

Bayesian estimator as

{H, s, u, τI} = arg max{H,s,u,τI}

f (z|H, s,u, τI) f(H)f(s)f(u)f(τI). (3.23)

However, the computational complexity of solving (3.23) directly is prohibitive.

To reduce the computational load in solving (3.23), we propose an itera-

tive receiver structure for interference detection/estimation, channel estimation

and information symbol detection, as shown in Fig. 3.2. Relative to the itera-

tive/progressive receiver for a time-varying channel of [27], the proposed structure

includes several new modules for interference detection and estimation. It is thus

a more general framework than the one in [27] in which only the self-interference

in the form of ICI is addressed.

The modules of the proposed receiver are briefly described as follows.

69

• Preprocessing. The main Doppler effect and residual Doppler shift are re-

moved via the resampling operation and the Doppler compensation, respec-

tively [45]. Set the initial value of the iteration index I = 0.

• GLRT interference estimation/detection. A generalized log-likelihood ratio

test (GLRT) detector is used to detect the interference. During this process,

maximum likelihood (ML) estimates of the interference u and the delay τI

are obtained. Comparison of the GLRT statistics with a predetermined

threshold yields a decision about the presence of the interference.

• Interference subtraction. If interference exists, the contributions of inter-

ference will be estimated and subtracted from the measurements.

• Channel estimation. Based on both pilot symbols and the soft decisions on

information symbols fed back from the decoder, channel estimation methods

from a conventional OFDM receiver can be applied. We herein adopt the

sparse channel estimation from [6].

• Channel equalization. Multiple equalizers, such as zero-forcing (ZF), mini-

mum mean square error (MMSE), and Markov-Chain Monte-Carlo (MCMC)

can be used. In this work, we adopt the linear MMSE equalizer [81]. The a

priori information about the data symbols comes from the nonbinary LDPC

decoder in the preceding iteration, and the extrinsic information from the

equalizer will be used as prior information to the LDPC decoder.

70

• Nonbinary LDPC decoding. Based on the extrinsic information from the

LMMSE equalizer, the nonbinary LDPC decoder [26] generates the decoded

information symbols and the soft decisions about the information symbols

for both channel estimation and LMMSE equalization in the next iteration.

• Noise variance update. Due to the iterative estimation of the interference,

the channel mixing matrix and information symbols, the noise variance is

kept updated within each iteration.

Once the information symbols have been successfully decoded, i.e., the parity

check conditions of the nonbinary LDPC decoder are satisfied, or the number of

iterations reaches a predetermined threshold Imax, the iterative loop will stop.

We start with the initialization of the proposed iterative receiver in Sec-

tion 3.4.1. A detailed description of GLRT interference detection will be pre-

sented in Section 3.4.2, and sparse channel estimation, LMMSE equalization,

and nonbinary LDPC decoding will be discussed in Section 3.4.3. Estimation for

the variance of noise within and outside of the interference band is described in

Section 3.4.4.

3.4.1 Initialization

In the OFDM signal design, null subcarriers are usually inserted into the

signal band to estimate the carrier frequency offset [45] and the variance of the

ambient noise [25]. To initialize the iterative interference cancellation in Fig. 3.2,

the following operations are carried out.

71

Preprocessing,I = 0

GLRT interfer-ence detection

Interference present?Yes

Interferencesubtraction

No

Channel estimation

Noise variance update

Channel equalization

Channel decoding

Success or I = Imax?

Yes

Output decisions

No

I = I + 1

Noisevarianceupdate

Figure 3.2: Receiver structure for interference mitigation and data detection.

1. Based on the frequency measurements at null subcarriers, an linear inter-

polation is performed to estimate the variance of interference within the

signal band.

2. Assume that the interference components at all the frequency subcarriers

are independent. A pre-whitening operation is performed for the frequency

measurements [5].

72

3. With the pre-whitened frequency measurements, the channel estimation

is carried out based on the frequency measurements at pilot subcarriers,

which is followed by the ICI equalization and nonbinary LDPC decoder to

estimate the information symbols and to recover the information bits.

4. If the parity check conditions of the nonbinary LDPC decoder cannot be

satisfied, the estimated information symbols are fed into the GLRT inter-

ference detector to initialize the iterative interference mitigation.

3.4.2 Interference Detection and Estimation

Let us first assume that both channel and symbol estimates (H and s) are

available. Within the interference band BI, there are MI = ⌈BIT ⌉ subcarriers

contaminated. Denote the set of subcarriers within the interference band as

{i1, · · · iMI}. Define a selector matrix Θ of size MI × K with unit entry at the

(m, im)th position (m = 1, · · · ,MI) and zeros elsewhere. The selection matrix Θ

is determined based on the prior knowledge of the interference frequency band.

The relevant measurements within the interference frequency band are con-

tained in

z = Θ(z− Hs) = B(τI)u+ w, (3.24)

where

B(τI) := ΘΛ(τI)ΓI, w = Θw +Θ(Hs−Hs). (3.25)

73

Here, w denotes the equivalent additive noise within the frequency band, which

consists of the ambient noise and the residual noise due to imperfect channel and

information symbol estimates.

Assume that the noise samples are independent and follow a complex Gaussian

distribution CN (0, σ2BIIMI

), where σ2BI

denotes the noise variance. The likelihood

function of the interference component z in the presence of interference is

f(z|τI,u) ∝ exp

[

− 1

σ2BI

‖z−B(τI)u‖2]

. (3.26)

Let H0 and H1 denote the absence and presence of interference, respectively.

To detect the presence of interference in one particular OFDM block, we define

the generalized log-likelihood ratio test (GLRT) statistic

L(z) = max{τI,u}

lnf(z|τI,u,H1)

f(z|H0)

= max{τI,u}

lnexp

[−‖z−B(τI)u‖2 /σ2

BI

]

exp[−‖z‖2 /σ2

BI

]

= max{τI,u}

1

σ2BI

[zHB(τI)u+ uHBH(τI)z− uHBH(τI)B(τI)u

]≷ Γth (3.27)

where Γth is a predetermined threshold.

Define an objective function to be maximized over {τI,u},

J , zHB(τI)u+ uHBH(τI)z− uHBH(τI)B(τI)u. (3.28)

Setting the derivative ∇Ju to zero yields the optimal estimate of u as

u =[BH(τI)B(τI)

]−1BH(τI)z, (3.29)

Substituting u into (3.28), the estimate of τI is obtained as

τI = argmaxτI

zHB(τI)[BH(τI)B(τI)

]−1B(τI)

Hz, (3.30)

74

which can be solved using the grid search.

Based on the estimated parameters {u, τI}, the test statistic is evaluated as

L(z) =1

σ2BI

uHBH(τI)B(τI)u ≷ Γth, (3.31)

where the estimate σ2BI

is obtained following the procedure to be discussed in

Section 3.4.4. The test statistic L(z) is actually the ratio of the energy of the

estimated interference to the energy of the equivalent noise.

3.4.2.1 Determination of the GLRT threshold

Note that L(z|H0) follows a central χ2 distribution f(L(z); κ), and L(z|H1)

follows a non-central χ2 distribution f(L(z); κ, λ), both with degrees of freedom

κ = MI. Denote the energy of the interference by EI = uHBH(τI)B(τI)u. The

noncentrality parameter is λ = EI/σ2BI. The test threshold Γth then can be

determined based on the predetermined probability of false alarm PFA or the

probability of detection PD

PFA =

∫ ∞

Γth

f(L(z|H0); κ)dL(z|H0) = 1− P (Γth/2, κ/2) (3.32)

PD =

∫ ∞

Γth

f(L(z|H1); κ, λ)dL(z|H1) = Qκ/2

(√λ,√

Γth

)

, (3.33)

where P (a, b) is the incomplete Gamma function, and QM (a, b) is the Marcum

Q-function [66].

75

3.4.2.2 Computational complexity reduction

One straightforward approach to solving (3.30) is an exhaustive search over

all possible values of τI. To reduce the computational load, we define Ψ as a

K ×K diagonal matrix with the diagonal elements formed by ΘHz, and a K × 1

column vector φ(τI) containing the diagonal entries of the matrix Λ(τI). It is

easy to verify that B(τI)HB(τI) = ΓH

I ΘHΘΓI. Hence, we can rewrite (3.30) as

τI = argmaxτI

φH(τI)ΨHΓI

(ΓH

I ΘHΘΓI

)−1ΓH

I Ψ︸ ︷︷ ︸

:=J

φ(τI). (3.34)

Given a predetermined searching step and searching range of τI, a partial

fast Fourier transform (FFT) matrix Φ can be formed by stacking the column

vectors φ(τI) at all possible values of τI. The optimal τI can be obtained by

finding the maximum diagonal element of ΦHJΦ, where J is defined in (3.34).

The matrix J can be pre-computed given the prior knowledge of the time du-

ration and frequency band of the interference. Using FFT to compute ΦHJ,

finding the diagonal elements of ΦHJΦ only requires a complexity on the order

of K2(log2(K) + 1).

3.4.3 Channel Estimation, Equalization and Nonbinary LDPC De-

coding

If the presence of interference is declared from the GLRT detector (either

true detection or false alarm), the desired OFDM component can be obtained by

76

subtracting the estimated interference from the received signal

z = z−Λ(τI)ΓIu = Hs+ w, (3.35)

where w denotes the equivalent noise which consists of the ambient noise and the

residual interference

w = w + [Λ(τI)ΓIu−Λ(τI)ΓIu]. (3.36)

If no interference is detected (either absence of interference or missed detection),

we simply set u = 0 in (3.35). The following processing will be carried out based

on z.

Based on the observation vector z and the symbol vector s, the sparse channel

estimator in [6] is adopted in this chapter to estimate the channel matrixH, where

the banded assumption in (3.9) is used to reduce computational complexity.

Channel equalization is then carried out according to the maximum a poste-

riori (MAP) or the minimum mean square error (MMSE) criteria. In this work,

the linear MMSE estimator is adopted as the performance benchmark [80],

s = s+ Cov(s, z)Cov(z, z)−1(z− Hs), (3.37)

where s is the prior mean vector, and Cov(a,b) denotes the covariance matrix

of vectors a and b. Since a nonbinary LDPC decoder [26] is involved in the

receiver, the prior information about the data symbols from the decoder should

be excluded from the LMMSE estimate by setting the prior mean and variance

77

of s[m] to 0 and Es, respectively,

s[m] = Cov(s[m], z)Cov(z, z)−1(z− Hs + hms[m]),

= fHm(z− Hs + hms[m]) (3.38)

with

fm , Es

[

σ2s HHH + σ2

wIK + (Es − σ2s )hmh

Hm

]−1

hm, (3.39)

where s[m] and σ2s are the prior mean and variance of information symbol s[m],

respectively, hm is the mth column of channel matrix H, and σ2w is the variance

of the equivalent noise which will be estimated in Section 3.4.4.

After inputting the LMMSE estimate of information symbols into the nonbi-

nary LDPC decoder, both hard and soft decisions on the information symbols can

be obtained, these being fed back for interference detection, channel estimation

and equalization in the next iteration. A detailed description of the nonbinary

LDPC decoder can be found in [26].

3.4.4 Noise Variance Estimation

Due to the partial-band property of the interference, the noise variance σ2w

should be estimated individually for noise within and outside of the interference

band BI based on the frequency measurements at null subcarriers. Based on the

estimates of the channel matrix and transmitted symbols, the variance of the

equivalent noise outside of the interference band, which consists of the ambient

noise and the residual ICI due to the banded assumption of the channel matrix,

78

can be estimated as

σ2BI

= E{m∈SN,fm /∈BI}

∥∥∥∥∥z[m]−

m+D∑

k=m−D

H [m, k]s[k]

∥∥∥∥∥

2

. (3.40)

For the equivalent noise within the interference band, which consists of the am-

bient noise, the residual ICI and the residual interference, the noise variance can

be estimated as

σ2BI=E{m∈SN,fm∈BI}

∥∥∥∥∥∥

z[m]−m+D∑

k=m−D

H [m, k]s[k]−NI/2−1∑

l=−NI/2

Λ(τI)[m,m]ΓI[m, l]u[l]

∥∥∥∥∥∥

2

.

(3.41)

The estimated variance is then used for interference detection and information

symbol estimation.

3.5 Simulation Results

We simulate a sparse channel consisting of 10 discrete paths, where the inter-

arrival time follows an exponential distribution with a mean of 1 ms. The ampli-

tudes are Rayleigh distributed with average power decreasing exponentially with

the delay, where the difference between the beginning and the end of the guard

time is 20 dB.

The ZP-OFDM signal parameters and subcarrier distribution are tailored

according to the setting of one field experiment in Section A.1. The data symbols

are encoded with a rate-1/2 nonbinary LDPC code [26] and modulated with a

16-QAM constellation, which leads to a data rate

R =1

2· |SD|T + Tg

· log2 16 = 10.4 kb/s, (3.42)

79

where SD denotes the set of data subcarriers.

The interference is generated by passing white Gaussian noise of a given du-

ration through a bandpass filter according to the following parameters: center

frequency fIc = 15 kHz, bandwidth BI = 2.4 kHz and time duration TI = 26.2 ms.

The delay of the interference relative to start of each OFDM block is uniformly

distributed within [0, T + Tg − TI].

Throughout this chapter, the signal-to-noise ratio (SNR) and signal-to-interference

ratio (SIR) are defined as

SNR = Ps/N0, SIR = Ps/PI, (3.43)

where Ps denotes the average power of OFDM frequency measurements within

the useful signal band, PI denotes the average power of interference frequency

components within the interference frequency band, and N0 denotes the variance

of the additive noise in frequency domain.

Four configurations are introduced to compare the performance of the pro-

posed receiver with the receiver which does not perform interference cancellation.

• Configuration 1: the interference-free environment; the conventional re-

ceiver is adopted;

• Configuration 2: the interference-free environment; the proposed receiver

is adopted;

• Configuration 3: the interference-present environment; the conventional

receiver is adopted;

80

• Configuration 4: the interference-present environment; the proposed re-

ceiver is adopted.

The block-error-rate (BLER) performance will be used as the performance metric.

When applying the proposed receiver in configurations 2 and 4, we assume that

the interference has been detected in each OFDM block such that interference

cancellation is always performed.

3.5.1 Time-Invariant UWA Channels

To examine the performance of the proposed receiver in a time-invariant chan-

nel, the Doppler rate of each path is set zero. Averaged over 2000 Monte Carlo

runs, Fig. 3.3 demonstrates the BLER performance of the four configurations

with SIR = 0 dB. In the presence of interference, the receiver without interference

cancellation does not work, while the proposed receiver can approach the perfor-

mance of the conventional receiver in the absence of interference. Meanwhile, in

the scenario without interference, there is only slight performance degradation of

the proposed receiver relative to the conventional receiver.

Fig. 3.4 shows the performance improvement of the proposed receiver with

different number of iterations. One can observe a large performance gap be-

tween the receiver without iteration, i.e. the receiver which performs interference

suppression via noise prewhitening as described in Section 3.4.1, and the pro-

posed receiver which iteratively mitigates the interference through interference

estimation and subtraction.

81

8 9 10 11 12 13 14 1510

−3

10−2

10−1

100

SNR per Symbol [dB]

BLE

R

Configuration 1Configuration 2Configuration 3Configuration 4

Figure 3.3: BLER performance of several receivers in the time-invariant scenario,SIR = 0 dB.

3.5.2 Time-Varying UWA Channels

To explore the receiver performance in a time-varying channel, the Doppler

rate of each path is drawn independently from a zero-mean uniform distribution

with the standard deviation σv m/s. To improve the channel estimation per-

formance in the presence of ICI, we convert 96 data subcarriers as extra pilot

subcarriers, which are grouped with the null subcarriers and original pilot sub-

carriers into clusters [6]. The new data rate R is recomputed as

R =|SD|/2− 96

T + Tglog216 = 7.4 kb/s. (3.44)

Fig. 3.5 shows the performance of the four configurations in the scenario with a

mild Doppler spread σv = 0.1 m/s and a significant Doppler spread σv = 0.2 m/s,

respectively. Resampling operation is not performed (i.e., a = 0). A banded as-

sumption of the channel matrix is adopted with the ICI depth D = 1. We can

82

8 9 10 11 12 13 14 1510

−3

10−2

10−1

100

SNR per Symbol [dB]

BLE

R

it 0it 1it 2it 3it 5it 9

Figure 3.4: BLER performance improvement against iterations of the proposedreceiver in the time-invariant scenario, SIR = 0 dB.

observe that in the presence of interference, the performance of the proposed

receiver still can approach that of the conventional receiver in the scenario with-

out interference, while the conventional receiver without interference cancellation

does not work.

3.5.3 Performance of the Proposed Receiver with Different SIRs

By varying the SIR level, performances of the proposed receiver in both time-

invariant and time-varying scenarios are shown in Fig. 3.6. One can observe that

when the SIR is very small, a BLER error floor shows up, and that as the SIR

increases, the decoding performance of the proposed receiver gradually converges

to the decoding performance in the scenario without interference.

83

7 8 9 10 11 12 13 1410

−3

10−2

10−1

100

SNR per Symbol [dB]

BLE

R

Configuration 1Configuration 2Configuration 3Configuration 4

(a) σv = 0.1 m/s

7 8 9 10 11 12 13 1410

−3

10−2

10−1

100

SNR per Symbol [dB]

BLE

R

Configuration 1Configuration 2Configuration 3Configuration 4

(b) σv = 0.2 m/s

Figure 3.5: BLER performance of receivers in the time-varying channels, D = 1,SIR = 0 dB.

3.5.4 Interference Detection and Estimation

Define EI as the interference energy, and N0 as the power of ambient noise.

The ROC curve of the GLRT detector with different EI/N0 and time-bandwidth

product of interference is shown in Fig. 3.7. We can observe that with an identical

EI/N0, the larger time-bandwidth product of the interference, the more difficult

for it to be detected, because it appears more like the ambient noise.

3.6 Experimental Results: AUTEC10

This experiment was held in March 2010 over the AUTEC network; the ex-

perimental description, ZP-OFDM signal design, and transmission data rate are

described in Section A.3. Relative to the experimental test in Section 2.6.2,

received signals at a different set of nodes are used.

84

8 9 10 11 12 13 14 1510

−3

10−2

10−1

100

SNR per Symbol [dB]

BLE

R

SIR = −12dBSIR = −9dBSIR = −6dBSIR = −3dBSIR = 0dBSIR = 6dB

(a) Time-invariant scenario, D = 0

7 8 9 10 11 12 13 1410

−3

10−2

10−1

100

SNR per Symbol [dB]

BLE

R

SIR = −12dBSIR = −9dBSIR = −6dBSIR = −3dBSIR = 0dBSIR = 6dB

(b) Time-varying scenario, σv = 0.1 m/s,D = 1

Figure 3.6: BLER performance of the proposed receiver at different SIR levels.

There are two transmission trials of an identical data set, with the first trial

and the second trial including 18 transmissions and 22 transmissions, respectively.

During the experiment, sonar operations were carried out by others simultane-

ously. At sensors close to the sonar operation, the received signal of all the

transmissions in the first trial and the first portion of transmissions in the second

trial were contaminated. Based on the received signal waveform in Fig. 3.1, the

receiver can infer that TI ≈ 45 ms and the frequency band [11, 15] kHz, and

hence sets fIc ≈ 13 kHz, the interfering bandwidth BI ≈ 2 kHz.

In the sequel, the proposed interference cancellation receiver will be tested

with the experimental data in two different cases. Note that as opposed to the

simulations, only parts of the OFDM blocks contain interference; we thus start the

interference detection module in the receiver to decide the necessity of interference

cancellation.

85

0 0.2 0.4 0.6 0.8 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

PD

PFA

EI/N

0 = 7 dB, B

IT

I = 64

−−−−−−−−−, BIT

I = 128

EI/N

0 = 13 dB, B

IT

I = 64

−−−−−−−−−, BIT

I = 128

Figure 3.7: ROC of the GLRT interference detector.

3.6.1 Test Case 1

In this test case, we investigate the interference cancellation performance of

the receiver at different SNR levels. Thirteen transmissions with the SIR level

ranging from 0 dB to 9 dB from the second trial are used for this test. With the

received interference-contaminated waveform shown in Fig. 3.1, white Gaussian

noise is added to the received signal to generate several emulated experimental

data sets with different SNRs.

The decoding performance of the emulated experimental data sets with and

without interference mitigation is shown in Fig. 3.8. One can observe that the

receiver with interference cancellation outperforms the receiver without interfer-

ence cancellation, and the performance gap between the iterative interference

cancellation method and the noise-prewhitening method is large.

86

7 8 9 10 11 120

0.001

0.01

0.1

1

SNR [dB]

BLE

R

it 0it 1it 3it 5

without interference cancellation

with interference cancellation

Figure 3.8: Block error rate of 13 transmissions with/without interference can-cellation (IC) versus different levels of added noise, Imax = 7.

3.6.2 Test Case 2

In this test case, we investigate the interference cancellation performance of

the receiver at different SIR levels. By modifying the weighting coefficients, the

emulated experimental data sets of different SIRs are constructed through adding

the received signal of pure interference with one received OFDM signal which is

not contaminated by interference. The received signal at two hydrophones are

shown in Fig. 3.9, where the signal at one hydrophone is interference-free, while

the signal at the other hydrophone is almost purely interference with a very weak

useful signal masked by ambient noise.

Fig. 3.10 shows the decoding performance of the emulated experimental data

sets with and without interference cancellation. Again, we can observe that the

87

0 2 4 6 8−0.02

−0.015

−0.01

−0.005

0

0.005

0.01

0.015

0.02

Time [s]

Pas

sban

d si

gnal

OFDM BlocksHFM Preamble

(a) OFDM signal at one hydrophone

0 2 4 6 8−0.02

−0.015

−0.01

−0.005

0

0.005

0.01

0.015

0.02

Time [s]

Pas

sban

d si

gnal

(b) Pure interference waveform at theother hydrophone

Figure 3.9: Sample of the received signals at two hydrophones after bandpassfiltering. The two data sets are added together with different weights to generatesemi-experimental data sets at different SIR levels.

receiver with interference cancellation outperforms that without interference can-

cellation considerably, and the performance improvement brought by the iterative

interference cancellation is significant.

3.7 Experimental Results: SPACE08

The Surface Processes and Acoustic Communications Experiment (SPACE08)

was held off the coast of Martha’s Vineyard, Massachusetts, from Oct. 14 to

Nov. 1, 2008. Detailed descriptions of the experiment and OFDM signal design

can be found in Section A.1.

During the experiment, two cycles of large waves showed up, one around

Julian date 297 and the other around Julian date 300. The latter storm was

more severe. We thus consider the data recorded from these two days to verify

88

−5 −4 −3 −2 −1 0 1 20

0.001

0.01

0.1

1

SIR [dB]

BLE

R

it 0, without ICit 1, −−−it 3, −−−it 5, −−−it 0, with ICit 1, −−−it 3, −−−it 5, −−−

Figure 3.10: BLER of 18 transmissions with/without interference cancella-tion (IC) versus different signal to interference power ratio, Imax = 7, SNR≈ 7.9 dB.

performance of the proposed method in the time-varying scenario. For each day,

there are twelve recorded files, each consisting of twenty OFDM blocks. We test

all the files on Julian date 297. On Julian date 300, five files recorded in the

afternoon were severely distorted; we thus only consider the seven files recorded

in the morning and evening.

Note that there was no external interference during this experiment. We

extract the interference from the recorded sonar waveform in the AUTEC10 ex-

periment at one hydrophone shown in Fig. 3.9 (b), and artificially add each sonar

waveform to each OFDM block to create an emulated experimental data set with

interference contamination. The delay of the added sonar waveform relative to

the OFDM block follows a uniform distribution within the interval [0, T+Tg−TI].

To estimate the channel accurately, 96 data subcarriers are used as extra pilot

89

2 4 6 8 10 120

0.001

0.01

0.1

1

phones

BLE

R

(a) S1, SIR = -3.0 dB,Julian date: 297

2 4 6 8 10 120

0.001

0.01

0.1

1

phones

BLE

R

(b) S3, SIR = -2.8 dB,Julian date: 297

2 4 6 8 10 120

0.001

0.01

0.1

1

phones

BLE

R

(c) S5, SIR = 0.4 dB,Julian date: 297

2 4 6 8 10 120

0.001

0.01

0.1

1

phones

BLE

R

(d) S1, SIR = -4.2 dB,Julian date: 300

2 4 6 8 10 120

0.001

0.01

0.1

1

phones

BLE

R

(e) S3, SIR = -3.5 dB,Julian date: 300

2 4 6 8 10 120

0.001

0.01

0.1

1

phonesB

LER

(f) S5, SIR = -2.1 dB,Julian date: 300

Figure 3.11: BLER performance comparison of receiver with/without interferencecancellation, 16-QAM, D = 3. Marker ∗: receiver without interference cancel-lation; marker o: proposed interference cancellation receiver; marker +: originalBLER without adding interference; dashed line: [0 1 5 9]th iteration, solid line:10th iteration.

subcarriers, as discussed in Section 3.5.2. The data rate as stated in (A.2) is

achieved. Again, different from the simulations, the receiver incorporates the

interference detection module to determine the necessity of interference cancella-

tion.

90

The decoding performance of the proposed receiver and the conventional re-

ceiver without interference cancellation, and the decoding performance of the sig-

nal without adding the interference are depicted in Fig. 3.11. One can find that

relative to the decoding performance of the original received signal, significant

performance degradation of the conventional receiver is incurred by introducing

the interference. Meanwhile, the proposed receiver can effectively eliminate the

interference after a number of iterations.

3.8 Summary

In this chapter, we developed an interference mitigation receiver for OFDM

in underwater acoustic communications. Assuming prior knowledge of frequency

band and time duration of the interference, the interference waveform was pa-

rameterized by a limited number of parameters, where the number of parameters

is equal to the time-bandwidth product. Incorporating the interference into the

OFDM system model while accounting for the unknown delay offset of the inter-

ference waveform relative to the OFDM block, an OFDM receiver with explicit

interference mitigation was developed. A GLRT was used for interference detec-

tion, and interference estimation and data decoding were carried out iteratively.

Both simulation and experimental results demonstrated that the iterative inter-

ference mitigation considerably outperforms the non-iterative noise-prewhitening

approach which treats interference as ambient noise. Particularly in our exper-

imental data sets, the performance of the proposed receiver in the presence of

91

interference can approach that of the traditional receiver in the scenario with-

out interference, which shows that the proposed receiver has robust performance

against interference.

Chapter 4

Asynchronous Multiuser Reception for OFDM

in Underwater Acoustic Communications

4.1 Introduction

With the increasing demand on high-rate wireless communications and net-

working, multiuser communication has been identified as an effective methodol-

ogy to increase network throughput. Especially, multiuser communication tech-

niques have been adopted in the recent 4G Long-Term Evolution (LTE) stan-

dards. Compared to the terrestrial radio environment, limited communication

bandwidth in water makes multiuser acoustic communications more attractive.

The last two decades have witnessed considerable progress on UWA com-

munications and networking. On the physical layer, significant advances have

been witnessed for both single-carrier and multicarrier transmissions; see, e.g.

92

93

[?, 1, 6, 11, 38, 39, 43–45, 68, 70, 72, 73, 79, 82, 85], and references therein, whereas a

majority of research was centered on point-to-point communications.

In this chapter, we consider the application of OFDMmodulation to multiuser

underwater acoustic communications. Should the signals from multiple users be

synchronized at the receiver on the OFDM block level, multiuser reception can be

viewed as a distributed multi-input multi-output (MIMO) problem, as considered

in [30,76,77]. However, due to large propagation delays and lack of a well-defined

network infrastructure, synchronization is an extremely challenging task in the

distributed underwater acoustic system.

4.1.1 Asynchronous OFDM Research in Radio Channels

Asynchronous multiuser reception has been extensively investigated with code-

division multiple access (CDMA) transmissions; see e.g., [31, 54, 83] and refer-

ences therein. The impact of the asynchronism of users on orthogonal frequency-

division multiple access (OFDMA) uplink transmission has been investigated

in [23, 63]. Related work on the asynchronous OFDM receiver is limited [23, 36,

37, 46, 63, 74, 75], and can be broadly grouped into two main categories.

The works in the first category focus on the demodulation and decoding mod-

ules of the receiver, assuming that perfect channel knowledge is available. In [75],

a maximum a posteriori (MAP) receiver over a three-dimensional trellis was de-

veloped for asynchronous multiuser OFDMA transmissions, where the trellis is

expanded by the user index, time index and subcarrier index. This method has

94

surfaceAUV

(a) A bottom-anchored network

bottom

buoy

sensor

(b) A data collection network

Figure 4.1: Two examples of underwater acoustic networks. The nodes anchoredat the water bottom in the first network are connected to a control center viacables. The gateways in the second network can communicate with satellites orships using radio waves.

very high computational complexity when the number of subcarriers is large.

Using the same truncation method as in the synchronous multiuser reception to

divide the received signal into individual processing units, Ref. [74] pointed out

that the conventional frequency-domain approaches for decoding and interference

suppression are not effective, as the orthogonality of subcarriers of the misaligned

users is lost due to the misalignment of the otherwise-orthogonal users’ signals.

Hence, the spatial-time filtering techniques were employed in [36, 46, 74] to ex-

ploit the spatial diversity of multiple receivers. In [103], a general message-passing

based equalization method was proposed in the presence of interference.

The works in the second category focus on channel estimation in asynchronous

OFDM systems. A subspace based semi-blind channel estimator was proposed

in [37] to separate the desired user’s channel vector from channel vectors of other

users. The method, although often very useful, can be expected to suffer when

the channel has fast time-variation.

95

Apparently, a complete receiver design for asynchronous OFDM with both

channel estimation and equalization is not available even for radio channels. In

addition, methods developed for radio channels may not be not directly applicable

for fast-varying underwater acoustic channels.

4.1.2 Our Work

Most works for underwater acoustic OFDM are focused on point-to-point

communications, e.g., [?, 43, 45], and extensions to cooperative OFDM usually

assume block-level synchronism among users [76]. In this chapter, we propose

a multiuser receiver for the asynchronous OFDM transmissions in underwater

acoustic channels. The main contributions are the following.

• To our best knowledge, this is the first work on the asynchronous mul-

tiuser OFDM reception in underwater acoustic channels. As the proposed

approach allows the simultaneous transmission of multiple users without

performing coordination, it has practical impacts on the MAC protocol

design for certain emerging underwater acoustic networks [3, 9, 12, 13].

• To achieve the asynchronous multiuser reception, we develop a burst-by-

burst processing method. In particular, an over-lapped truncation approach

is proposed to retain the desired block-information from all the users within

one truncation. By taking the aggregated cochannel interference caused by

the asynchronism as one interference, the asynchronous multiuser problem

is converted to a quasi-synchronous multiuser problem with interference

96

contamination. Moreover, the overlapped truncation and the interference

aggregation enable the interference parameterization and cancellation re-

gardless of the number of users, hence simplify the receiver design.

• Extensive simulation and emulated experimental results are used to validate

the performance of the proposed receiver in both time-invariant and time-

varying scenarios. These results highlight the dependence of the decoding

performance on the maximum relative delay among users.

Although the network throughput can be greatly increased by allowing simul-

taneous transmissions from asynchronous multiusers, the computational complex-

ity of the asynchronous multiuser reception is much higher than its synchronous

counterpart, hence requiring a high computational capability of the processing

unit. Two examples of underwater acoustic networks are shown in Fig. 4.1, where

in the left one multiple autonomous underwater vehicles (AUVs) communicate to

a fixed cabled network on the sea bottom (c.f. the AUTEC network in Fig. 1.2),

and in the right one multiple sensor nodes communicate data back to the buoys

on the water surface. In both cases, the receiving nodes, either anchored at the

sea bottom or attached to a surface buoy, are assumed to have the processing

power needed to decode simultaneous transmissions from multiple users.

Remark 1: In this chapter, we mainly focus on the scenario that all the users are

stationary or have similar moving speeds. Investigation on the asynchronous mul-

tiuser reception in a scenario where different users have different moving speeds is

97

beyond the scope of this work. By assuming the synchronous transmission from

multiple user, receiver designs dealing with quite different speeds of different users

have recently been studied in [30, 76, 77].

The rest of the chapter is organized as follows. A burst-by-burst asynchronous

multiuser OFDM reception approach is developed in Section 4.2, with several key

modules detailed in Section 4.3. Investigation on the time duration of the aggre-

gated interference in an example network is provided in Section 4.4. Simulations

and emulated experimental results are presented in Sections 4.5 and 4.6, respec-

tively. Conclusions are contained in Section 4.7. This chapter collects the results

published in [91, 93–95].

4.2 The Proposed Receiver for Asynchronous OFDM Transmissions

Consider an underwater system consisting of Nu asynchronous users and a

receiver equipped with Nr receiving hydrophones, and Nr > Nu. Assume that

all users use the ZP-OFDM block transmission with an identical parameter set,

which includes the center frequency fc, bandwidth B, number of subcarriers K,

symbol duration T and a silent guard interval of length Tg with Tbl = T + Tg.

The kth frequency subcarrier is denoted as

fk = fc +k

T, k = −K

2, · · · , K

2− 1. (4.1)

Out of the total K subcarriers, there are data subcarriers for information deliv-

ery, pilot and null subcarriers for channel and noise variance estimation. Define

98

sµ[k;n] as the symbol transmitted at the kth subcarrier of the nth block from

the µth user, and assume Nbl blocks in each transmission burst. The transmitted

signal from the µth user is

xµ(t) =

Nbl∑

n=1

sµ(t− nTbl;n), t ∈ [0, NblTbl] (4.2)

where the nth transmitted block is expressed as

sµ(t;n) = 2R

K/2−1∑

k=−K/2

sµ[k;n]ej2πfktg(t)

, t ∈ [0, Tbl] (4.3)

with g(t) being a rectangular window which has nonzero support within [0, T ],

as defined in (2.8).

Using a path-based channel model [6], the channel impulse response between

the µth user and the νth receiving hydrophone during the transmission of the

nth block is expressed as

hν,µ(τ, t;n) =

N(n)pa,ν,µ∑

p=1

A(n)ν,µ,pδ

(τ − (τ (n)ν,µ,p − a(n)ν,µ,pt)

), (4.4)

where N(n)pa,ν,µ is the number of discrete channel paths, A

(n)ν,µ,p, τ

(n)ν,µ,p and a

(n)ν,µ,p are

the amplitude, initial delay, and Doppler scaling factor of the pth path, respec-

tively. The Doppler scaling factor a(n)ν,µ,p is related to the speed of the pth path

v(n)ν,µ,p via a

(n)ν,µ,p = a

(n)ν,µ,p/c, where c is the sound speed in water. The triplets

(A(n)ν,µ,p, τ

(n)ν,µ,p, a

(n)ν,µ,p) are assumed independent across blocks. The signal from the

µth user at the νth receiving hydrophone can be expressed as

yν,µ(t) =

Nbl∑

n=1

yν,µ(t− nTbl;n), t ∈ [0, NblTbl] (4.5)

99

t

t

t

t

εµ

εNu

yν(t;n)

Iν(t;n) with t ∈ [0, εmax] Iν(t;n) with t ∈ [Tbl, Tbl + εmax]

n− 1 n n + 1

n− 1 n n + 1

n− 1 n n + 1

yν,1(t)

yν,µ(t− εµ)

yν,Nu(t− εNu

)

yν(t)

Figure 4.2: Illustration of the overlapped partition of the received signal and theaggregated interference in an asynchronous Nu-user system.

with

yν,µ(t;n) =

N(n)pa,ν,µ∑

p=1

A(n)ν,µ,psµ

((1 + a(n)ν,µ,p)t− τ (n)ν,µ,p

). (4.6)

Let εµ denote the time-of-arrival the µth user, which can be obtained at the

receiver by detecting the preamble of this user. On the block level, we can assume

that εµ ≤ Tbl/2, as integer block delays can be incorporated by reindexing the

blocks. Without loss of generality, we assume that 0 = ε1 ≤ ε2 ≤ · · · εNu ≤ Tbl/2,

and define εmax := εNu . The passband signal at the νth receiving element is the

superposition of Nu waveforms,

yν(t) =

Nu∑

µ=1

yν,µ(t− εµ) + wν(t), (4.7)

where yν,µ(t) is the signal at the νth receiving element from the µth user, and

wν(t) denotes the ambient noise.

100

4.2.1 Overlapped Truncation

To facilitate the decoding operation at the receiver, the received signal is

usually truncated into individual processing units. For synchronous multiuser

transmissions, the truncation can be easily carried out according to the block

structure of the transmitted signal. However, for asynchronous transmissions, the

block structure of the transmitted signal at the receiver is destroyed. As shown

in Fig. 4.2, a block from one user can collide with multiple blocks from other

users. Different truncation methods could lead to different decoding schemes [23].

One existing method is to synchronize the truncation to the time-of-arrival of

one desired user [36, 37, 46, 74], with each truncation having a block length Tbl,

including the complete information of one block from the desired user and partial

block information from others. However, this method is not effective when the

overlap length of the desired user and others is large.

In this work, we consider an overlapped truncation method as shown in

Fig. 4.2, where each truncated block length is Tbl := Tbl+εmax. The nth truncated

block consists of the information from (3Nu − 2) transmitted blocks, including:

(i) part of the (n − 1)th blocks from users 2 ∼ Nu at the beginning of this

truncation;

(ii) complete information of the nth blocks from the Nu users;

(iii) part of the (n + 1)th blocks from users 1 ∼ (Nu − 1) at the end of this

truncation.

101

The received signal within the nth truncation can be expressed as

yν(t;n) =Nu−1∑

µ=1

yν,µ(t− εµ − Tbl;n+ 1)

︸ ︷︷ ︸

interference from preceding processing units

+Nu∑

µ=1

yν,µ(t− εµ;n)

︸ ︷︷ ︸

desired OFDM signal

+Nu∑

µ=2

yν,µ(t− εµ + Tbl;n− 1)

︸ ︷︷ ︸

interference from succeeding processing units

+wν(t;n), t ∈ [0, Tbl]. (4.8)

for t ∈ [0, Tbl].

With (4.8), an optimal receiver can be designed by treating the asynchronous

Nu-user problem as a synchronous (3Nu−2)-user problem [83]. However, solving

the problem therein usually requires more efforts than solving a typical syn-

chronous (3Nu − 2)-user problem, since the orthogonality of subcarriers of the

(2Nu − 2) misaligned users in (4.8) is destroyed.

4.2.2 Interference Aggregation

In this chapter, rather than modeling the partial block interferences from

(2Nu − 2) users individually with the transmitted signal, we use an interference

aggregation concept to treat the aggregated IBI as one interfering waveform as

shown in Fig. 4.2, which is formulated as

Iν(t;n) =

∑Nu

µ=2 yν,µ(t− εµ + Tbl;n− 1), t ∈ [0, εmax]

0, t ∈ [εmax, Tbl]

∑Nu−1µ=1 yν,µ(t− εµ − Tbl;n+ 1), t ∈ [Tbl, Tbl].

(4.9)

The bandwidth of the aggregated interference is taken as identical to that of the

useful signal denoted by B. Given the maximum delay εmax, one can see that

102

the number of the degrees-of-freedom (DoF) of the interfering waveform, i.e.,

the time-bandwidth product of the aggregated interference ⌈2Bεmax⌉, does not

change as the number of asynchronous users increases.

We then have (4.8) reformulated as

yν(t;n) =

Nu∑

µ=1

yν,µ(t− εµ;n) + Iν(t;n) + wν(t;n) (4.10)

for t ∈ [0, Tbl]. Hence, the asynchronous Nu-user problem can be regarded as a

synchronous Nu-user problem in the presence of an external interference.

4.2.3 The Overall Structure of the Proposed Receiver

As shown in [75], the IBI arising from the asynchronism of users can be op-

timally mitigated by performing a joint decoding of blocks in one transmission

from all users. However, this is usually computationally prohibitive. Leverag-

ing the overlapped truncation method and the interference aggregation concept,

we next propose a multiuser reception approach by performing a burst-by-burst

decoding with interference cancellation.

Different from the external interference considered in [92], the time-domain

input-output relationship in (4.8) shows the interference term in (4.10) actually

consists of part of useful signals corresponding to the (n− 1)th and the (n+1)th

transmitted blocks from the Nu users. If these blocks have been successfully

decoded or estimates of transmitted symbols within these blocks are available,

one can get initial estimates of the interferences that spill over from these blocks

to the nth block, and thus take the estimates as the a priori knowledge of the

103

Forward processing backward processing

Truncation1

Truncationn − 1

Truncationn

Truncationn + 1

TruncationNbl

The nth trun-cation, I = 0

Interference subtraction

Frequency-domainoversampling

Residual interferenceestimation & subtraction

MultiuserOFDM reception

Success or I = Imax?

Yes

Interferencereconstruction

Output decisions

No

Soft information;I = I + 1

Iν(t;n+1) fort ∈ [0, εmax]

Iν(t;n−1) fort ∈ [Tbl, Tbl]

Iν(t;n+1) fort ∈ [0, εmax]

Iν(t;n−1) fort ∈ [Tbl, Tbl]

Figure 4.3: Illustration of the proposed burst-by-burst asynchronous multiuser re-ceiver with iterative forward/backward processing, with Nbl blocks in each burst.

interferences. After subtracting initial estimates of the interferences from the

received signal, the joint multiuser decoding and cancellation of the aggregated

residual interference can be performed in the nth block.

The proposed asynchronous multiuser receiver for each block consists of the

following four steps.

104

• Step (1) Interference subtraction: With the estimated interference passed

from the preceding and the succeeding processing units, interference sub-

traction can be carried out prior to the multiuser decoding;

• Step (2) Joint multiuser processing with residual interference cancellation:

Techniques for synchronous multiuser decoding and approaches for external

interference cancellation can be used;

• Step (3) Interference reconstruction: Based on the multiuser decoding re-

sults, the interference of the current block to the preceding and the suc-

ceeding blocks will be reconstructed.

• Step (4) Iteration among Steps (1) ∼ (3): To improve the interference can-

cellation performance, an iterative forward/backward processing of blocks

within one burst can be performed, as shown in Fig. 4.3. As the iteration

goes on, the accuracy of interference estimation improves gradually, thus

leading to a better multiuser decoding performance, which in turn boosts

the performance of interference estimation.

A detailed description of three modules in the proposed receiver will be pro-

vided in Section 4.3. Note that the proposed scheme can be extended to both

cyclic-prefixed (CP)-OFDM transmissions and single-carrier block transmissions

if the OFDM multiuser decoding module is replaced by a similar module tailored

to the corresponding signalling format.

105

4.2.4 Discussions on the Proposed Receiver

Compared with a synchronous multiuser receiver, the proposed asynchronous

multiuser receiver can only perform multiuser decoding after receiving the whole

burst from all users, hence suffering a processing latency. Similar to the Viterbi

algorithm for channel equalization, the latency can be reduced by using the slid-

ing block techniques proposed in, e.g. [51, 84], which leads to a batch-by-batch

processing, with the batch size depending on the maximum tolerant latency and

the storage capability of the receiver.

When the batch size is one, the proposed receiver degrades to a block-by-

block receiver. Relative to the block-by-block decoding, burst-by-burst decoding

leverages the decoding results of preceding and succeeding blocks for interference

cancellation, hence enjoys a better decoding performance; however, it suffers a

processing latency of the batch size.

Hereafter, we mainly focus on the receiver design for burst-by-burst process-

ing, and the block-by-block receiver can be obtained as a special case whose

performance will also be tested in Sections 4.5 and 4.6.

Remark 2: In a practical OFDM system with Nu users, the time-of-arrival of

the signal from each user can be estimated by transmitting a preamble prior to

the useful data stream at the transmitter side. Preambles for Nu users could

be obtained from a set of m-sequence waveforms or a set of Costas waveforms,

which have low cross correlation values. At the receiver side, Nu matched filters

106

are used to detect the arrival of the useful signal from each user in the presence

of multiuser interference. Note that the matched filter gain is equal to the time-

bandwith product of the preamble waveform. A large time duration or bandwidth

is desirable when the multiuser interference is severe.

4.3 Descriptions of Receiver Modules

This section provides detailed descriptions on different modules of the pro-

posed receiver for asynchronous OFDM transmissions. The modules are pre-

sented according to their order in the receiver processing.

Prior to the interference subtraction, the passband-to-baseband downshifting

and baseband lowpass filtering are performed. Define yν(t;n) as the baseband

waveform corresponding to the passband signal yν(t;n). In the sequel, we focus

on the receiver modules operating in the baseband.

4.3.1 Interference Subtraction

For the sake of computational complexity reduction, the interference subtrac-

tion is performed with the baseband discrete samples. Define yν(t;n) as the

baseband waveform corresponding to the passband signal yν(t;n). Assume the

a priori knowledge of the time-domain interference waveform in baseband which

is denoted by Iν(t;n) (its availability will be discussed in Section 4.3.4). Prior

to the receiver processing, subtraction of the initial interference estimate from

107

yν(t;n) in (4.10) leads to

yν(t;n) =Nu∑

µ=1

yν,µ(t− εµ;n) + Iν(t;n)− Iν(t;n)︸ ︷︷ ︸

:=ην(t;n)

+wν(t;n) (4.11)

=

Nu∑

µ=1

yν,µ(t− εµ;n) + ην(t;n) + wν(t;n) (4.12)

for t ∈ [0, Tbl], where ην(t;n) denotes the residual interference. As the residual

interference has an identical time duration and bandwidth as the interference

Iν(t;n), the number of DoF of ην(t;n) is also ⌈2Bεmax⌉.

In the initial forward block-to-block decoding of the proposed receiver, the a

priori knowledge of the interference from the subsequent block is not available.

Hence, we set it as zero at the beginning. Once all the blocks have been processed,

the initial estimates of the interference spilled over from both neighboring blocks

are available. During the following processing, the latest estimates of the decoded

blocks are used for interference cancellation.

4.3.2 Frequency-Domain Oversampling

Define α as the frequency-domain oversampling factor. The mth frequency

component of the time-domain signal yν(t;n) can be obtained via

zν [m;n] =

∫ Tbl

0

yν(t;n)e−j2π m

αTtdt, (4.13)

for m = −αK/2, · · · , αK/2−1. Similarly, the mth frequency component ην [m;n]

of the residual interference ην(t;n) can be obtained.

Stack the frequency components zν [m;n] and ην [m;n] into vectors zν [n] and

ην [n] of size αK×1, respectively. The input-output relationship in the frequency

108

domain corresponding to (4.11) can be compactly expressed as

zν [n] =Nu∑

µ=1

Λ(εµ)Hν,µ[n]sµ[n] + ην [n] +wν [n], (4.14)

where wν [n] is the ambient noise vector, and the first summation term denotes

the desired OFDM signal, with sµ[n] being a K × 1 vector formed by the trans-

mitted symbols at all subcarriers from the µth user, Hν,µ[n] denoting an αK×K

channel matrix between the µth user and the νth receiving element, and Λ(εµ)

instantiating a generic diagonal matrix defined as

[Λ(τ)]m,m = e−j2π mαT

τ . (4.15)

Remark 3: Using the baseband sampling rate B = K/T , there are ⌈TblB⌉ =

⌈TblK/T ⌉ samples in each processing unit. To avoid information loss during the

Fourier transform, the frequency-domain oversampling factor α should satisfy

αK ≥ TblK/T , i.e., αT ≥ Tbl. Based on εmax < Tbl/2, we require α ≥ 3(1 +

Tg/T )/2. Taking α = 2 for example, the guard interval should satisfy Tg ≤ T/3.

4.3.3 Multiuser Channel Estimation and Data Decoding with Inter-

ference Cancellation

Based on the frequency-domain input-output relationship in (4.14), there are

several unknowns to estimate, including: (i) the channel matrices {Hν,µ[n]}, (ii)

the information symbols in {sµ[n]}, and (iii) the interference {ην [n]}. To this

end, we propose a receiver structure for iterative multiuser channel estimation

109

and data decoding and residual interference estimation within each block, as

shown in Fig. 4.3.

During the iterative processing, the multiuser decoding step takes the residual

interference estimate in the last iteration as the input, and based on the estimated

desired OFDM component after subtracting residual interference from zν [n], it

outputs the estimated channel matrices and information symbols. Taking the

output of multiuser decoding step as input, the residual interference cancella-

tion step will subtract the reconstructed OFDM component from the frequency

measurement zν [n], so as to update the residual interference estimate which is

then fed back for the next iteration. Once the parity check conditions of the

channel decoders of all users are satisfied, or the number of iterations reaches a

predetermined threshold Imax, the iteration stops.

For the initialization of the iterative receiver, we first treat the residual inter-

ference as the ambient noise to get the initial estimates of channel matrices and

information symbols, which are then used to initialize the iterative operation.

The two critical components of the receiver are described next.

4.3.3.1 Parameterized residual interference estimation and subtrac-

tion

With the estimated channel matrices {Hν,µ[n]} and transmitted symbols {sµ[n]}

from initialization or from the last iteration, the frequency-domain measurements

110

after subtracting the OFDM components are

ξν [n] = zν [n]−Nu∑

µ=1

Λ(εµ)Hν,µ[n]sµ[n], (4.16)

which includes both the residual interference, and the the equivalent ambient

noise consisting of both ambient noise, and the channel and information symbol

estimation errors.

To facilitate the residual interference estimation, we introduce a parameter-

ized interference representation. Based on the time-bandwidth product NI :=

⌈Bεmax⌉, the interference in baseband can be approximated by the Fourier series

expansion

ην(t;n) ≈

∑NI/2l=−NI/2

cl,ν,heej2π l

εmaxt, t ∈ [0, εmax]

0, t ∈ [εmax, Tbl]

∑NI/2l=−NI/2

cl,ν,taej2π l

εmaxt, t ∈ [Tbl, Tbl]

(4.17)

where {cl,ν,he} and {cl,ν,ta} represent the Fourier series coefficients of the front

and end portions of the interference, respectively.

Following the time-to-frequency transform in (4.13), the mth frequency sam-

ple of ην(t;n) is formulated as

ην [m;n] = (ul,ν,he + ul,ν,tae−j2π m

αTTbl)Γ[m, l], (4.18)

111

where

ul,ν,he :=εmax

Tcν,l,he, ul,ν,ta :=

εmax

Tcν,l,ta,

Γ[m, l] : =sin(

π(

mαT

− lεmax

)

εmax

)

π(

mαT

− lεmax

)

εmax

e−π( mαT

− lεmax

)εmax.

Stack ul,ν,he and ul,ν,ta into vectors uν,he and uν,ta of size NI× 1, respectively, and

stack Γ[m, l] into an matrix Γ of size αK ×NI, and define

Ψ := [Γ Λ(Tbl)Γ], uν [n] := [uThe,ν uT

ta,ν ]T. (4.19)

Eq. (4.18) can be compactly expressed as

ην [n] = Ψuν [n]. (4.20)

Based on the measurements in (4.16), the least-squares estimate of the inter-

ference vector is

uν [n] = (ΨHΨ)−1ΨHξν [n]. (4.21)

Note that (ΨHΨ)−1ΨH only depends on εmax, hence can be pre-computed before

receiver processing.

4.3.3.2 Multiuser channel estimation and data detection

The desired OFDM component is obtained by subtracting residual interfer-

ence from the frequency measurements,

zν [n] = zν [n]−Ψuν [n],

=

Nu∑

µ=1

Λ(εµ)Hν,µ[n]sµ[n] + wν [n], (4.22)

112

where the equivalent noise term consists of both the ambient noise and the inter-

ference estimation error,

wν [n] = Ψ(uν [n]− uν [n]) +wν [n]. (4.23)

For simplicity, we assume that wν [n] follows a zero-mean complex Gaussian dis-

tribution with a covariance matrix N0[n]IαK , where IαK is an identity matrix

of size αK × αK, and N0[n] is the average power of frequency samples at null

subcarriers.

With {zν[n]}Nr

ν=1, the conventional multi-input multi-output (MIMO) OFDM

receiver processing is then carried out. Rather than estimating the channel ma-

trices directly, a sparse channel estimation is achieved by estimating the path

parameters specified by the triplet (A(n)ν,µ,p, a

(n)ν,µ,p, τ

(n)ν,µ,p) in (4.4) for each receiv-

ing hydrophone individually; see, e.g., [6] and [29] for detailed description on

the sparse channel estimation. A linear MMSE equalizer [44] and a nonbinary

low-density parity-check (LDPC) decoder [26] are used for channel equalization

and decoding, respectively. After inputting the LMMSE estimate of information

symbols into the nonbinary LDPC decoder, both hard and soft decisions on the

information symbols can be obtained, these being fed back for the residual inter-

ference estimation, channel estimation and symbol detection in the next iteration.

For detailed description on the MIMO-OFDM receiver design, please refer [44]

and references therein.

113

4.3.4 Interference Reconstruction

Once the processing of the nth block stops, with the estimated channel matri-

ces and the information symbols the time-domain OFDM waveform in baseband

can be reconstructed via the inverse discrete-time Fourier transform,

yν,µ(t;n) =

αK/2−1∑

m=−αK/2

K/2−1∑

k=−K/2

Hν,µ[m, k;n]sµ[k]ej2π m

αTt, (4.24)

for t ∈ [0, Tbl]. Based on the aggregated interference representation in (4.9),

estimates of the interference components in Iν(t;n − 1) and Iν(t;n + 1), which

are spilled over from the nth block to the (n − 1)th and the (n + 1)th blocks,

respectively, can be obtained by replacing yν,µ(t;n) by yν,µ(t;n) in (4.9). They

are then passed to the preceding and the succeeding processing units.

4.4 Investigation on the Time Duration of Aggregated Interference

As shown in (4.9) and (4.17), the number of degrees of freedom of the inter-

ference are decided by its time-bandwidth product ⌈2Bεmax⌉. In this section, we

investigate on the time duration of the interference in an example network.

We consider a network with one data collection unit and multiple sensors,

which operates in a collision-tolerant fashion by allowing simultaneous transmis-

sions from Nu sensors. For simplicity, we assume that the receiver and sensors

are at the same depth in water, the sensors are uniformly distributed within a

circle of diameter DN, and the receiver is located at the origin.

114

Suppose the network operating according to a MAC protocol with handshak-

ing. The data collection unit first broadcasts the clear-to-send (CTS) frame to

allow simultaneous transmissions of Nu active sensors which requested to send

packets. Once receiving the CTS frame, each sensor starts the data transmission.

Let di denote the distance between the ith active sensor and the receiver.

Based on the uniform distribution of the ith sensor within the circle, the proba-

bility density function (pdf) of di will satisfy

f(di) ∝ 2πdi, (4.25)

which leads to the formulation,

f(di) =8diD2

N

, for di ∈ [0, DN/2]. (4.26)

Assuming that the acoustic waveform propagates along a straight line, the time-

of-arrival of packets from the ith sensor is thus εi = 2di/c, with the pdf,

g(εi) =2c2εiD2

N

, for εi ∈ [0, DN/c] (4.27)

with c being the sound speed in water.

Notice that for the block transmissions, the time-of-arrival of the package εi

and the time-of-arrival of each block within the package εi is related via

εi = [εi]mod Tbl/2= [2di/c]mod Tbl/2

. (4.28)

Take Tbl = 200 ms and c = 1500 m/s as an example. For di = 15 m, we have

εi = 20 ms; for di = 45 m, we have εi = 60 ms and for di = 75 m, we have εi = 0

ms.

115

0 20 40 60 80 1000

0.005

0.01

0.015

0.02

0.025

Time duration of interference [ms]

Pro

babi

lity

dens

ity2 users

3 users4 users

5 users

(a) with different number of users, DN =300 m

0 20 40 60 80 1000

0.005

0.01

0.015

0.02

0.025

0.03

Time duration of interference [ms]

Pro

babi

lity

dens

ity

D

N = 150 m

DN = 300 m

DN = 1500 m

2 users4 users

(b) with different values of DN

Figure 4.4: Probability density function of the maximum asynchronism on theOFDM block level in an asynchronous multiuser system, where the users areuniformly distributed within a circle of diameter DN.

Hence, the pdf of εi is the folded summation of g(εi), with

f(εi) =

L∑

l=0

g

(

εi +lTbl

2

)

=

L∑

l=0

8(εi + lTbl/2)

D2N

, (4.29)

for εi ∈ [0, Tbl/2], where L = ⌈2DN

Tblc⌉, and the cumulative distribution func-

tion (cdf) of εi follows as

F (εi) =L∑

l=0

4(ε2i + lTbl)

D2N

, (4.30)

for εi ∈ [0, Tbl/2]. Substituting (4.29) and (4.30) into (4.32), the distribution of

the interference time duration εmax can be obtained.

Assume that the arrival times of Nu users follow an independent and identical

distribution with the pdf f(ε) and cdf F (ε). The maximum delay εmax is the

range of the arrival-time sequence [16],

εmax = max{ε1, ε2, · · · , εNu} −min{ε1, ε2, · · · , εNu}, (4.31)

116

which has the pdf expressed as [16]

fNu(εmax) = Nu(Nu − 1) ·∫ ∞

−∞

f(ε)[F (ε+ εmax)− F (ε)]Nu−2f(ε+ εmax)dε.

(4.32)

Using the numerical integration, the pdf of εmax corresponding to different

number of users is shown in Fig. 4.4, where DN takes integer multiples of Tblc.

One can see that as the number of users increases, the pdf shifts to the large value

region of εmax gradually. A similar trend happens as the diameter DN increases,

but the pdf shifts quite slowly.

4.5 Simulation Results

In simulation, the underwater acoustic channel between each user and each

receiving hydrophone during each block transmission is generated randomly. We

assume that each channel consists of 10 discrete paths. The inter-arrival-time of

paths follows an exponential distribution with a mean of 1 ms. The amplitudes of

paths are Rayleigh distributed with the average power decreasing exponentially

with the delay, where the difference between the beginning and the end of the

guard time is 20 dB. The times-of-arrivals of users’ signals follow a uniform dis-

tribution within a certain interval. In each simulation instance, we assume that

the time-of-arrivals of users’ signals are perfectly known at the receiver.

We consider Nbl = 10 blocks in each transmission burst. The ZP-OFDM

parameters are specified in Table A.1, with an identical subcarrier distribution

as in the experiment described in Section A.1. The data symbols are encoded with

117

a rate-1/2 nonbinary LDPC code [26] and modulated by a QPSK constellation,

which leads to a data rate of each user

R =1

2· |SD|T + Tg

· log2 4 = 5.2 kb/user/s. (4.33)

Throughout this chapter, we adopt the block-error-rate (BLER) averaged over

all users as the performance metric. A frequency-domain oversampling factor

α = 2 is used.

The decoding performance of four receiver processing configurations will be

compared.

• Configuration 1: A block-by-block multiuser reception: By treating the

interference as ambient noise, the conventional iterative multiuser decoding

techniques in Section 4.3.3.2 are used;

• Configuration 2: A block-by-block multiuser reception with interference

cancellation: By treating the interference as an external interference, the

iterative joint multiuser processing and interference cancellation in Sec-

tion 4.3.3 is performed;

• Configuration 3: A block-to-block receiver with forward interference cancel-

lation: After the interference subtraction based on the interference estimate

from the preceding block, iterative joint multiuser decoding and residual in-

terference cancellation are performed, as in Section 4.3;

118

• Configuration 4: The proposed burst-by-burst receiver with multiple rounds

of forward and backward processing.

For fairness of comparison, the frequency-domain oversampling is used for all

the configurations, and we set an identical iteration number threshold (Imax =

4) in each block processing. Four rounds of forward/backward block-to-block

processing in configuration 4 are used. In configuration 4, we take 10 blocks

within one burst as one batch, while for configurations 1 ∼ 3, the batch size can

be regarded as one.

In terms of the decoding complexity, one can see that configuration 1 has the

lowest complexity, the complexities of configurations 2 and 3 are similar, and

configuration 4 has about eight times of the complexity of configuration 3 due to

the iterative forward and backward processing. Meanwhile, configurations 1 ∼ 3

are capable of on-line processing without decoding latency, while configuration 4

suffers a decoding latency of the burst length.

4.5.1 Two-User Systems with Time-Varying Channels

To explore the receiver performance in the time-varying UWA channels, we

draw the Doppler rate of each path independently from a zero-mean uniform

distribution with standard deviation (std) σv m/s according to the path-based

channel model in (4.4). To achieve a good decoding performance, the ICI in-

curred by the channel variation is considered explicitly. For the sake of receiver

complexity, a band-limitedness assumption of the channel matrix is adopted by

119

0 1 2 3 4 510

−3

10−2

10−1

100

SNR per Symbol per User per Antenna [dB]

BLE

R

Config. 1Config. 2Config. 3Config. 4

Figure 4.5: BLER performance of four receiving configurations, σv = 0.1 m/s.

assuming that only the elements in the main diagonal and one off-diagonal on

each side are nonzero in this setting.

For ICI estimation with regularly distributed pilots, a progressive decoding

procedure in [29] is employed. During the iterative processing, the receiver as-

sumes the absence of ICI to get an initial estimate of the transmitted information

symbols. Coupled with pilots, the information symbol estimates are then used in

the following iterations for channel estimation.

We assume three receiving hydrophones at the receiver and that the relative

delay of the second user is uniformly distributed within the interval [0, Tbl/2].

In the channel with a mild Doppler spread σv = 0.1 m/s, Fig. 4.5 shows the

BLER performance of the four receiving configurations with different signal-to-

noise ratio (SNR) levels. One can see that the conventional receiver without

interference cancellation almost cannot work, that the block-by-block interference

120

0 1 2 3 4 510

−3

10−2

10−1

100

SNR per Symbol per User per Antenna [dB]

BLE

R

[0 0.1]xT

bl

[0.1 0.2]xTbl

[0.2 0.3]xTbl

[0.3 0.4]xTbl

[0.4 0.5]xTbl

Figure 4.6: BLER performance of the proposed receiver in a two-user systemwith different relative delays, σv = 0.1 m/s; three receiving hydrophones.

cancellation brings some performance improvement, and that the burst-by-burst

receiver has the best performance. Relative to the one-way message passing in

the block-to-block receiver, the two-way message passing in the proposed burst-

by-burst receiver improves the decoding performance considerably.

Corresponding to a mild Doppler spread with σv = 0.1 m/s, Fig. 4.6 shows the

BLER performance of the burst-by-burst receiver when the relative delay of the

second user is uniformly distributed within five consecutive intervals: [0, 0.1]Tbl,

[0.1, 0.2]Tbl, [0.2, 0.3]Tbl, [0.3, 0.4]Tbl and [0.4, 0.5]Tbl. One can see that as

the relative delay of the second user, i.e., the time duration of the interference

increases, the required SNR for successful decoding of the two data streams also

increases.

121

2 3 4 5 6 7 810

−3

10−2

10−1

100

SNR per Symbol per User per Antenna [dB]

BLE

R

Config. 1Config. 2Config. 3Config. 4

Figure 4.7: BLER performance of four receiving configurations, solid lines: σv =0.3 m/s; dashed lines: σv = 0.5 m/s.

With three receiving hydrophones, the BLER performance of the four receiv-

ing configurations in the channel with severe Doppler spreads σv = 0.3 m/s and

σv = 0.5 m/s are shown in Fig. 4.7. Similar to the observation in the channel

with a mild Doppler spread, the proposed burst-by-burst receiver with forward

and backward message passing outperforms other configurations considerably.

Assuming two receiving hydrophones, the BLER performance of the conven-

tional receiver and the proposed receiver with and without perfect channel knowl-

edge is shown in Fig. 4.8. Relative to the scenario with channel estimation, one

can see that the performance gap between the two receiving schemes decreases

when perfect channel knowledge is available. One could infer that channel estima-

tion accuracy degrades drastically if the interblock interference is not accounted

for.

122

0 2 4 6 8 10 1210

−4

10−3

10−2

10−1

100

SNR per Symbol per User per Antenna [dB]

BLE

R

Config. 1Config. 4

with channel estimation

with full channel knowledge

Figure 4.8: BLER performance of two receiving configurations with and withoutperfect channel knowledge, two receiving hydrophones are used, and σv = 0.3m/s.

4.5.2 Multiuser Systems with Time-Invariant Channels

To examine the performance of the proposed burst-by-burst receiver as a func-

tion of number of users, we set ε1 = 0, and assume that the relative delay of the

second user is uniformly distributed within a certain interval, and that the delays

of users 3 ∼ Nu are uniformly distributed between zero and the upper bound

of this interval. By dividing half of the OFDM block duration [0, Tbl/2] into

five intervals: [0, 0.1]Tbl, [0.1, 0.2]Tbl, [0.2, 0.3]Tbl, [0.3, 0.4]Tbl and [0.4, 0.5]Tbl,

Figs. 4.9 and 4.10 show the BLER performance of the proposed receiver with four

asynchronous users and six hydrophones at the receiver. Relative to the BLER

performance in the two-user scenario in Fig. 4.6, one can see that as the number

of users increases, the maximum delay of the users, i.e., the time duration of the

123

−4 −2 0 2 4 610

−3

10−2

10−1

100

SNR per Symbol per User per Antenna [dB]

BLE

R

[0 0.1]xT

bl

[0.1 0.2]xTbl

[0.2 0.3]xTbl

[0.3 0.4]xTbl

[0.4 0.5]xTbl

Figure 4.9: BLER performance of the proposed receiver in a four-user systemwith different relative delays, six receiving hydrophones.

interference has more impact on the decoding performance. Meanwhile, one can

also observe a considerable performance improvement brought by the iterative

forward and backward message passing.

4.6 Emulated Experimental Results: MACE10

For the receiver performance evaluation, we use the data set collected in

MACE10 experiment to emulate the data set collected in an asynchronous mul-

tiuser communication system; the experimental setup and OFDM parameters can

be found in Section A.2.

We consider the data files with a rate-1/2 nonbinary LDPC code and a QPSK

constellation for information bit encoding and mapping. The data rate of each

124

−1 0 1 2 3 410

−3

10−2

10−1

100

SNR per Symbol per User [dB]

BLE

R

round 1round 2round 3round 4

Figure 4.10: BLER performance of the proposed receiver with four rounds offorward/backward processing, εmax ∼ U [0.3, 0.4] × Tbl, four users, six receivinghydrophones.

user is

R =1

2· |SD|T + Tg

· log24 = 2.7 kb/user/s. (4.34)

To test the proposed receiver for asynchronous Nu-user transmissions, we gen-

erate an emulated experimental data set by consecutively dividing received data

blocks within each transmission into Nu groups and regarding the blocks within

each group as the signal from each user. The received experimental waveform is

emulated by adding the Nu groups together. A resampling operation is then used

to remove the Doppler effect caused by the mobility of the source array. Note

that due to the existence of ambient noise in the received data blocks, the SNR

per user in the emulated experimental data set decreases according to 10 log(Nu)

dB as the number of users increases.

125

3 4 5 6 7 8 9 10 11 12

1

0.1

0.01

0.0010

number of phones

BLE

R

Config. 1Config. 2Config. 3Config. 4

Figure 4.11: BLER performance of four receiving configurations, MACE10 datasets.

Similar to the simulation setup, the relative delay of each user is uniformly dis-

tributed within a certain interval. By setting the distribution interval correspond-

ing to the second user as [0, Tbl/2], Fig. 4.11 shows the decoding performance of

the four configurations in the simulation, and four rounds of forward/backward

block-to-block processing in configuration 4 are used. Again, one can see that the

conventional multiuser reception approach without interference cancellation al-

most cannot work, the block-by-block interference cancellation method improves

the performance slightly, and the proposed burst-by-burst receiver with the for-

ward and backward message passing is the best.

With different distribution intervals of the relative delay, the BLER perfor-

mance of the proposed burst-by-burst receiver with two asynchronous users is

shown in Fig. 4.12. One can see that as the relative delay increases, i.e., the time

126

3 4 5 6 7 8 9 10 11 12

1

0.1

0.01

0.0010.0010

number of phones

BLE

R

[0 0.1]× T

bl

[0.1 0.2]× Tbl

[0.2 0.3]× Tbl

[0.3 0.4]× Tbl

[0.4 0.5]× Tbl

Figure 4.12: BLER performance of the proposed receiver with different rela-tive delays, four rounds of forward and backward processing and eight iterationswithin each block processing; MACE10 data sets.

duration of the interference increases, more receiving hydrophones are required

for successful decoding.

Assuming that the relative delays of users are uniformly distributed within

[0, Tbl/2], Fig. 4.13 shows the packet-success-rate of the proposed receiver with

different number of users. One can see that as the number of users increases, the

decoding performance gets worse gradually. The degradation can be attributed

to the increased multiuser interference and the increased ambient noise power

due to the generation of the emulated experimental data sets.

To achieve a robust decoding performance of the proposed receiver, a block-

level Reed-Solomon (RS) erasure-correction code over Galois field can be used

as an interblock code while the nonbinary LDPC code is used as an intra-block

code [50]; the optimal combination between the erasure- and error-correction

127

1 2 30

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

number of users

pack

et s

ucce

ss r

ate

without RSrate−8/10 RS

Figure 4.13: PSR of the proposed receiver with different number of users withand without a rate-8/10 Reed-Solomon erasure-correction code across 10 blocks,four rounds of forward/backward processing, eight iterations within each blockprocessing.

codes for the layered coding approach has been studied in [7]. With a rate-

8/10 block-level shortened RS codeword applied for each data subcarrier across

a packet consisting of 10 blocks, any two blocks can be received in error (hence

erased), while the whole data burst can be recovered. Here, a shortened RS code

can be obtained by setting some information symbols as zeros from a RS code of

longer length [50]. Fig. 4.13 shows the packet-success-rate (PSR) of the proposed

receiver with different number of users. Compared with the packet-success-rate

without using erasure-correction coding, introducing two redundant blocks leads

to a considerable performance improvement. This option is appealing for practical

systems with asynchronous users.

128

4.7 Summary

In this chapter, we proposed an asynchronous multiuser reception method for

OFDM in underwater acoustic communications. With an overlapped truncation

of the received signal and using the interference aggregation concept, the asyn-

chronous multiuser problem was converted to a synchronous multiuser problem

with interference, where interference mitigation and multiuser decoding are car-

ried out in an iterative fashion. Extensive simulation and emulated experimental

results demonstrated that the proposed receiver can effectively recover the trans-

mitted symbols from multiple asynchronous users. The decoding performance

can be further improved by using a block-level RS erasure-correction code.

Chapter 5

Conclusions

The water world has been fascinating humans for thousands of years, yet

less than 1% of this mysterious environment has been explored. Driven by the

tremendous success of wireless communications and networking in the terrestrial

radio environment, we are at the stage to revolutionize underwater exploration;

the powerful tool we shall use is the underwater acoustic networked system.

This thesis aims to identify and address challenges posed in practical UWA

networked systems. Three research directions were pursued:

• Communication techniques for UWA channels with multipath clusters which

are widely separated;

• Interference mitigation for UWA communications and networking;

• Asynchronous multiuser reception for underwater OFDM.

129

130

Proposed solutions have been verified by data sets collected from real systems.

Despite taking OFDM as the underlying modulation, techniques developed in

this thesis can be applied to systems using other modulation techniques with

slight modification.

The research process followed a bottom-up research methodology to approach

the goal of efficient and reliable wireless communications and networking in water.

Techniques developed here could lead to a paradigm shift in UWA networking —

existing networking protocols in water are mainly derived from their counterparts

in the terrestrial radio environment which differs from the UWA environment in

many fundamental aspects. Meanwhile, research directions within this thesis

would open the door to many challenges which have not been identified toward

practical applications of UWA networked systems.

Appendix A

Experimental Description

A.1 Experimental Setting: SPACE08

The surface processes and acoustic communication experiment (abbreviatedas SPACE08) was conducted off the coast of Martha’s Vineyard, MA, from Oct. 14to Nov. 1, 2008. The water depth was about 15 meters, the transmitter wasapproximately 4 meters from the sea floor, and the top of the receive arrays wereabout 3.25 meters above the sea floor, as shown in Fig. A.1. We consider threereceivers, labeled as S1, S3, and S5, which were 60 m, 200 m, and 1,000 m fromthe transmitter, respectively. Each receiver array has twelve hydrophones.

The significant wave height and average wind speed across all the days areshown in Fig. A.2. The significant wave height is calculated as H = 4

√m0, where

m0 is the zeroth-moment of the variance spectrum obtained by integration of thevariance spectrum.

A transmission occurred every two hours, resulting in 12 recorded files eachday. There are 20 OFDM blocks in each transmission. The ZP-OFDM parame-ters are specified in Table A.1. Out of 1024 subcarriers, |SP| = 256 subcarrierscarry pilots for channel estimation, and |SN| = 96 subcarriers are used as nullsubcarriers with 24 on each edge of the signal band for band protection and 48uniformly distributed in the middle of the signal band for mean Doppler shift es-timation [45]. The remaining |SD| = 672 subcarriers are for data delivery. Datasymbols are encoded with a nonbinary LDPC code with rate denoted by rc [26]and modulated with a QAM constellation of size M , leading to a data rate

R = rc ·|SD|

T + Tg

· log2M. (A.1)

A.2 Experimental Setting: MACE10

The Mobile Acoustic Communication Experiment (MACE10) was carried outoff the coast of Martha’s Vineyard, Massachusetts, June, 2010. The water depth

131

132

Table A.1: OFDM Parameters in the SPACE08 Experiment

carrier frequency fc 13 kHzbandwidth B 9.77 kHzno. subcarriers K 1024symbol duration T 104.86 ms

subcarrier spacing ∆f , 1/T 9.54 Hzguard interval Tg 24.6 ms# of null subcarriers |SN| 96# of pilot subcarriers |SP| 256# of data subcarriers |SD| 672channel coding rate rc 0.5

4 m

15 m

Tx60 m

S1

3.2

5 m

1.2

m

S3S5

3.2

5 m

1.2

m

3.2

5 m

1.2

m

200 m

1000 m

Figure A.1: Setup of the SPACE08 experiment

was about 80 meters. The receiving array was stationary, while the source wastowed slowly away from the receiver and then towed back, at a speed around1 m/s. The relative distance of the transmitter and the receiver changed from500 m to 4.5 km. Out of two tows in the experiment, we only consider the datacollected in the first tow. There are 31 transmissions in this tow, with 20 blocksin each transmission. We exclude one transmission file recorded during the turnof the source, where the SNR of the received signal is quite low. The averageSNR of considered files is around 20 dB.

Parameters of this experiment are summarized in Table A.2. The subcarrierdistribution is identical to that in SPACE08 experiment. A rate-1/2 nonbinaryLDPC code is used, where the size of the Galois field matches the size of theconstellation [26].

Fig. A.3 shows the received signal magnitude fluctuation during the tow du-ration. The received signal strength becomes gradually weaker as the transmitterarray was towed away from the receiver, and then becomes gradually strongerwhen it was towed back.

133

295 296 297 298 299 300 301 302 3030

1

2

3

4

Julian Date in 2008

Wav

e he

ight

(m

)

295 296 297 298 299 300 301 302 3030

5

10

15

20

Julian Date in 2008

Win

d sp

eed

(m/s

)

Figure A.2: Significant wave height and average wind speed for selected days inSPACE08

Table A.2: OFDM Parameters in the MACE10 Experiment

center frequency fc 13 kHzbandwidth B 4.883 kHz

# of subcarriers K 1024symbol duration T 209.7 ms

frequency spacing ∆f , 1/T 4.77 Hzguard interval Tg 40.3 ms

For each block, we estimate the Doppler scaling factor based on null sub-carriers [86]. The relative speed between the transmitter and the receiver wasestimated as v = a · c, using a nominal sound speed of c = 1500 m/s. Fig. A.4shows the relative speed for the duration of tow 1, which reflects the experimentalsettings. The relative speed was about 1.2 m/s when the transmitter was movingaway from the receiver array, and about 1 m/s when it was towed back. Wesee that the estimated speed changes from negative to positive after 60 minutes,indicating that the transmitter array began to be towed back from the maximumrange at 60th minute.

The Doppler shifts are about 10 Hz, which are much larger than the OFDMsubcarrier spacing 4.7 Hz. Hence, re-scaling the waveform is necessary to mitigatethe Doppler effect in the frequency domain for the MACE10 data.

A.3 Experimental Setting: AUTEC

Two experimental data sets were collected at the Atlantic Undersea Test andEvaluation Center (AUTEC) around Andros Island near the Tongue of the Ocean,

134

0 20 40 60 80 100 120−0.015

−0.01

−0.005

0

0.005

0.01

0.015

Time [min]

Mag

nitu

de

Figure A.3: Received signal magnitude fluctuations in MACE10

Table A.3: OFDM Parameters in the AUTEC08 Experiment

center frequency fc 11 kHzbandwidth B 6 kHz

# of subcarriers K 1024symbol duration T 170.7 ms

subcarrier spacing ∆f , 1/T 5.86 Hzguard interval Tg 85.3 ms

# of blocks per transmission Nb 20

Bahamas [24]; see Section 1.1 for descriptions on the AUTEC network. One was inDecember 2008, and the other was in March 2010, which are termed as AUTEC08and AUTEC10, respectively. In the experiment, there is one transmitter and 95receivers located in an area of the size 30 km × 30 km, while only several receiversare used in this chapter. The receivers are at least 4 km apart from each other.The depths of the transmitter and the receivers vary from 1.5 km to 2 km.

A.3.1 AUTEC08

The ZP-OFDM parameters in this experiment are are shown in Table A.3.Relative to the subcarrier distribution in SPACE08 experiment, distributions ofpilot and data subcarriers are exchanged with |SP| = 672 and |SD| = 256. Anonbinary LDPC code over GF(4) [26] and a QPSK constellation are used.

A.3.2 AUTEC10

The ZP-OFDM parameters in this experiment are described in Table A.4.Compared with the AUTEC08 experiment, we redesigned the length of guardinterval, since based on the received signal in the AUTEC08 experiment, wefound that a guard interval length of 85.3 ms is not long enough to accommodate

135

0 20 40 60 80 100 120−2

−1.5

−1

−0.5

0

0.5

1

1.5

Time [min]

Est

imat

ed r

elat

ive

spee

d [m

/s]

Figure A.4: Estimated relative moving speed in Tow 1

Table A.4: OFDM Parameters in the AUTEC10 Experiment

center frequency fc 11 kHzbandwidth B 5 kHz

# of subcarriers K 860symbol duration T 170.7 ms

subcarrier spacing ∆f , 1/T 5.86 Hzguard interval Tg 250 ms

# of blocks per transmission Nb 10

the large delay spread of the second cluster in the AUTEC environment. Besides,the effective bandwidth was changed from 6 kHz to 5 kHz due to the limitationon the hardware. In the new signal design, 860 subcarriers are formed by therandom distribution of three pilot subcarrier patterns and three data subcarrierpatterns,

• pilot patterns:{[N P N](50), [P P](16), [P P P](114)

}

• data patterns:{[D](48), [D D](105), [D D D](26)

},

where N,P and D denote null subcarrier, pilot subcarrier and data subcarrier,respectively, and the sub-index denotes the number of different patterns, whichresults in 424 pilot subcarriers and 336 data subcarriers in total. A rate-1/2nonbinary LDPC code and a QPSK constellation are used, leading to a data rate

R =1

2· 336

0.1707 + 0.25· log24 = 798.7 bits/s (A.2)

or 38R = 299.5 Bytes/(3s).

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