MINISTRY OF EDUCATION & TRAINING

MINISTRY OF NATIONAL DEFENSE

MILITARY TECHNICAL ACADEMY

LE THI THANH HUYEN

REPEATED INDEX MODULATION

FOR OFDM SYSTEMS

A Thesis for the Degree of Doctor of Philosophy

HA NOI - 2020

MINISTRY OF EDUCATION & TRAINING

MINISTRY OF NATIONAL DEFENSE

MILITARY TECHNICAL ACADEMY

LE THI THANH HUYEN

REPEATED INDEX MODULATION

FOR OFDM SYSTEMS

A Thesis for the Degree of Doctor of Philosophy

Specialization: Electronic Engineering

Specialization code: 9 52 02 03

SUPERVISOR

Prof. TRAN XUAN NAM

HA NOI - 2020

ASSURANCE

I hereby declare that this thesis was carried out by myself under

the guidance of my supervisor. The presented results and data in

the the-sis are reliable and have not been published anywhere in the

form of books, monographs or articles. The references in the thesis

are cited in accordance with the university’s regulations.

Hanoi, May 17th, 2019

Author

Le Thi Thanh Huyen

ACKNOWLEDGEMENTS

It is a pleasure to take this opportunity to send my very great appreciation to those who made this thesis possible with their supports.

First, I would like to express my deep gratitude to my supervisor,

Prof. Tran Xuan Nam, for his guidance, encouragement and

meaningful critiques during my researching process. This thesis

would not have been completed without him.

My special thanks are sent to my lecturers in Faculty of Radio - Electronics, especially my lecturers and colleagues in Department of Communications who share a variety of di culties for me to have more time to

concentrate on researching. I also would like to sincerely thank my

research group for sharing their knowledge and valuable assistance.

Finally, my gratitude is for my family members who support my

stud-ies with strong encouragement and sympathy. Especially, my

deepest love is for my mother and two little sons who always are my

endless inspiration and motivation for me to overcome all obstacles.

Author

Le Thi Thanh Huyen

TABLE OF CONTENTS

Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

List of abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv List of

gures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii List of

tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x List of

symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi

INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

Chapter 1. RESEARCH BACKGROUND . . . . . . . . . . . . . . . 8

1.1. Basic principle of IM-OFDM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

8

1.1.1. IM-OFDM model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

9

1.1.2. Sub-carrier mapping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

12

1.1.3. IM-OFDM signal detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

14

1.1.4. Advantages and disadvantages of IM-OFDM . . . . . . . . . . . .

16

1.2. Related works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

17

1.3. Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

23 Chapter 2. REPEATED INDEX MODULATION FOR OFDM WITH

DIVERSITY RECEPTION . . . . . . . . . . . . . . . . . . . . . . 24 2.1. RIM-OFDM with

diversity reception model . . . . . . . . . . . . . . . . 24

2.2. Performance analysis of RIM-OFDM-MRC/SC under perfect CSI

28

2.2.1. Performance analysis for RIM-OFDM-MRC . . . . . . . . . . . .

29

i

2.2.2. Performance analysis for RIM-OFDM-SC . . . . . . . . . . . . . . .

34

2.3. Performance analysis of RIM-OFDM-MRC/SC under imperfect

CSI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . 35 2.3.1. Performance analysis for RIM-OFDM-MRC .

. . . . . . . . . . . 35

2.3.2. Performance analysis for RIM-OFDM-SC . . . . . . . . . . . . . . .

40

2.4. Performance evaluation and discussion . . . . . . . . . . . . . . . . . . . . . 41

2.4.1. Performance evaluation under perfect CSI . . . . . . . . . . . . . .

41

2.4.2. SEP performance evaluation under imperfect CSI condition .

48

2.4.3. Comparison of the computational complexity . . . . . . . . . . .

49

2.5. Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

50

Chapter 3. REPEATED INDEX MODULATION FOR OFDM

WITH COORDINATE INTERLEAVING . . . . . . . . . . . . . . .

51

3.1. RIM-OFDM-CI system model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

51

3.2. Performance analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

56

3.2.1. Symbol error probability derivation . . . . . . . . . . . . . . . . . . . . .

56

3.2.2. Asymptotic analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

59

3.2.3. Optimization of rotation angle . . . . . . . . . . . . . . . . . . . . . . . . . .

60

3.3. Low-complexity detectors for RIM-OFDM-CI. . . . . . . . . . . . . . . 62

3.3.1. Low-complexity ML detector . . . . . . . . . . . . . . . . . . . . . . . . . . .

62

3.3.2. LLR detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

65

3.3.3. GD detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

66

3.4. Complexity Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

67

3.5. Performance evaluations and discussion. . . . . . . . . . . . . . . . . . . . .

69

ii

3.6. Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

75 CONCLUSIONS AND FUTURE WORK . . . . . . . . . . . . . . . 76

PUBLICATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

BIBLIOGRAPHY. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

iii

LIST OF ABBREVIATIONS

Abbreviation

De nition

AWGN

Additive White Gaussian Noise

BEP

Bit Error Probability

BER

Bit Error Rate

CI

Coordinate Interleaving

CS

Compressed Sensing

CSI

Channel State Information

D2D

Device to Device

ESIM-OFDM

Enhanced Sub-carrier Index Modulation for Or-

thogonal Frequency Division Multiplexing

FBMC

Filter Bank Multi-Carrier

FFT

Fast Fourier Transform

GD

Greedy Detection

ICI

Inter-Channel Interference

IEP

Index Error Probability

IFFT

Inverse Fast Fourier Transform

IM

Index Modulation

IM-OFDM

Index Modulation for OFDM

iv

IM-OFDM-CI

Index Modulation for OFDM with Coordinate

Interleaving

IoT

Internet of Things

ISI

Inter-Symbol Interference

ITU

International Telecommunications Union

LowML

Low-complexity Maximum Likelihood

LLR

Log Likelihood Ratio

LUT

Look-up Table

M2M

Machine to Machine

Mbps

Megabit per second

MGF

Moment Generating Function

MIMO

Multiple Input Multiple Output

ML

Maximum Likelihood

MM-IM-OFDM

Multi-Mode IM-OFDM

MRC

Maximal Ratio Combining

NOMA

Non-Orthogonal Multiple Access

OFDM

Orthogonal Frequency Division Multiplexing

OFDM-GIM

OFDM with Generalized IM

OFDM-I/Q-IM

OFDM with In-phase and Quadrature Index

Modulation

OFDM-SS

OFDM Spread Spectrum

PAPR

Peak-to-Average Power Ratio

PEP

Pairwise Error Probability

PIEP

Pairwise Index Error Probability

v

PSK

Phase Shift Keying

QAM

Quadrature Amplitude Modulation

RIM-OFDM

Repeated Index Modulation for OFDM

RIM-OFDM-MRC

Repeated Index Modulation for OFDM with

Maximal Ratio Combining

RIM-OFDM-SC

Repeated Index Modulation for OFDM with Se-

lection Combining

RIM-OFDM-CI

Repeated Index Modulation for OFDM with Co-

ordinate Interleaving

SC

Selection Combining

SEP

Symbol Error Probability

SIMO

Single Input Multiple Output

S-IM-OFDM

Spread IM-OFDM

SNR

Signal to Noise Ratio

SM

Spatial Modulation

SS

Spread Spectrum

UWA

Underwater Acoustic

V2V

Vehicle to Vehicle

V2X

Vehicle to Everything

xG

x-th Generation

vi

LIST OF FIGURES

1.1 Block diagram of an IM-OFDM system. . . . . . . . . . . .

2.1 Structure of the RIM-OFDM-MRC/SC transceiver. . . . . .

10

25

2.2 The SEP comparison between RIM-OFDM-MRC and the

conventional IM-OFDM-MRC system when N = 4, K =

2, L = 2, M = f4; 8g. . . . . . . . . . . . . . . . . . . . . . . 42

2.3 The SEP performance of RIM-OFDM-SC in comparison

with IM-OFDM-SC for N = 4, K = 2, L = 2, M = f4; 8g. .

43

2.4 The relationship between the index error probability of

RIM-OFDM-MRC/SC and the modulation order M in

comparison with IM-OFDM-MRC/SC for N = 4, K = 2,

M = f2; 4; 8; 16g. . . . . . . . . . . . . . . . . . . . . . . . . 44

2.5 The impact of L on the SEP performance of RIM-OFDMMRC and RIM-OFDM-SC for M = 4; N = 4; K = 2 and

L = f1; 2; 4; 6g. . . . . . . . . . . . . . . . . . . . . . . . . . 45

2.6 The SEP performance of RIM-OFDM-MRC under in uence of K for M = f2; 4; 8; 16g, N = f5; 8g, K = f2; 3; 4; 5g.

46

2.7 The SEP performance of RIM-OFDM-SC under in uence

of K when M = f2; 4; 8; 16g, N = f5; 8g, K = f2; 3; 4; 5g. . .

46

2.8 In uence of modulation size on the SEP of RIM-OFDMMRC/SC for N = 5, K = 4, and M = f2; 4; 8; 16; 32g. . . . .

47

vii

2.9 The SEP performance of RIM-OFDM-MRC in comparison with IM-OFDM-MRC under imperfect CSI when N =

4, K = 2, M = f4; 8g, and

2

= f0:01; 0:05g. . . . . . . . . .

48

2.10 The SEP performance of RIM-OFDM-SC in comparison

with IM-OFDM-SC under imperfect CSI when N = 4,

K = 2, M = f4; 8g, and

2

= 0:01. . . . . . . . . . . . . . . .

49

3.1 Block diagram of a typical RIM-OFDM-CI sub-block. . . . .

52

3.2 Rotated signal constellation. . . . . . . . . . . . . . . . . . .

60

3.3 Computational complexity comparison of LLR, GD, ML

and lowML detectors when a) N = 8; M = 16; K =

f1; 2; : : : ; 7g and b) N = 8; K = 4; M = f2; 4; 8; 16; 32; 64g. . 68

3.4 Index error performance comparison of RIM-OFDM-CI,

IM-OFDM, IM-OFDM-CI and ReMO systems at the spectral e ciency (SE) of 1 bit/s/Hz, M = f2; 4g, N = 4,

K = f2; 3g. . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

3.5 SEP performance comparison between RIM-OFDM-CI,

IM-OFDM and CI-IM-OFDM using ML detection at the

spectral e ciency of 1 bit/s/Hz when M = f2; 4g, N = 4,

K = f2; 3g. . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

3.6 BER comparison between the proposed scheme and the

benchmark ones when N = 4, K = f2; 3g, M = f2; 4g. . . .

3.7 BER comparison between the proposed and benchmark

schemes at SE of 1.25 bits/s/Hz when N = f4; 8g, K =

f2; 4g, M = f2; 4; 8g. . . . . . . . . . . . . . . . . . . . . . . 73

viii

72

3.8

SEP performance of RIM-OFDM-CI and benchmark sys-

tems using di erent detectors. . . . . . . . . . . . . . . . . . 74

ix

LIST OF TABLES

1.1 An example of look-up table when N = 4, K = 2, p1 = 2 . .

2.1 Complexity comparison between the proposed schemes

13

and the benchmark. . . . . . . . . . . . . . . . . . . . . . . .

50

3.1 Example of LUT for N = 4, K = 2, pI = 2. . . . . . . . . . .

54

3.2 Complexity comparison between ML, LowML, LLR and

GD dectectors. . . . . . . . . . . . . . . . . . . . . . . . . .

x

68

LIST OF SYMBOLS

Symbol

Meaning

a

A complex number

aR

Real part of a

aI

Imaginary part of a

jaj

Modulus of a

a

A vector

A

A matrix

AH

The Hermitian transpose of A

AT

The transpose of A

c

Number of possible combinations of active in-

dices

f (:)

Probability density function

G

Number of sub-blocks

K

Number of active sub-carriers

N

Number of sub-carriers in each sub-block

NF

Number of sub-carriers in IM-OFDM system

L

Number of receive antennas

P (:)

The probability of an event

PI

Index symbol error probability

PM

M-ary modulated symbol error probability

xi

P

Symbol error probability

s

(:)

Q

The tail probability of the standard Gaussian

distribution

Average SNR at each sub-carrier

Set of possible active sub-carrier indices

I

(:)

M

The moment generating function.

Complex signal constellation

S

Rotated complex signal constellation

S

Index of an active sub-carrier

Channel estimation error variance

Big-Theta notation

Rotation angle of signal constellation

opt

Optimal rotation angle of signal constellation

k:k2F

Frobenius norm of a matrix

diag(:)

C (N; K)

Diagonal matrix

Binomial coe cient, C (N; K) =

bxc

Rounding down to the closest integer

log2 (:)

The base 2 logarithm

f:g

Expectation operation.

E

xii

N!

K!(N

K)!

INTRODUCTION

Motivation

Wireless communication has been considered to be the fastest developing eld of the communication industry. Through more than 30 years of

research and development, various generations of wireless communications have been born. The achievable data rate of wireless systems

has increased to several thousands of times higher (the fourth generation - 4G) than that of the second generation (2G) wireless systems.

Particularly, the 4G wireless communication systems, supported by key

technologies such as multiple-input multiple-output (MIMO), orthogonal

frequency division multiplexing (OFDM), cooperative communications,

have already achieved the data rate of hundreds Mbps [1].

The MIMO technique exploits the diversity of multiple transmit antennas and multiple receive antennas to enhance channel capacity without either increasing the transmit power or requiring more bandwidth.

Meanwhile, OFDM is known as an e cient multi-carrier transmission

technique which has high resistance to the multi-path fading. The OFDM

system o ers a variety of advantages such as inter-symbol in-terference

(ISI)

resistance,

easy

implementation

by

inverse

fast

Fourier

transform/fast Fourier transform (IFFT/FFT). It can also provide higher

spectral e ciency over the single carrier system since its orthogonal sub1

carriers overlap in the frequency domain.

Due to vast developments of smart terminals, new applications with

high-density usage, fast and continuous mobility such as cloud services,

machine-to-machine (M2M) communications, autonomous cars, smart

home, smart health care, Internet of Things (IoT), etc, the 5G sys-tem

has promoted challenging researches in the wireless communication

community [2]. It is expected that ubiquitous communications between

anybody, anything at anytime with high data rate and transmission reliability, low latency are soon available [3]. Although there are several 5G

trial systems installed worldwide, so far there have not been any o cial

standards released yet. The International Telecommunications Union

(ITU) has set 2020 as the deadline for the IMT-2020 standards. According

to a recent report of the ITU [3], 5G can provide data rate signi cantly

higher, about tens to hundreds of times faster than that of 4G. For latency

issue, the response time to a request of 5G can reduce to be about 1

millisecond compared to that around 120 milliseconds and between

roughly 15-60 milliseconds of 3G and 4G, respectively [3].

In order to achieve the above signi cant improvement, the 5G system

continues employing OFDM as one of the primary modulation technologies [2]. Meanwhile, based on OFDM, index modulation for OFDM (IMOFDM) has been proposed and emerged as a promising multi-carrier

transmission technique. IM-OFDM utilizes the indices of active subcarriers of OFDM systems to convey additional information bits. There

are several advantages over the conventional OFDM proved for IMOFDM such as the improved transmission reliability, energy e 2

ciency and the exible trade-o between the error performance and

the spectral e ciency [4], [5]. However, in order to be accepted for

possible inclusion in the 5G standards and have a full understanding

about the IM-OFDM capability, more studies should be carried out.

Inspired by the motivation of OFDM in the framework of 5G and the

application potentials of IM-OFDM to the future commercial standards,

the present thesis has adopted IM-OFDM as the research theme for its

study with the title \Repeated index modulation for OFDM systems".

Within the scope of the research topic, the thesis aims to conduct a

thorough study on the IM-OFDM system, and make its contributions to

enhance performances of this attractive system.

Research Objectives

Motivated by the application potentials of IM-OFDM and the fact that

its limitations, such as high computational complexity and limited

transmission reliability, which may prevent it from possible implementation, this research aims at proposing enhanced IM-OFDM systems to

tackle these problems. Moreover, a mathematical framework for the

performance analysis is also developed to evaluate the performance of

the proposed systems under various channel conditions. The speci c

objectives of the thesis research can be summarized as follows:

Upon studying the related IM-OFDM systems in the literature, e - cient

signal processing techniques such as repetition code and coordi-

nate interleaving are proposed to employ in the considered systems.

E cient signal detectors for the IM-OFDM system, which can bal3

ance the error performance with computational complexity, are

stud-ied and proposed for the considered systems.

Developing mathematical frameworks for performance analysis of

the proposed systems, which can give an insight into the system

behavior under the impacts of the system parameters.

Research areas

Wireless communication systems under the impact of di erent

fad-ing conditions.

Multi-carrier transmission using OFDM and index

modulation. Detection theory and complexity analysis.

Research method

In this thesis, both the theoretical analysis and the Monte-Carlo simulation are used to evaluate the performance of the considered systems.

The analytical methods are used for calculating the computational

complexity of the detection algorithms and to derive the closed-

form expressions for symbol error and bit error probabilities of

the proposed systems.

The Monte-Carlo simulation is applied to validate the analytical

results and to make comparison between the performance of the

proposed systems and that of the benchmarks.

Thesis contribution

The major contributions of the thesis can be summarized as follows:

4

Contributions to IM-OFDM with diversity reception

{ Based on the concept of IM-OFDM with diversity reception [6],

an enhanced IM-OFDM system with spatial diversity using the

maximal ratio combination and selection combination (abv. as

RIM-OFDM-MRC and RIM-OFDM-SC, respectively) is

proposed to improve the error performance over the

conventional IM-OFDM system with diversity reception.

{ The closed-form expressions for the index error probability

(IEP) and symbol error probability (SEP) of RIM-OFDM-MRC

and RIM-OFDM-SC under both perfect and imperfect

channel state information (CSI) conditions are derived to

analyze the error performance and the impacts of the system

parameters on the transmission reliability. Simulation results

are also provided to validate the theoretical analysis.

Contributions to IM-OFDM with coordinate interleaving

{ Based on the idea of IM-OFDM with coordinate interleaving

(IM-OFDM-CI) [7], an enhanced scheme of IM-OFDM,

referred to as repeated IM-OFDM-CI (RIM-OFDM-CI) is

proposed to improve the transmission reliability and exibility

of the conven-tional IM-OFDM-CI system. The closed-form

expressions for symbol and bit error probabilities of the

proposed system are also derived.

{ Three low-complexity detectors for RIM-OFDM-CI, which can signi

cantly reduce the computational complexity while still achiev5

ing near-optimal and optimal system error performance of

the ML detector, are proposed.

Thesis structure

The thesis is organized in three chapters as follows:

Chapter 1: Research background

This chapter introduces the research background of IM-OFDM

and related studies. Particularly, it presents a comprehensive

review on the recent studies of IM-OFDM and outlines several

challenging open problems which motivate the contributions of

the thesis in the sub-sequent chapters.

Chapter 2: Repeated IM-OFDM with diversity reception

This chapter proposes an enhanced IM-OFDM system with diver-sity

reception using maximal ratio combination (RIM-OFDM-MRC) and

selection combination (RIM-OFDM-SC). Performance analysis is

carried out to determine the diversity and coding gains of the proposed system under both perfect and imperfect CSI conditions. Performance comparisons between the proposed system and the related

benchmark ones are provided using numerical and simulation results.

Chapter 3: Repeated IM-OFDM with coordinate interleaving

In this chapter, a repeated IM-OFDM with coordinate interleav-ing

(RIM-OFDM-CI) is proposed. Three low-complexity detectors,

namely low-complexity ML (lowML), log-likelihood ratio (LLR), and

greedy detection (GD) are presented for the RIM-OFDM-CI system

6

to relax the detection complexity. An optimal rotation angle for

the M-QAM modulation constellation is determined to improve

the error performance of the system. Numerical and simulation

results are provided to evaluate the RIM-OFDM-CI system

performance of against benchmark systems.

7

MINISTRY OF NATIONAL DEFENSE

MILITARY TECHNICAL ACADEMY

LE THI THANH HUYEN

REPEATED INDEX MODULATION

FOR OFDM SYSTEMS

A Thesis for the Degree of Doctor of Philosophy

HA NOI - 2020

MINISTRY OF EDUCATION & TRAINING

MINISTRY OF NATIONAL DEFENSE

MILITARY TECHNICAL ACADEMY

LE THI THANH HUYEN

REPEATED INDEX MODULATION

FOR OFDM SYSTEMS

A Thesis for the Degree of Doctor of Philosophy

Specialization: Electronic Engineering

Specialization code: 9 52 02 03

SUPERVISOR

Prof. TRAN XUAN NAM

HA NOI - 2020

ASSURANCE

I hereby declare that this thesis was carried out by myself under

the guidance of my supervisor. The presented results and data in

the the-sis are reliable and have not been published anywhere in the

form of books, monographs or articles. The references in the thesis

are cited in accordance with the university’s regulations.

Hanoi, May 17th, 2019

Author

Le Thi Thanh Huyen

ACKNOWLEDGEMENTS

It is a pleasure to take this opportunity to send my very great appreciation to those who made this thesis possible with their supports.

First, I would like to express my deep gratitude to my supervisor,

Prof. Tran Xuan Nam, for his guidance, encouragement and

meaningful critiques during my researching process. This thesis

would not have been completed without him.

My special thanks are sent to my lecturers in Faculty of Radio - Electronics, especially my lecturers and colleagues in Department of Communications who share a variety of di culties for me to have more time to

concentrate on researching. I also would like to sincerely thank my

research group for sharing their knowledge and valuable assistance.

Finally, my gratitude is for my family members who support my

stud-ies with strong encouragement and sympathy. Especially, my

deepest love is for my mother and two little sons who always are my

endless inspiration and motivation for me to overcome all obstacles.

Author

Le Thi Thanh Huyen

TABLE OF CONTENTS

Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

List of abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv List of

gures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii List of

tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x List of

symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi

INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

Chapter 1. RESEARCH BACKGROUND . . . . . . . . . . . . . . . 8

1.1. Basic principle of IM-OFDM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

8

1.1.1. IM-OFDM model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

9

1.1.2. Sub-carrier mapping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

12

1.1.3. IM-OFDM signal detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

14

1.1.4. Advantages and disadvantages of IM-OFDM . . . . . . . . . . . .

16

1.2. Related works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

17

1.3. Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

23 Chapter 2. REPEATED INDEX MODULATION FOR OFDM WITH

DIVERSITY RECEPTION . . . . . . . . . . . . . . . . . . . . . . 24 2.1. RIM-OFDM with

diversity reception model . . . . . . . . . . . . . . . . 24

2.2. Performance analysis of RIM-OFDM-MRC/SC under perfect CSI

28

2.2.1. Performance analysis for RIM-OFDM-MRC . . . . . . . . . . . .

29

i

2.2.2. Performance analysis for RIM-OFDM-SC . . . . . . . . . . . . . . .

34

2.3. Performance analysis of RIM-OFDM-MRC/SC under imperfect

CSI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . 35 2.3.1. Performance analysis for RIM-OFDM-MRC .

. . . . . . . . . . . 35

2.3.2. Performance analysis for RIM-OFDM-SC . . . . . . . . . . . . . . .

40

2.4. Performance evaluation and discussion . . . . . . . . . . . . . . . . . . . . . 41

2.4.1. Performance evaluation under perfect CSI . . . . . . . . . . . . . .

41

2.4.2. SEP performance evaluation under imperfect CSI condition .

48

2.4.3. Comparison of the computational complexity . . . . . . . . . . .

49

2.5. Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

50

Chapter 3. REPEATED INDEX MODULATION FOR OFDM

WITH COORDINATE INTERLEAVING . . . . . . . . . . . . . . .

51

3.1. RIM-OFDM-CI system model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

51

3.2. Performance analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

56

3.2.1. Symbol error probability derivation . . . . . . . . . . . . . . . . . . . . .

56

3.2.2. Asymptotic analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

59

3.2.3. Optimization of rotation angle . . . . . . . . . . . . . . . . . . . . . . . . . .

60

3.3. Low-complexity detectors for RIM-OFDM-CI. . . . . . . . . . . . . . . 62

3.3.1. Low-complexity ML detector . . . . . . . . . . . . . . . . . . . . . . . . . . .

62

3.3.2. LLR detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

65

3.3.3. GD detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

66

3.4. Complexity Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

67

3.5. Performance evaluations and discussion. . . . . . . . . . . . . . . . . . . . .

69

ii

3.6. Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

75 CONCLUSIONS AND FUTURE WORK . . . . . . . . . . . . . . . 76

PUBLICATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

BIBLIOGRAPHY. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

iii

LIST OF ABBREVIATIONS

Abbreviation

De nition

AWGN

Additive White Gaussian Noise

BEP

Bit Error Probability

BER

Bit Error Rate

CI

Coordinate Interleaving

CS

Compressed Sensing

CSI

Channel State Information

D2D

Device to Device

ESIM-OFDM

Enhanced Sub-carrier Index Modulation for Or-

thogonal Frequency Division Multiplexing

FBMC

Filter Bank Multi-Carrier

FFT

Fast Fourier Transform

GD

Greedy Detection

ICI

Inter-Channel Interference

IEP

Index Error Probability

IFFT

Inverse Fast Fourier Transform

IM

Index Modulation

IM-OFDM

Index Modulation for OFDM

iv

IM-OFDM-CI

Index Modulation for OFDM with Coordinate

Interleaving

IoT

Internet of Things

ISI

Inter-Symbol Interference

ITU

International Telecommunications Union

LowML

Low-complexity Maximum Likelihood

LLR

Log Likelihood Ratio

LUT

Look-up Table

M2M

Machine to Machine

Mbps

Megabit per second

MGF

Moment Generating Function

MIMO

Multiple Input Multiple Output

ML

Maximum Likelihood

MM-IM-OFDM

Multi-Mode IM-OFDM

MRC

Maximal Ratio Combining

NOMA

Non-Orthogonal Multiple Access

OFDM

Orthogonal Frequency Division Multiplexing

OFDM-GIM

OFDM with Generalized IM

OFDM-I/Q-IM

OFDM with In-phase and Quadrature Index

Modulation

OFDM-SS

OFDM Spread Spectrum

PAPR

Peak-to-Average Power Ratio

PEP

Pairwise Error Probability

PIEP

Pairwise Index Error Probability

v

PSK

Phase Shift Keying

QAM

Quadrature Amplitude Modulation

RIM-OFDM

Repeated Index Modulation for OFDM

RIM-OFDM-MRC

Repeated Index Modulation for OFDM with

Maximal Ratio Combining

RIM-OFDM-SC

Repeated Index Modulation for OFDM with Se-

lection Combining

RIM-OFDM-CI

Repeated Index Modulation for OFDM with Co-

ordinate Interleaving

SC

Selection Combining

SEP

Symbol Error Probability

SIMO

Single Input Multiple Output

S-IM-OFDM

Spread IM-OFDM

SNR

Signal to Noise Ratio

SM

Spatial Modulation

SS

Spread Spectrum

UWA

Underwater Acoustic

V2V

Vehicle to Vehicle

V2X

Vehicle to Everything

xG

x-th Generation

vi

LIST OF FIGURES

1.1 Block diagram of an IM-OFDM system. . . . . . . . . . . .

2.1 Structure of the RIM-OFDM-MRC/SC transceiver. . . . . .

10

25

2.2 The SEP comparison between RIM-OFDM-MRC and the

conventional IM-OFDM-MRC system when N = 4, K =

2, L = 2, M = f4; 8g. . . . . . . . . . . . . . . . . . . . . . . 42

2.3 The SEP performance of RIM-OFDM-SC in comparison

with IM-OFDM-SC for N = 4, K = 2, L = 2, M = f4; 8g. .

43

2.4 The relationship between the index error probability of

RIM-OFDM-MRC/SC and the modulation order M in

comparison with IM-OFDM-MRC/SC for N = 4, K = 2,

M = f2; 4; 8; 16g. . . . . . . . . . . . . . . . . . . . . . . . . 44

2.5 The impact of L on the SEP performance of RIM-OFDMMRC and RIM-OFDM-SC for M = 4; N = 4; K = 2 and

L = f1; 2; 4; 6g. . . . . . . . . . . . . . . . . . . . . . . . . . 45

2.6 The SEP performance of RIM-OFDM-MRC under in uence of K for M = f2; 4; 8; 16g, N = f5; 8g, K = f2; 3; 4; 5g.

46

2.7 The SEP performance of RIM-OFDM-SC under in uence

of K when M = f2; 4; 8; 16g, N = f5; 8g, K = f2; 3; 4; 5g. . .

46

2.8 In uence of modulation size on the SEP of RIM-OFDMMRC/SC for N = 5, K = 4, and M = f2; 4; 8; 16; 32g. . . . .

47

vii

2.9 The SEP performance of RIM-OFDM-MRC in comparison with IM-OFDM-MRC under imperfect CSI when N =

4, K = 2, M = f4; 8g, and

2

= f0:01; 0:05g. . . . . . . . . .

48

2.10 The SEP performance of RIM-OFDM-SC in comparison

with IM-OFDM-SC under imperfect CSI when N = 4,

K = 2, M = f4; 8g, and

2

= 0:01. . . . . . . . . . . . . . . .

49

3.1 Block diagram of a typical RIM-OFDM-CI sub-block. . . . .

52

3.2 Rotated signal constellation. . . . . . . . . . . . . . . . . . .

60

3.3 Computational complexity comparison of LLR, GD, ML

and lowML detectors when a) N = 8; M = 16; K =

f1; 2; : : : ; 7g and b) N = 8; K = 4; M = f2; 4; 8; 16; 32; 64g. . 68

3.4 Index error performance comparison of RIM-OFDM-CI,

IM-OFDM, IM-OFDM-CI and ReMO systems at the spectral e ciency (SE) of 1 bit/s/Hz, M = f2; 4g, N = 4,

K = f2; 3g. . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

3.5 SEP performance comparison between RIM-OFDM-CI,

IM-OFDM and CI-IM-OFDM using ML detection at the

spectral e ciency of 1 bit/s/Hz when M = f2; 4g, N = 4,

K = f2; 3g. . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

3.6 BER comparison between the proposed scheme and the

benchmark ones when N = 4, K = f2; 3g, M = f2; 4g. . . .

3.7 BER comparison between the proposed and benchmark

schemes at SE of 1.25 bits/s/Hz when N = f4; 8g, K =

f2; 4g, M = f2; 4; 8g. . . . . . . . . . . . . . . . . . . . . . . 73

viii

72

3.8

SEP performance of RIM-OFDM-CI and benchmark sys-

tems using di erent detectors. . . . . . . . . . . . . . . . . . 74

ix

LIST OF TABLES

1.1 An example of look-up table when N = 4, K = 2, p1 = 2 . .

2.1 Complexity comparison between the proposed schemes

13

and the benchmark. . . . . . . . . . . . . . . . . . . . . . . .

50

3.1 Example of LUT for N = 4, K = 2, pI = 2. . . . . . . . . . .

54

3.2 Complexity comparison between ML, LowML, LLR and

GD dectectors. . . . . . . . . . . . . . . . . . . . . . . . . .

x

68

LIST OF SYMBOLS

Symbol

Meaning

a

A complex number

aR

Real part of a

aI

Imaginary part of a

jaj

Modulus of a

a

A vector

A

A matrix

AH

The Hermitian transpose of A

AT

The transpose of A

c

Number of possible combinations of active in-

dices

f (:)

Probability density function

G

Number of sub-blocks

K

Number of active sub-carriers

N

Number of sub-carriers in each sub-block

NF

Number of sub-carriers in IM-OFDM system

L

Number of receive antennas

P (:)

The probability of an event

PI

Index symbol error probability

PM

M-ary modulated symbol error probability

xi

P

Symbol error probability

s

(:)

Q

The tail probability of the standard Gaussian

distribution

Average SNR at each sub-carrier

Set of possible active sub-carrier indices

I

(:)

M

The moment generating function.

Complex signal constellation

S

Rotated complex signal constellation

S

Index of an active sub-carrier

Channel estimation error variance

Big-Theta notation

Rotation angle of signal constellation

opt

Optimal rotation angle of signal constellation

k:k2F

Frobenius norm of a matrix

diag(:)

C (N; K)

Diagonal matrix

Binomial coe cient, C (N; K) =

bxc

Rounding down to the closest integer

log2 (:)

The base 2 logarithm

f:g

Expectation operation.

E

xii

N!

K!(N

K)!

INTRODUCTION

Motivation

Wireless communication has been considered to be the fastest developing eld of the communication industry. Through more than 30 years of

research and development, various generations of wireless communications have been born. The achievable data rate of wireless systems

has increased to several thousands of times higher (the fourth generation - 4G) than that of the second generation (2G) wireless systems.

Particularly, the 4G wireless communication systems, supported by key

technologies such as multiple-input multiple-output (MIMO), orthogonal

frequency division multiplexing (OFDM), cooperative communications,

have already achieved the data rate of hundreds Mbps [1].

The MIMO technique exploits the diversity of multiple transmit antennas and multiple receive antennas to enhance channel capacity without either increasing the transmit power or requiring more bandwidth.

Meanwhile, OFDM is known as an e cient multi-carrier transmission

technique which has high resistance to the multi-path fading. The OFDM

system o ers a variety of advantages such as inter-symbol in-terference

(ISI)

resistance,

easy

implementation

by

inverse

fast

Fourier

transform/fast Fourier transform (IFFT/FFT). It can also provide higher

spectral e ciency over the single carrier system since its orthogonal sub1

carriers overlap in the frequency domain.

Due to vast developments of smart terminals, new applications with

high-density usage, fast and continuous mobility such as cloud services,

machine-to-machine (M2M) communications, autonomous cars, smart

home, smart health care, Internet of Things (IoT), etc, the 5G sys-tem

has promoted challenging researches in the wireless communication

community [2]. It is expected that ubiquitous communications between

anybody, anything at anytime with high data rate and transmission reliability, low latency are soon available [3]. Although there are several 5G

trial systems installed worldwide, so far there have not been any o cial

standards released yet. The International Telecommunications Union

(ITU) has set 2020 as the deadline for the IMT-2020 standards. According

to a recent report of the ITU [3], 5G can provide data rate signi cantly

higher, about tens to hundreds of times faster than that of 4G. For latency

issue, the response time to a request of 5G can reduce to be about 1

millisecond compared to that around 120 milliseconds and between

roughly 15-60 milliseconds of 3G and 4G, respectively [3].

In order to achieve the above signi cant improvement, the 5G system

continues employing OFDM as one of the primary modulation technologies [2]. Meanwhile, based on OFDM, index modulation for OFDM (IMOFDM) has been proposed and emerged as a promising multi-carrier

transmission technique. IM-OFDM utilizes the indices of active subcarriers of OFDM systems to convey additional information bits. There

are several advantages over the conventional OFDM proved for IMOFDM such as the improved transmission reliability, energy e 2

ciency and the exible trade-o between the error performance and

the spectral e ciency [4], [5]. However, in order to be accepted for

possible inclusion in the 5G standards and have a full understanding

about the IM-OFDM capability, more studies should be carried out.

Inspired by the motivation of OFDM in the framework of 5G and the

application potentials of IM-OFDM to the future commercial standards,

the present thesis has adopted IM-OFDM as the research theme for its

study with the title \Repeated index modulation for OFDM systems".

Within the scope of the research topic, the thesis aims to conduct a

thorough study on the IM-OFDM system, and make its contributions to

enhance performances of this attractive system.

Research Objectives

Motivated by the application potentials of IM-OFDM and the fact that

its limitations, such as high computational complexity and limited

transmission reliability, which may prevent it from possible implementation, this research aims at proposing enhanced IM-OFDM systems to

tackle these problems. Moreover, a mathematical framework for the

performance analysis is also developed to evaluate the performance of

the proposed systems under various channel conditions. The speci c

objectives of the thesis research can be summarized as follows:

Upon studying the related IM-OFDM systems in the literature, e - cient

signal processing techniques such as repetition code and coordi-

nate interleaving are proposed to employ in the considered systems.

E cient signal detectors for the IM-OFDM system, which can bal3

ance the error performance with computational complexity, are

stud-ied and proposed for the considered systems.

Developing mathematical frameworks for performance analysis of

the proposed systems, which can give an insight into the system

behavior under the impacts of the system parameters.

Research areas

Wireless communication systems under the impact of di erent

fad-ing conditions.

Multi-carrier transmission using OFDM and index

modulation. Detection theory and complexity analysis.

Research method

In this thesis, both the theoretical analysis and the Monte-Carlo simulation are used to evaluate the performance of the considered systems.

The analytical methods are used for calculating the computational

complexity of the detection algorithms and to derive the closed-

form expressions for symbol error and bit error probabilities of

the proposed systems.

The Monte-Carlo simulation is applied to validate the analytical

results and to make comparison between the performance of the

proposed systems and that of the benchmarks.

Thesis contribution

The major contributions of the thesis can be summarized as follows:

4

Contributions to IM-OFDM with diversity reception

{ Based on the concept of IM-OFDM with diversity reception [6],

an enhanced IM-OFDM system with spatial diversity using the

maximal ratio combination and selection combination (abv. as

RIM-OFDM-MRC and RIM-OFDM-SC, respectively) is

proposed to improve the error performance over the

conventional IM-OFDM system with diversity reception.

{ The closed-form expressions for the index error probability

(IEP) and symbol error probability (SEP) of RIM-OFDM-MRC

and RIM-OFDM-SC under both perfect and imperfect

channel state information (CSI) conditions are derived to

analyze the error performance and the impacts of the system

parameters on the transmission reliability. Simulation results

are also provided to validate the theoretical analysis.

Contributions to IM-OFDM with coordinate interleaving

{ Based on the idea of IM-OFDM with coordinate interleaving

(IM-OFDM-CI) [7], an enhanced scheme of IM-OFDM,

referred to as repeated IM-OFDM-CI (RIM-OFDM-CI) is

proposed to improve the transmission reliability and exibility

of the conven-tional IM-OFDM-CI system. The closed-form

expressions for symbol and bit error probabilities of the

proposed system are also derived.

{ Three low-complexity detectors for RIM-OFDM-CI, which can signi

cantly reduce the computational complexity while still achiev5

ing near-optimal and optimal system error performance of

the ML detector, are proposed.

Thesis structure

The thesis is organized in three chapters as follows:

Chapter 1: Research background

This chapter introduces the research background of IM-OFDM

and related studies. Particularly, it presents a comprehensive

review on the recent studies of IM-OFDM and outlines several

challenging open problems which motivate the contributions of

the thesis in the sub-sequent chapters.

Chapter 2: Repeated IM-OFDM with diversity reception

This chapter proposes an enhanced IM-OFDM system with diver-sity

reception using maximal ratio combination (RIM-OFDM-MRC) and

selection combination (RIM-OFDM-SC). Performance analysis is

carried out to determine the diversity and coding gains of the proposed system under both perfect and imperfect CSI conditions. Performance comparisons between the proposed system and the related

benchmark ones are provided using numerical and simulation results.

Chapter 3: Repeated IM-OFDM with coordinate interleaving

In this chapter, a repeated IM-OFDM with coordinate interleav-ing

(RIM-OFDM-CI) is proposed. Three low-complexity detectors,

namely low-complexity ML (lowML), log-likelihood ratio (LLR), and

greedy detection (GD) are presented for the RIM-OFDM-CI system

6

to relax the detection complexity. An optimal rotation angle for

the M-QAM modulation constellation is determined to improve

the error performance of the system. Numerical and simulation

results are provided to evaluate the RIM-OFDM-CI system

performance of against benchmark systems.

7

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