Nghiên cứu kỹ thuật điều chế chỉ số lặp lại cho các hệ thống OFDM

• 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 themaximal rati

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 EngineeringSpecialization code: 9 52 02 03

SUPERVISORProf TRAN XUAN NAM

HA NOI - 2020

I hereby declare that this thesis was carried out by myself under theguidance of my supervisor The presented results and data in the the-sis are reliable and have not been published anywhere in the form ofbooks, monographs or articles The references in the thesis are cited inaccordance with the university’s regulations

Hanoi, May 17th, 2019

Author

Le Thi Thanh Huyen

It is a pleasure to take this opportunity to send my very great ciation 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 meaningfulcritiques during my researching process This thesis would not have beencompleted without him

appre-My special thanks are sent to my lecturers in Faculty of Radio - tronics, especially my lecturers and colleagues in Department of Com-munications who share a variety of difficulties for me to have more time

Elec-to concentrate on researching I also would like Elec-to sincerely thank myresearch 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 deepestlove is for my mother and two little sons who always are my endlessinspiration and motivation for me to overcome all obstacles

Author

Le Thi Thanh Huyen

TABLE OF CONTENTS

Contents

List of abbreviations iv

List of figures 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

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

3.6 Summary 75

CONCLUSIONS AND FUTURE WORK 76

PUBLICATIONS 79

BIBLIOGRAPHY 81

LIST OF ABBREVIATIONS

ESIM-OFDM Enhanced Sub-carrier Index Modulation for

Or-thogonal Frequency Division Multiplexing

IM-OFDM-CI Index Modulation for OFDM with Coordinate

Interleaving

OFDM Orthogonal Frequency Division Multiplexing

OFDM-I/Q-IM OFDM with In-phase and Quadrature Index

Modulation

PSK Phase Shift Keying

RIM-OFDM Repeated Index Modulation for OFDM

RIM-OFDM-MRC Repeated Index Modulation for OFDM with

Maximal Ratio CombiningRIM-OFDM-SC Repeated Index Modulation for OFDM with Se-

lection CombiningRIM-OFDM-CI Repeated Index Modulation for OFDM with Co-

ordinate Interleaving

LIST OF FIGURES

1.1 Block diagram of an IM-OFDM system 10

2.1 Structure of the RIM-OFDM-MRC/SC transceiver 252.2 The SEP comparison between RIM-OFDM-MRC and the

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

2, L = 2, M = {4, 8} 422.3 The SEP performance of RIM-OFDM-SC in comparison

with IM-OFDM-SC for N = 4, K = 2, L = 2, M = {4, 8} 432.4 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 = {2, 4, 8, 16} 442.5 The impact of L on the SEP performance of RIM-OFDM-

MRC and RIM-OFDM-SC for M = 4, N = 4, K = 2 and

L = {1, 2, 4, 6} 452.6 The SEP performance of RIM-OFDM-MRC under influ-

ence of K for M = {2, 4, 8, 16}, N = {5, 8}, K = {2, 3, 4, 5} 462.7 The SEP performance of RIM-OFDM-SC under influence

of K when M = {2, 4, 8, 16}, N = {5, 8}, K = {2, 3, 4, 5} 462.8 Influence of modulation size on the SEP of RIM-OFDM-

MRC/SC for N = 5, K = 4, and M = {2, 4, 8, 16, 32} 47

2.9 The SEP performance of RIM-OFDM-MRC in

compari-son with IM-OFDM-MRC under imperfect CSI when N =

4, K = 2, M = {4, 8}, and ǫ2 = {0.01, 0.05} 482.10 The SEP performance of RIM-OFDM-SC in comparison

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

K = 2, M = {4, 8}, and ǫ2 = 0.01 49

3.1 Block diagram of a typical RIM-OFDM-CI sub-block 523.2 Rotated signal constellation 603.3 Computational complexity comparison of LLR, GD, ML

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

{1, 2, , 7} and b) N = 8, K = 4, M = {2, 4, 8, 16, 32, 64} 683.4 Index error performance comparison of RIM-OFDM-CI,

IM-OFDM, IM-OFDM-CI and ReMO systems at the

spec-tral efficiency (SE) of 1 bit/s/Hz, M = {2, 4}, N = 4,

K = {2, 3} 703.5 SEP performance comparison between RIM-OFDM-CI,

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

spectral efficiency of 1 bit/s/Hz when M = {2, 4}, N = 4,

K = {2, 3} 713.6 BER comparison between the proposed scheme and the

benchmark ones when N = 4, K = {2, 3}, M = {2, 4} 723.7 BER comparison between the proposed and benchmark

schemes at SE of 1.25 bits/s/Hz when N = {4, 8}, K =

{2, 4}, M = {2, 4, 8} 73

3.8 SEP performance of RIM-OFDM-CI and benchmark

sys-tems using different detectors 74

LIST OF TABLES

1.1 An example of look-up table when N = 4, K = 2, p1 = 2 13

2.1 Complexity comparison between the proposed schemes

and the benchmark 50

3.1 Example of LUT for N = 4, K = 2, pI = 2 543.2 Complexity comparison between ML, LowML, LLR and

GD dectectors 68

N Number of sub-carriers in each sub-block

NF Number of sub-carriers in IM-OFDM system

P (.) The probability of an event

PI Index symbol error probability

PM M -ary modulated symbol error probability

Ps Symbol error probability

Q (.) The tail probability of the standard Gaussian

distribution

I Set of possible active sub-carrier indices

M (.) The moment generating function

Sφ Rotated complex signal constellation

φ Rotation angle of signal constellation

φopt Optimal rotation angle of signal constellationk.k2F Frobenius norm of a matrix

C (N, K) Binomial coefficient, C (N, K) = N!

K !(N −K)!

⌊x⌋ Rounding down to the closest integer

log2(.) The base 2 logarithm

E{.} Expectation operation

communi-The MIMO technique exploits the diversity of multiple transmit tennas and multiple receive antennas to enhance channel capacity with-out either increasing the transmit power or requiring more bandwidth.Meanwhile, OFDM is known as an efficient multi-carrier transmissiontechnique which has high resistance to the multi-path fading TheOFDM system offers a variety of advantages such as inter-symbol in-terference (ISI) resistance, easy implementation by inverse fast Fouriertransform/fast Fourier transform (IFFT/FFT) It can also provide higherspectral efficiency over the single carrier system since its orthogonal sub-

an-carriers overlap in the frequency domain.

Due to vast developments of smart terminals, new applications withhigh-density usage, fast and continuous mobility such as cloud services,machine-to-machine (M2M) communications, autonomous cars, smarthome, smart health care, Internet of Things (IoT), etc, the 5G sys-tem has promoted challenging researches in the wireless communicationcommunity [2] It is expected that ubiquitous communications betweenanybody, anything at anytime with high data rate and transmission re-liability, low latency are soon available [3] Although there are several5G trial systems installed worldwide, so far there have not been anyofficial standards released yet The International TelecommunicationsUnion (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 ratesignificantly higher, about tens to hundreds of times faster than that of4G For latency issue, the response time to a request of 5G can reduce

to be about 1 millisecond compared to that around 120 milliseconds andbetween roughly 15-60 milliseconds of 3G and 4G, respectively [3]

In order to achieve the above significant improvement, the 5G systemcontinues employing OFDM as one of the primary modulation technolo-gies [2] Meanwhile, based on OFDM, index modulation for OFDM(IM-OFDM) has been proposed and emerged as a promising multi-carrier transmission technique IM-OFDM utilizes the indices of activesub-carriers of OFDM systems to convey additional information bits.There are several advantages over the conventional OFDM proved forIM-OFDM such as the improved transmission reliability, energy effi-

ciency and the flexible trade-off between the error performance and thespectral efficiency [4], [5] However, in order to be accepted for possibleinclusion in the 5G standards and have a full understanding about theIM-OFDM capability, more studies should be carried out.

Inspired by the motivation of OFDM in the framework of 5G and theapplication potentials of IM-OFDM to the future commercial standards,the present thesis has adopted IM-OFDM as the research theme for itsstudy with the title “Repeated index modulation for OFDM systems”.Within the scope of the research topic, the thesis aims to conduct athorough study on the IM-OFDM system, and make its contributions toenhance performances of this attractive system

Research Objectives

Motivated by the application potentials of IM-OFDM and the factthat its limitations, such as high computational complexity and limitedtransmission reliability, which may prevent it from possible implemen-tation, this research aims at proposing enhanced IM-OFDM systems totackle these problems Moreover, a mathematical framework for theperformance analysis is also developed to evaluate the performance ofthe proposed systems under various channel conditions The specificobjectives of the thesis research can be summarized as follows:

• Upon studying the related IM-OFDM systems in the literature, cient signal processing techniques such as repetition code and coordi-nate interleaving are proposed to employ in the considered systems

effi-• Efficient signal detectors for the IM-OFDM system, which can

bal-ance the error performbal-ance with computational complexity, are ied and proposed for the considered systems.

stud-• Developing mathematical frameworks for performance analysis ofthe proposed systems, which can give an insight into the systembehavior under the impacts of the system parameters

Research areas

• Wireless communication systems under the impact of different ing conditions

fad-• Multi-carrier transmission using OFDM and index modulation

• Detection theory and complexity analysis

• The Monte-Carlo simulation is applied to validate the analyticalresults and to make comparison between the performance of theproposed systems and that of the benchmarks

Thesis contribution

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

• 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 themaximal ratio combination and selection combination (abv asRIM-OFDM-MRC and RIM-OFDM-SC, respectively) is proposed

to improve the error performance over the conventional IM-OFDMsystem with diversity reception

– The closed-form expressions for the index error probability (IEP)and symbol error probability (SEP) of RIM-OFDM-MRC andRIM-OFDM-SC under both perfect and imperfect channel stateinformation (CSI) conditions are derived to analyze the errorperformance and the impacts of the system parameters on thetransmission reliability Simulation results are also provided tovalidate 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 toimprove the transmission reliability and flexibility of the conven-tional IM-OFDM-CI system The closed-form expressions forsymbol and bit error probabilities of the proposed system arealso derived

– Three low-complexity detectors for RIM-OFDM-CI, which cansignificantly reduce the computational complexity while still achiev-

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 andrelated studies Particularly, it presents a comprehensive review onthe recent studies of IM-OFDM and outlines several challenging openproblems 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 sity reception using maximal ratio combination (RIM-OFDM-MRC)and selection combination (RIM-OFDM-SC) Performance analysis

diver-is carried out to determine the diversity and coding gains of the posed system under both perfect and imperfect CSI conditions Per-formance comparisons between the proposed system and the relatedbenchmark ones are provided using numerical and simulation results

pro-• Chapter 3: Repeated IM-OFDM with coordinate interleaving

In this chapter, a repeated IM-OFDM with coordinate ing (RIM-OFDM-CI) is proposed Three low-complexity detectors,namely low-complexity ML (lowML), log-likelihood ratio (LLR), andgreedy detection (GD) are presented for the RIM-OFDM-CI system

interleav-to relax the detection complexity An optimal rotation angle forthe M -QAM modulation constellation is determined to improve theerror performance of the system Numerical and simulation resultsare provided to evaluate the RIM-OFDM-CI system performance ofagainst benchmark systems.

Chapter 1RESEARCH BACKGROUND

This chapter provides research background for the present thesis Thefirst section introduces the basic principle of IM-OFDM and outlinesthe advantages and disadvantages of IM-OFDM over the conventionalOFDM The next section offers a literature review of the related studies

on IM-OFDM and identifies the research scope for the present thesis.1.1 Basic principle of IM-OFDM

Index modulation for OFDM is an OFDM-based transmission nique which utilizes the sub-carrier index to convey more data bits inaddition to the M -ary modulation The idea of IM-OFDM is similar

tech-to that of spatial modulation (SM) in which additional data bits can

be transmitted by means of indexing separate channels in either tial or frequency domain using a portion of bits The concept of IM-OFDM was first introduced in [8] and then developed in [9] In liter-ature, it was referred to as different names such as sub-carrier indexmodulation OFDM (SIM-OFDM) [8], OFDM with index modulation(OFDM-IM) [9], multi-carrier index keying OFDM (MCIK-OFDM) [10],OFDM with sub-carrier index modulation (OFDM-SIM) [11], select-ing sub-carrier modulation (SSCM) [12], etc Despite the variations innames, their basic principles are the same Throughout this thesis, for

spa-the sake of consistence and except ospa-therwise stated explicitly, spa-the term

“index modulation for OFDM (IM-OFDM)” will be used instead

Similar to SM [13], the incoming data bits in IM-OFDM are dividedinto two parts The first part is used to select the indices of activesub-carriers, while the second part is fed to an M -ary mapper as in theconventional OFDM system However, it differs from the conventionalOFDM that IM-OFDM only activates a subset of sub-carriers, leavingthe remaining sub-carriers to be zero padded Since the informationbits are transferred not only by the M -ary modulated symbols but also

by the indices of the active sub-carriers, IM-OFDM can attain bettertransmission reliability and higher energy efficiency than that of theconventional OFDM system [9]

1.1.1 IM-OFDM model

The block diagram of a typical IM-OFDM system is illustrated inFig 1.1 The system consists of NF sub-carriers which are separated into

G sub-blocks, each with N sub-carriers At the transmitter, a sequence

of incoming m bits is first separated into G groups of p bits For theg-th sub-block, the incoming p bits are then split into two bit sequences.The first p1 = ⌊log2(C (N, K))⌋ bits are fed to a corresponding indexmapper to select K out of N sub-carriers, where N ={2, 4, 8, 16, 32, 64},

1 ≤ K ≤ N and C (N, K) = N !

K !(N −K)! is the binomial coefficient Notethat when all the available sub-carriers are activated, i.e K = N , IM-OFDM becomes the conventional OFDM system The set of active sub-carrier indices in the g-th sub-block is denoted by θg = {α1, , αK},

Index mapper

OFDM block

Insert CP&

P/S

M-ary

mapper

Index mapper

X

OFDM Sub-block

IM-1

OFDM Sub-block

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

where αk ∈ {1, , N}, g = 1, , G and k = 1, , K Thus, the number

of transmitted bits via the indices of active sub-carriers are m1 = p1G =

The second bit sequence of length p2 = Klog2M is the input of an

M -ary mapper to determine the complex modulated symbols that aretransmitted over the active sub-carriers The modulated symbols at theoutput of the M -ary mapper are given by sg = [sg(α1) , , sg(αK)],

where sg(αk) ∈ S, g = 1, , G, k = 1, , K and S denotes the signalconstellation Based on the defined K symbols sg and index set θ, the IM-OFDM sub-block maps each modulated symbol sg(αk), for k = 1, , K,

to the transmitted signal over the corresponding activated sub-carrier

xg,k The output of each IM-OFDM sub-block is the vector xg ∈ CN×1,whose elements corresponding to αk equal to sg(αk), otherwise 0, for

g = 1, , G These G vectors xg are combined into vector x by the OFDM block x contains NF elements x (1) , x (2) , , x (NF), where

Vector n = [n (1) , n (2) , , n (N )]T presents the additive white sian noise, whose each element n (α) follows the complex Gaussian dis-tribution with zero mean and variance N0, i.e n (α) ∼ CN (0, N0) Foreach sub-carrier α, the transmit power of the data symbol is given by

Gaus-ϕEs, where ϕ = N/K is the power allocation coefficient and Es denotesthe average transmit Consequently, the signal to noise ratio (SNR) ofthe received signal at each active sub-carrier is given by ¯γ = ϕEs/N0.Using the above assumptions, and without taking into account the CP,the spectral efficiency of the IM-OFDM system, measured in bit/s/Hz,

is given as follows [9], [14]

η = ⌊log2(C(N, K))⌋ + Klog2M

It can be seen from (1.2) that the IM-OFDM scheme with K out of

N active sub-carriers has the lower spectral efficiency than that of theconventional OFDM system However, since the number of active sub-carriers of the IM-OFDM system can be adjusted accordingly to reachthe desired error performance and/or spectral efficiency, it can attainthe flexible trade-off between the reliability and the spectral efficiency.1.1.2 Sub-carrier mapping

In the IM-OFDM system, the index mapper maps the incoming p1 bitsinto the combinations of active sub-carriers in each sub-block There aretwo methods to perform such mapping of sub-carriers namely look-uptable (LUT) and combination number system [9], as presented below

a) Look-up table method

In look-up table method, the index mapping is carried out by using theLUT with size of c = 2⌊log 2 (C(N,K))⌋ For each sub-block, the active indices

of the corresponding p1 bits are provided in the LUT at the transmitter.This table is also applied to the receiver for demapping An example of

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

Data bits Indices Transmitted signal

b) Combinational number system

The combinational number system allows for a one to one mappingbetween an integer number and the K-combinations for all N and K[15], [16] In particular, it maps an integer number to a sequence ofdecreasing order P = {cK, , c1}, where cK > > c1 For the given

N and K, all Z ∈ [0, C (N, K) − 1] can be represented by a sequence P

of size K, whose elements are selected from the set {0, , N − 1} which

is given as follows [9]:

Z = C(cK, K) + + C(c2, 2) + C(c1, 1) (1.3)

For the given N and K, the algorithm to find the P sequences of cographical order can be summarized as follows: beginning with selectingthe maximal cK so that C (cK, K) < Z, then selecting the maximal cK −1that satisfies C (cK −1, K − 1) < Z − C (cK, K) and so on [15]

lexi-As an example for N = 8, K = 4, C (8, 4) = 70, Z ∈ [0, , 69], Pcan be determined as follows [9]:

of the indices, it is easy to determine the integer number ˆZ utilizing(1.3) This number is then put to a p1-bit decimal-to-binary converter.For large N and K, the combinational number system is more suitablethan the LUT for reducing the system complexity

1.1.3 IM-OFDM signal detection

In order to recover the transmitted bits, the receiver needs to detectboth the active sub-carrier indices and the corresponding data symbols

In IM-OFDM systems, although ML detector is able to achieve optimalperformance, it necessitates an exhaustive search to jointly detect theactive indices and data symbols, which makes itself difficult to implementfor the practical high rate systems In order to reduce the detectioncomplexity, a low complexity LLR detector is then introduced The MLand LLR detectors are presented in detail as follows

a) ML detector

The ML detector is optimal for minimizing detection errors For OFDM, ML detection is applied to each OFDM sub-block for joint de-tection of the active sub-carrier indices and transmitted symbols

O (cMK) which exponentially increases with M Thus, low-complexitydetectors are necessary for practical implementation

b) LLR detector

In order to reduce the complexity of the ML detector, an LLR detectorfor IM-OFDM was proposed in [9] The LLR detector estimates theindices of the active sub-carriers first, followed by the correspondingdata symbols It calculates a probabilistic measure on the active status

of a given carrier by considering the fact that the corresponding carrier can be either active or inactive Particularly, the LLR detectorcomputes N LLR values for each sub-block, then selects the K largestones to decide the active sub-carriers The LLR value for each sub-carrier

OFDM detection.

1.1.4 Advantages and disadvantages of IM-OFDM

In comparison with the conventional OFDM system, IM-OFDM has

a number of advantages as follows [5]

• IM-OFDM can provide a flexible trade-off between the error mance and spectral efficiency thanks to the adjustable number ofactive sub-carriers

perfor-• IM-OFDM can achieve improved BER performance over the tional OFDM system at the same spectral efficiency and the cost of

conven-an acceptable detection complexity This achievable BER ment can be realized by the fact that the information bits carried onthe M -ary modulated symbols require lower modulation order thanthat in the conventional OFDM system

improve-• Since sub-carrier index modulation is conducted for a sub-block gusing smaller number of sub-carriers, IM-OFDM is less influenced

by the peak-to-average power ratio (PAPR) problem than that ofOFDM It is also more robust to inter-carrier interference (ICI)thanks to the activation of only a subset of sub-carriers [5]

In spite of the above attractive benefits, the IM-OFDM system stillsuffers from some drawbacks as summarized below [4]:

• The error performance of uncoded/coded IM-OFDM system is erally worse than that of the conventional OFDM system at lowSNR regime This is due to the fact that the index detection is more

gen-vulnerable to error under the impact of large noise.

• The detection complexity of the ML detectors for IM-OFDM ishigher than that of the conventional OFDM system due to jointestimation of both active indices and the M -ary modulated sym-bols This limitation can be facilitated by using the LLR and GDdetectors at a slight loss of the transmission reliability

1.2 Related works

Thanks to its advantages as mentioned above, IM-OFDM has beenconsidered a potential candidate to replace the conventional OFDM inthe next generation wireless communication systems [1] Since the firstintroduction in [8], IM-OFDM has attracted great attention from re-searchers worldwide and various enhanced IM-OFDM systems were pro-posed These contributions to IM-OFDM can be summarized in thefollowing directions [4]

• Introducing generalized and enhanced IM-OFDM systems to achieveimproved error performance over the conventional IM-OFDM system[18–20], [7], [14], [21]

• Proposing low-complexity detectors for IM-OFDM [9], [22–24], [25]

• Analyzing performance of the IM-OFDM systems under various nel conditions [10], [26–29], [9], [30], [31]

chan-• Considering the applications of IM-OFDM to vehicle-to-vehicle (V2V),vehicle-to-infrastructure, vehicle-to-everything (V2X), device-to-device(D2D) systems [32], [33], [22], [34]

• Integrating IM-OFDM to various communication systems such asoptical OFDM, non-orthogonal multiple access (NOMA), direct se-quence spread spectrum, filter-bank multi-carrier (FBMC) [35–37].

The first IM-OFDM system, dated back to 2009 [8], used a fix number

of active sub-carriers and assumed perfect detection of the index bits atthe receiver However, a mis-detection of a sub-carrier state will lead tothe incorrect demodulation of all M -ary modulated symbols Thus, theerror performance of this IM-OFDM scheme is limited

In order to improve the error performance, the sub-carriers of OFDM are interleaved in [20] to increase the Euclidean distance betweenthe complex data symbols The study [26] proposed the interleavedsub-carrier grouping method and investigated the achievable rate of theIM-OFDM system The problem of unbalanced sub-carrier activation

IM-to improve the BER performance of the conventional IM-OFDM systemwas reported in [19] The enhanced IM-OFDM proposed in [18] activatedonly one sub-carrier at a time to avoid error propagation at the cost ofspectral efficiency loss In order to obtain a flexible trade-off between thetransmission reliability and spectral efficiency, the works in [9], [38], [39]proposed the IM-OFDM schemes with an adjustable number of activesub-carriers according to the incoming bits

Aiming at achieving diversity gain, the coordinate interleaved OFDM scheme in [7] distributed the real and imaginary components

IM-of the M -ary modulated data symbols over distinctive sub-carriers Thepaper [21] presented an IM-OFDM scheme with transmit diversity, which

utilized multiple signal constellations to carry the same data bits overthe active sub-carriers In a recent work [17], the coded IM-OFDMwith transmit diversity (TD-IM-OFDM) was proposed to increase thereliability of sub-carrier index detection The authors in [24] intro-duced a spread IM-OFDM scheme to improve the transmit diversity.

To achieve further diversity gain and BER performance improvement,the IM-OFDM concept was extended to MIMO systems in [40–46].Concerning the detection complexity, the LLR detector was proposedfor the IM-OFDM system in [9] In the later proposals [22], [23], near-

ML detectors with the same computational complexity as the LLR wereintroduced A spread IM-OFDM scheme with low-complexity detectorswere introduced in [24] A low-complexity greedy detection (GD) algo-rithm, which provides nearly same error performance of the ML detector,was proposed for IM-OFDM in [47] More recently, the authors in [25]introduced the first proposal of applying deep learning to detect databits of the IM-OFDM systems The proposed detector can provide anear optimal performance while considerably reducing the runtime overthe existing detectors

In order to reduce complexity while still attaining diversity gain ofIM-OFDM, the study in [6] introduced an IM-OFDM system with GDand diversity reception Its BER performance under imperfect CSI wasanalyzed in [48] A repeated IM-OFDM system (ReMO) was presented

in [49] to achieve the transmit diversity

Aiming at improving the spectral efficiency, the work in [12] posed an effective scheme for selecting an optimal number of active

pro-sub-carriers as well as the optimal sub-carrier grouping Another timal sub-carrier activation method was presented in [50] A constel-lation mapping method was proposed for the generalized IM-OFDMscheme in [51] to further improve the spectral efficiency of IM-OFDM

op-at the cost of the BER performance The work in [23] proposed anIM-OFDM-I/Q scheme which performs index modulation over both thein-phase and quadrature components of the M -ary modulated symbols

In another solution, the dual-mode OFDM (DM-OFDM) was presented

in [52] DM-OFDM utilized inactive sub-carriers to carry further databits in addition to the active sub-carriers Different signal constellationswere employed to convey complex data symbols over both active andinactive sub-carriers Extending this idea, the work in [53] introduced

a multi-mode IM-OFDM (MM-IM-OFDM) scheme which activates allsub-carriers More information bits can be conveyed by permuted trans-mission modes, which allows this scheme to enjoy further increased spec-tral efficiency

In order to achieve both spectral efficiency and diversity gain, theauthors in [14] introduced a linear constellation precoder (LPC) for IM-OFDM In another effort, the study in [11] applied the compressed sens-ing technique to IM-OFDM to attain performance enhancement withrespect to both diversity gain and energy efficiency

Recently, various researchers have also concentrated on analyzing formance of the IM-OFDM system The work in [10] successfully derived

per-a tight bound for BER of IM-OFDM The lineper-ar processing-bper-ased ICIcancellation and capacity maximization were applied to IM-OFDM over

rapidly time-varying channels in [54] Besides, the error performance

of IM-OFDM in the presence of carrier frequency offset (CFO) was ported in [31], [32], [28] In addition, ergodic capacity of IM-OFDM wasevaluated in [26] The work [27] investigated the outage probability ofthe IM-OFDM scheme operating over the two-way diffused-power fad-ing channels The transmission reliability in terms of SEP of IM-OFDMand IM-OFDM employing greedy detection under imperfect CSI wasinvestigated in [29] and [55], respectively

re-In another aspect, the work [56] investigated PAPR and BER of OFDM with ICI It was shown that IM-OFDM can significantly decreasePAPR and is more robust to ICI compared to the conventional OFDM.The ratio of the number of active sub-carriers to the total number ofsub-carriers in IM-OFDM has strongly influenced on PAPR The recentworks in [18], [57], [58] were introduced to reduce the number of activesub-carriers in the IM-OFDM system to decrease PAPR

IM-Motivated by the benefits of IM-OFDM, it was applied to ous communication systems [22], [32–34] Particularly, IM-OFDM-aidedvehicular communication systems were proposed in [33] The worksreported promising results in terms of BER and derived its maximalachievable rate The authors in [34] exploited the potential of IM-OFDMfor low-rate, low-cost and low-power IoT devices Besides, the works

numer-in [22], [32] numer-introduced IM-OFDM to underwater acoustic tions They also developed an ICI self-cancellation scheme for this par-ticular implementation case The possible combination of NOMA andIM-OFDM was investigated in [37] Based on the code index modula-

communica-tion [59], the IM-OFDM spread spectrum (IM-OFDM-SS) system in [60]uses indices of spreading codes to convey data bits Inspired by theOFDM-SS system with the rotated Walsh-Hadamard transform [61] andthe pre-coding matrix for MIMO-OFDM [62], a spread IM-OFDM (S-IM-OFDM) system was proposed in [24] A precoder for S-IM-OFDMwas also introduced in [63].

Within the scope of this thesis, the author has concentrated on thesolutions to improve the performance of the conventional IM-OFDMsystem in terms of reliability and detection complexity Particularly, thetwo related systems of interest are described as follows:

• The IM-OFDM system with spatial diversity in [6]: In this system,multiple antennas are employed at the receiver to attain receptiondiversity via either MRC or SC The ML and GD detectors werealso proposed to jointly detect the indices and the M -ary mod-ulated symbols The IM-OFDM system with diversity receptionachieves significantly better symbol error performance than that ofthe conventional IM-OFDM thanks to spatial diversity gain Perfor-mance analysis was conducted for the Rayleigh fading channel withassumption of perfect CSI estimation However, the problem of si-multaneous exploitation of the frequency and spatial diversities wasnot considered Besides, the system behaviors under the impact ofimperfect CSI and using SC were also neglected These limitations

of IM-OFDM with diversity reception will be covered in chapter 2

• The IM-OFDM system with coordinate interleaving (IM-OFDM-CI)

in [7]: This system achieved considerable improvement in sion reliability IM-OFDM-CI exploited the diversity potential ofthe conventional IM-OFDM by distributing the real and imaginarycomponents of the M -ary modulated data symbols over distinctivesub-carriers to obtain additional diversity gain IM-OFDM-CI canachieve the second-order diversity which is double that of the con-ventional IM-OFDM However, the IM-OFDM-CI system still suffersfrom a number of limitations such as high index detection error, ap-plicable to only IM-OFDM systems with an even number of activesub-carriers Besides, the rotation angle of the signal constellationwas determined by the computer search, which is not efficient forhigh rate transmission systems These limitations of the IM-OFDM-

transmis-CI system will be addressed in chapter 3

1.3 Summary

This chapter has introduced the research background of the presentthesis and summarized its related works As has been shown, IM-OFDMhas several advantages over the conventional OFDM such as improvedperformance, robust to ICI, and flexible trade-off between the error per-formance and the spectral efficiency For this reason, IM-OFDM hasattracted great attention of the wireless communication research com-munity A variety of studies have recommended it for the next generation

of wireless communication However, IM-OFDM still suffers from somedrawbacks such as the limitation of error performance and high detectioncomplexity These problems will be addressed in the next chapters

Chapter 2REPEATED INDEX MODULATION FOR OFDM WITH

DIVERSITY RECEPTION

This chapter introduces an enhanced IM-OFDM system, namely peated IM-OFDM with spatial diversity using either MRC or SC Theproposed systems, abbreviated as RIM-OFDM-MRC and RIM-OFDM-

re-SC, simultaneously exploit the frequency and spatial diversity to achievethe improved error performance over the conventional IM-OFDM sys-tem with diversity reception The closed-form expressions for the indexand symbol error probabilities of RIM-OFDM-MRC and RIM-OFDM-

SC under various channel conditions are also derived as a frameworkfor investigation of the system performance Based on the performanceanalysis, the system behavior under the impact of the system parametersand the imperfect CSI is also evaluated The results in this chapter werepublished in [C1], [J1], [J2]

2.1 RIM-OFDM with diversity reception model

Consider an up-link SIMO-IM-OFDM system as illustrated in Fig 2.1.The transmitter is equipped with a single antenna while the receiver has

L antennas for diversity reception The system uses a total of NF carriers which are divided into G sub-blocks of N sub-carriers, i.e N =

sub-NF/G Similar to the conventional IM-OFDM system, each sub-block