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

IM-OFDM utilizes the indices of active sub-carriers of OFDM systems to convey additional information bits.. However, in order to be accepted forpossible inclusion in the 5G standards and

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 underthe guidance of my supervisor The presented results and data inthe the-sis are reliable and have not been published anywhere in theform of books, monographs or articles The references in the thesisare cited in accordance with the university’s regulations

Hanoi, May 17th, 2019

Author

Le Thi Thanh Huyen

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 di culties for me to have more time toconcentrate on researching I also would like to sincerely thank myresearch group for sharing their knowledge and valuable assistance.

Elec-Finally, my gratitude is for my family members who support mystud-ies with strong encouragement and sympathy Especially, mydeepest love is for my mother and two little sons who always are myendless 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

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

352.3.2 Performance analysis for RIM-OFDM-SC

40

2.4 Performance evaluation and discussion 412.4.1 Performance evaluation under perfect CSI 412.4.2 SEP performance evaluation under imperfect CSI condition 48

2.4.3 Comparison of the computational complexity

49

2.5 Summary

50Chapter 3 REPEATED INDEX MODULATION FOR OFDM

WITH COORDINATE INTERLEAVING 51

3.1 RIM-OFDM-CI system model

51 3.2 Performance analysis 563.2.1 Symbol error probability derivation 56 3.2.2 Asymptotic analysis

59

3.2.3 Optimization of rotation angle

603.3 Low-complexity detectors for RIM-OFDM-CI 62

3.3.1 Low-complexity ML detector 62 3.3.2 LLR detector

3.6 Summary

75 CONCLUSIONS AND FUTURE WORK 76

PUBLICATIONS 79

BIBLIOGRAPHY 81

LIST OF ABBREVIATIONS

Abbreviation De nition

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

MRC/SC for N = 5, K = 4, and M = f2; 4; 8; 16; 32g 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 = 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 = 0:01 493.1 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 =

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

spec-tral 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 72

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

3.8 SEP performance of RIM-OFDM-CI and benchmark

sys-tems using di erent detectors 74

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

Average SNR at each sub-carrierSet of possible active sub-carrier indicesThe moment generating function.

Complex signal constellationRotated complex signal constellationIndex of an active sub-carrier

Channel estimation error varianceBig-Theta notation

Rotation angle of signal constellationOptimal rotation angle of signal constellationFrobenius norm of a matrix

Diagonal matrixBinomial coe cient, C (N; K) = N!

K!(N K)!

Rounding down to the closest integerThe base 2 logarithm

Expectation operation

Motivation

Wireless communication has been considered to be the fastest oping eld of the communication industry Through more than 30 years ofresearch and development, various generations of wireless communi-cations have been born The achievable data rate of wireless systemshas increased to several thousands of times higher (the fourth genera-tion - 4G) than that of the second generation (2G) wireless systems.Particularly, the 4G wireless communication systems, supported by keytechnologies such as multiple-input multiple-output (MIMO), orthogonalfrequency division multiplexing (OFDM), cooperative communications,have already achieved the data rate of hundreds Mbps [1]

devel-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 e cient multi-carrier transmissiontechnique which has high resistance to the multi-path fading The OFDMsystem o ers 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 e ciency 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-temhas 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 several 5Gtrial systems installed worldwide, so far there have not been any o cialstandards 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 cantlyhigher, about tens to hundreds of times faster than that of 4G For latencyissue, the response time to a request of 5G can reduce to be about 1millisecond compared to that around 120 milliseconds and betweenroughly 15-60 milliseconds of 3G and 4G, respectively [3]

In order to achieve the above signi cant 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-carriertransmission technique IM-OFDM utilizes the indices of active sub-carriers of OFDM systems to convey additional information bits Thereare several advantages over the conventional OFDM proved for IM-OFDM such as the improved transmission reliability, energy e -

ciency and the exible trade-o between the error performance andthe spectral e ciency [4], [5] However, in order to be accepted forpossible inclusion in the 5G standards and have a full understandingabout the IM-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 fact thatits 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 speci cobjectives 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

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

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 di erent fad-ing conditions

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 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-MRCand 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 systemparameters 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 signicantly 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-OFDMand related studies Particularly, it presents a comprehensivereview on the recent studies of IM-OFDM and outlines severalchallenging open problems which motivate the contributions ofthe thesis in the sub-sequent chapters

Chapter 2: Repeated IM-OFDM with diversity reception

This chapter proposes an enhanced IM-OFDM system with diver-sityreception using maximal ratio combination (RIM-OFDM-MRC) andselection combination (RIM-OFDM-SC) Performance analysis iscarried out to determine the diversity and coding gains of the pro-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

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

to relax the detection complexity An optimal rotation angle forthe M-QAM modulation constellation is determined to improvethe error performance of the system Numerical and simulationresults are provided to evaluate the RIM-OFDM-CI systemperformance of against benchmark systems.

Chapter 1RESEARCH BACKGROUND

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

on IM-OFDM and identi es 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 tothat of spatial modulation (SM) in which additional data bits can betransmitted by means of indexing separate channels in either spa-tial

tech-or frequency domain using a ptech-ortion of bits The concept of IM-OFDMwas rst introduced in [8] and then developed in [9] In liter-ature, it wasreferred to as di erent names such as sub-carrier index modulationOFDM (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-carriermodulation (SSCM) [12], etc Despite the variations in names, theirbasic principles are the same Throughout this thesis, for

the sake of consistence and except otherwise stated explicitly, theterm \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 rst part is used to select the indices of active sub-carriers, while the second part is fed to an M-ary mapper as in theconventional OFDM system However, it di ers 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 butalso by the indices of the active sub-carriers, IM-OFDM can attainbetter transmission reliability and higher energy e ciency than that ofthe conventional OFDM system [9].

1.1.1 IM-OFDM model

The block diagram of a typical IM-OFDM system is illustrated in Fig.1.1 The system consists of NF sub-carriers which are separated into Gsub-blocks, each with N sub-carriers At the transmitter, a sequence ofincoming m bits is rst separated into G groups of p bits For the g-th sub-block, the incoming p bits are then split into two bit sequences The rst p1

= blog2 (C (N; K))c bits are fed to a corresponding index mapper to select

K out of N sub-carriers, where N = f2; 4; 8; 16; 32; 64g,

K!(N K)!

that when all the available sub-carriers are activated, i.e K = N, OFDM becomes the conventional OFDM system The set of activesub-carrier indices in the g-th sub-block is denoted by g = f 1; : : : ; K g,

IM-p1 bits Index 1

IM-p bits mapper OFDM x1

p bits s Sub-block

M-ary

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

where k 2 f1; :::; Ng, g = 1; : : : ; G and k = 1; : : : ; K Thus, thenumber of transmitted bits via the indices of active sub-carriers are

m1 = p1G = blog2(C(N; K))c G bits

It is noted that g can have a total of c = 2p1 di erent combinationswhich make the selection of active sub-carriers complicated for large

NF To relax this problem, each IM-OFDM block is then divided into

G sub-blocks for ease of implementation

The second bit sequence of length p2 = Klog2M is the input of an 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 ( 1) ; : : : ; sg ( K )],

M-where sg ( k) 2 S, g = 1; : : : ; G, k = 1; : : : ; K and S denotes thesignal constellation Based on the de ned K symbols sg and indexset , the IM-OFDM sub-block maps each modulated symbol sg ( k),for k = 1; : : : ; K, to the transmitted signal over the correspondingactivated sub-carrier xg;k The output of each IM-OFDM sub-block isthe vector xg 2 CN 1, whose elements corresponding to k equal to sg (

k), otherwise 0, for g = 1; : : : ; G These G vectors xg are combinedinto vector x by the IM-OFDM block x contains NF elements x (1) ; x(2) ; : : : ; x (NF ), where x ( ) 2 f0; Sg, = 1; : : : ; N

The same procedure as in the conventional OFDM system is then plied to convert the transmit symbols into the time domain and append acyclic pre x (CP) to deal with the impacts of the inter-symbol interfer-ence(ISI) due to frequency selectivity of the multi-path fading channel

ap-At the receiver, after extracted from CP and converted into the quency domain, the received signal of the IM-OFDM system is given as

where H = diagfh (1) ; h (2) ; : : : ; h (N)g denotes the diagonalchannel matrix; h ( ), for = 1; : : : ; N, is the channel coe cient of eachsub-channel, which is modeled by a complex Gaussian randomvariable with zero mean and unit variance, i.e h ( ) CN (0; 1)

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

Gaus-’Es, where ’ = N=K is the power allocation coe cient and Es denotes theaverage transmit Consequently, the signal to noise ratio (SNR) of thereceived signal at each active sub-carrier is given by = ’Es=N0.

Using the above assumptions, and without taking into account the

CP, the spectral e ciency of the IM-OFDM system, measured inbit/s/Hz, is given as follows [9], [14]

= blog2(C(N; K))c + Klog

2M

N

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

N active sub-carriers has the lower spectral e ciency 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 e ciency, it can attain theexible trade-o between the reliability and the spectral e ciency

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 = 2blog2 (C(N;K))c For each sub-block, the active indices ofthe corresponding p1 bits are provided in the LUT at the transmitter Thistable 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, p 1 = 2

Data bits Indices Transmitted signal

00 [1; 2] [s ; s ; 0; 0]T

01 [2; 3] [0; s ; s ; 0]T

10 [2; 4] [0; s ; 0; s ]T

11 [1; 3] [s ; 0; s ; 0]T

the LUT for N = 4; K = 2; p1 = 2 is presented in Table 1.1 This is an

e cient method as it is easy to search for an entry in the table.However, for high rate OFDM systems, c becomes very large, a verybig-size LUT makes this method di cult for implementation

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 = fcK ; : : : ; c1g, where cK > : : : > c1 For the given

N and K, all Z 2 [0; C (N; K) 1] can be represented by a sequence P

of size K, whose elements are selected from the set f0; : : : ; N 1g 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 nd the P sequences oflexi-cographical order can be summarized as follows: beginning withselecting the maximal cK so that C (cK ; K) < Z, then selecting themaximal cK 1 that satis es C (cK 1; K 1) < Z C (cK ; K) and so on [15]

As an example for N = 8, K = 4, C (8; 4) = 70, Z 2 [0; : : : ; 69], P can be determined as follows [9]:

^

of the indices, it is easy to determine the integer number Z 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 moresuitable than 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 di cult to implementfor the practical high rate systems In order to reduce the detectioncomplexity, a low complexity LLR detector is then introduced The ML andLLR 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

b) LLR detector

In order to reduce the complexity of the ML detector, an LLRdetector for IM-OFDM was proposed in [9] The LLR detectorestimates the indices of the active sub-carriers rst, followed by thecorresponding data symbols It calculates a probabilistic measure onthe active status of a given sub-carrier by considering the fact thatthe corresponding sub-carrier can be either active or inactive.Particularly, the LLR detector computes N LLR values for each sub-block, then selects the K largest ones to decide the active sub-carriers The LLR value for each sub-carrier is given by [17]

( ) = j y ( ) j 2 min y ( ) h ( )sj 2 ; (1.6)

s 2S jUpon the estimation of the active sub-carrier indices, the correspondingdata symbols can be detected straightforwardly as in the OFDM system

The computational complexity of the LLR detector linearly increaseswith M, i.e O (M), which is equivalent to that of the conventional

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 exible trade-o between the error mance and spectral e ciency 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 e ciency and the cost of

conven-an acceptable detection complexity This achievable BERimprove-ment can be realized by the fact that the informationbits carried on the M-ary modulated symbols require lowermodulation order than that in the conventional OFDM system.Since sub-carrier index modulation is conducted for a sub-block gusing smaller number of sub-carriers, IM-OFDM is less in uenced

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 bene ts, the IM-OFDM system still su ers 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 low

gen-SNR regime This is due to the fact that the index detection is more

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 hasbeen considered a potential candidate to replace the conventionalOFDM in the next generation wireless communication systems [1].Since the rst introduction in [8], IM-OFDM has attracted greatattention from re-searchers worldwide and various enhanced IM-OFDM systems were pro-posed These contributions to IM-OFDMcan be summarized in the following 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 chan-nel conditions [10], [26{29], [9], [30], [31]

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, lter-bank multi-carrier (FBMC) [35{37].The rst IM-OFDM system, dated back to 2009 [8], used a x number

of active sub-carriers and assumed perfect detection of the index bits

at the receiver However, a mis-detection of a sub-carrier state will lead

to the incorrect demodulation of all M-ary modulated symbols Thus,the error 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 interleaved sub-carrier grouping method and investigated the achievable rate of the IM-OFDM system The problem of unbalanced sub-carrier activation toimprove the BER performance of the conventional IM-OFDM system wasreported in [19] The enhanced IM-OFDM proposed in [18] activated onlyone sub-carrier at a time to avoid error propagation at the cost of spectral

IM-e ciIM-ency loss In ordIM-er to obtain a IM-exiblIM-e tradIM-e-o bIM-etwIM-eIM-en thIM-etransmission reliability and spectral e ciency, 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 ofthe M-ary modulated data symbols over distinctive sub-carriers Thepaper [21] presented an IM-OFDM scheme with transmit diversity, which

IM-utilized multiple signal constellations to carry the same data bits overthe active sub-carriers In a recent work [17], the coded IM-OFDM withtransmit 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 Toachieve further diversity gain and BER performance improvement, theIM-OFDM concept was extended to MIMO systems in [40{46]

Concerning the detection complexity, the LLR detector wasproposed for the IM-OFDM system in [9] In the later proposals [22],[23], near-ML detectors with the same computational complexity asthe LLR were introduced A spread IM-OFDM scheme with low-complexity detectors were introduced in [24] A low-complexitygreedy detection (GD) algo-rithm, which provides nearly same errorperformance of the ML detector, was proposed for IM-OFDM in [47].More recently, the authors in [25] introduced the rst proposal ofapplying deep learning to detect data bits of the IM-OFDM systems.The proposed detector can provide a near optimal performancewhile considerably reducing the runtime over the 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 CSIwas analyzed in [48] A repeated IM-OFDM system (ReMO) waspresented in [49] to achieve the transmit diversity

Aiming at improving the spectral e ciency, the work in [12] posed an e ective 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 e ciency 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 boththe in-phase and quadrature components of the M-ary modulatedsymbols In another solution, the dual-mode OFDM (DM-OFDM)was presented in [52] DM-OFDM utilized inactive sub-carriers tocarry further data bits in addition to the active sub-carriers Di erentsignal constellations were employed to convey complex datasymbols over both active and inactive sub-carriers Extending thisidea, the work in [53] introduced a multi-mode IM-OFDM (MM-IM-OFDM) scheme which activates all sub-carriers More informationbits can be conveyed by permuted trans-mission modes, whichallows this scheme to enjoy further increased spec-tral e ciency

In order to achieve both spectral e ciency and diversity gain, theauthors in [14] introduced a linear constellation precoder (LPC) forIM-OFDM In another e ort, the study in [11] applied the compressedsens-ing technique to IM-OFDM to attain performance enhancementwith respect to both diversity gain and energy e ciency

Recently, various researchers have also concentrated on analyzing formance of the IM-OFDM system The work in [10] successfully derived a tight bound for BER of IM-OFDM The linear processing-based ICI cancellation and capacity maximization were applied to IM-OFDM over

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

of IM-OFDM in the presence of carrier frequency o set (CFO) wasre-ported in [31], [32], [28] In addition, ergodic capacity of IM-OFDMwas evaluated in [26] The work [27] investigated the outageprobability of the IM-OFDM scheme operating over the two-way diused-power fad-ing channels The transmission reliability in terms ofSEP of IM-OFDM and IM-OFDM employing greedy detection underimperfect CSI was investigated in [29] and [55], respectively

In another aspect, the work [56] investigated PAPR and BER of OFDM with ICI It was shown that IM-OFDM can signi cantly 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 in uenced 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 bene ts of IM-OFDM, it was applied to numer-ouscommunication 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 in[22], [32] introduced IM-OFDM to underwater acoustic communica-tions.They also developed an ICI self-cancellation scheme for this par-ticularimplementation case The possible combination of NOMA and IM-OFDMwas investigated in [37] Based on the code index modula-

tion [59], the IM-OFDM spread spectrum (IM-OFDM-SS) system in[60] uses indices of spreading codes to convey data bits Inspired bythe OFDM-SS system with the rotated Walsh-Hadamard transform[61] and the pre-coding matrix for MIMO-OFDM [62], a spread IM-OFDM (S-IM-OFDM) system was proposed in [24] A precoder for S-IM-OFDM was 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,the two 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 reception

diversity via either MRC or SC The ML and GD detectors were alsoproposed to jointly detect the indices and the M-ary mod-ulatedsymbols The IM-OFDM system with diversity reception achievessigni cantly better symbol error performance than that of theconventional IM-OFDM thanks to spatial diversity gain Perfor-manceanalysis 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 ofIM-OFDM with diversity reception will be covered in chapter 2

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