IEEE COMMUNICATIONS SURVEYS & TUTORIALS, VOL. 21, NO. 1, FIRST QUARTER 2019 315 Novel Index Modulation Techniques: A Survey Tianqi Mao , Student Member, IEEE,QiWang , Member, IEEE, Zhaocheng Wang , Senior Member, IEEE, and Sheng Chen , Fellow, IEEE
Abstract—In fifth generation wireless networks, the escalating BICM-ID Bit-Interleaved Coded Modulation with teletraffic and energy consumption has necessitated the devel- Iterative Decoding opment of green communication techniques in order to further BLAST Bell Labs Layered Space-Time enhance both the system’s spectral efficiency and energy effi- ciency. In the past few years, the novel index modulation (IM) BMST Block Markov superposition has emerged as a promising technology that is widely employed transmission in wireless communications. In this paper, we present a survey BPSK Binary Phase Shift Keying on IM in order to provide the readers with a better understand- CD Channel Domain ing of its principles, advantages, and potential applications. We CD-IM Channel-Domain IM start with a comprehensive literature review, where the concept of IM is introduced, and various existing IM schemes are classi- CIR Channel Impulse Response fied according to their signal domains, including the frequency CP Cyclic Prefix domain, spatial domain, time domain and channel domain. Then CPEP Conditioned PEP the principles of different IM-aided systems are detailed, where CSI Channel State Information the transceiver design is illustrated, followed by descriptions of CSIT CSI at the Transmitter typical systems and corresponding performance evaluation. A range of challenges and open issues on IM are discussed before D/A Digital-to-Analog Converter we conclude this survey. DCO-OFDM DC-Biased Optical OFDM DMBM Differential MBM Index Terms—Index modulation, orthogonal frequency division multiplexing, spatial modulation, media-based DM-OFDM Dual-Mode IM-Aided OFDM modulation, constellation design, maximum-likelihood detection, DM-SCIM Dual-mode SC-IM low-complexity receiver design. ED Euclidean Distance EGSIM-OFDM Enhanced GSIM-OFDM EGSIM-OFDM1 EGSIM-OFDM Version 1 GLOSSARY EGSIM-OFDM2 EGSIM-OFDM Version 2 4G Fourth Generation EGSIM-OFDM-JIQ In EGSIM-OFDM, IM Conducted on 5G Fifth Generation I/Q Components Jointly ABEP Average Bit Error Probability ESIM-OFDM Enhanced SIM-OFDM ACE Active Constellation Expansion ESM Enhanced SM ACO-OFDM Asymmetrically Clipped Optical FD Frequency Domain OFDM FDE FD Equalization A/D Analog-to-Digital Converter FD-IM Frequency-Domain IM APM Amplitude/Phase Modulation FFT Fast Fourier Transform AWGN Additive White Gaussian Noise FSK Frequency Shift Keying BER Bit Error Rate FSO Free-Space Optical FTN-IM Faster-than-Nyquist Rate SC-IM Manuscript received August 17, 2017; revised January 23, 2018 and GDM-OFDM Generalized DM-OFDM May 21, 2018; accepted July 19, 2018. Date of publication July 23, 2018; date of current version February 22, 2019. This work was sup- GPQSM Generalized Precoded QSM ported in part by the National Natural Science Foundation of China under GPSM Generalized PSM Grant 61571267, in part by the Shenzhen Subject Arrangements under GSIM-OFDM Generalized ESIM-OFDM Grant JCYJ20160331184124954, and in part by the Shenzhen Fundamental Research under Project JCYJ20170307153116785. (Corresponding author: GSM Generalized SM Zhaocheng Wang.) GSM-MBM GSM Combined with MBM T. Mao and Z. Wang are with the Beijing National Research Center GSSK Generalized SSK for Information Science and Technology, Department of Electronic Engineering, Tsinghua University, Beijing 100084, China (e-mail: GSTSK Generalized STSK [email protected]; [email protected]). IAS Inter-Antenna Synchronization Q. Wang was with the School of Electronics and Computer Science, IBI Inter-Block Interference University of Southampton, Southampton SO17 1BJ, U.K. He is now with Huawei Technologies Company Ltd., Shenzhen 518129, China (e-mail: ICI Inter-Channel Interference [email protected]). IFFT Inverse Fast Fourier Transform S. Chen is with the School of Electronics and Computer Science, University IM Index Modulation of Southampton, Southampton SO17 1BJ, U.K., and also with King Abdulaziz University, Jeddah 21589, Saudi Arabia (e-mail: [email protected]). IM-OFDM IM-Aided OFDM Digital Object Identifier 10.1109/COMST.2018.2858567 IoT Internet of Things 1553-877X c 2018 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. 316 IEEE COMMUNICATIONS SURVEYS & TUTORIALS, VOL. 21, NO. 1, FIRST QUARTER 2019
I/Q In-phase and Quadrature SM-OFDM SM Combined with OFDM ISI Intersymbol Interference SNR Signal-to-Noise Power Ratio ItM/DD Intensity Modulation with Direct S/P Serial-to-Parallel Converter Detection SSK Space Shift Keying LDPC Low-Density Parity Check Code STBC Space-Time Block Codes LED Light Emitting Diode STCM Space-Time Channel Modulation LLR Log-Likelihood Ratio STFSK Space-Time-Frequency Shift Keying LMG-SSTSK Layered Multi-Group Steered STSK ST-IM Space-Time IM LMIMO-MBM Layered MIMO-MBM STSK Space-Time Shift Keying LTE Long-Term Evolution TCSM Trellis Coded Spatial Modulation MAP Mirror Activation Pattern TD Time Domain MA-SM Multiple Active-SM TDD Time Division Duplexing MBM Media-Based Modulation TD-IM Time-Domain IM MI Mutual Information TX Transmitter MIAD Minimum Intra-Mode Distance U-OFDM Unipolar OFDM MIMO Multiple-Input Multiple-Output UPEP Unconditioned PEP MIMO-OFDM-IM GSIM-OFDM Combined with MIMO VLC Visible Light Communications MIRD Minimum Inter-mode Distance ZF Zero-Forcing ML Maximum Likelihood ZTM-OFDM Zero-Padded Tri-Mode IM-Aided MM-OFDM Multi-Mode IM-Aided OFDM OFDM. MMSE Minimum Mean-Squared Error mmWave Millimeter-wave MSF-STSK Multi-Space-Frequency STSK I. INTRODUCTION MS-STSK Multi-Set STSK UE TO the fast evolution of smart communication termi- O-DM-OFDM Optical DM-OFDM D nals and in order to meet the explosive increase of mobile OFDM Orthogonal Frequency Division traffic, high-rate transmission schemes have attracted increas- Multiplexing ing attention from both the academia and industry, featured by O-GSIM-OFDM Optical GSIM-OFDM orthogonal frequency division multiplexing (OFDM) [1] and OOK On-Off Keying single-carrier frequency-domain equalization (SC-FDE) [2]. PAM Pulse Amplitude Modulation OFDM, which has fast become one of the most dominant PAM-DMT PAM Discrete Multi-Tone techniques in 4G communication, is widely employed in PAPR Peak-to-Average Power Ratio multiple wireless standards including Wi-Fi, IEEE 802.11 a/g, PEP Pairwise Error Probability 802.16 WiMAX and Long-Term Evolution (LTE) [3]Ð[6], PLC Power Line Communications owing to its distinctive merits of resilience to frequency selec- PPM Pulse-Position Modulation tive fading channels and facilitating low-complexity hardware PSK Phase Shift Keying implementation with one-tap frequency-domain equalization PSM Precoded SM (FDE) [7]Ð[9]. However, OFDM symbols suffer from the PTS Partial Transmit Sequence drawback of high peak-to-average power ratio (PAPR), leading QAM Quadrature Amplitude Modulation to inevitable nonlinear distortion by the transmitter (TX) power QCM Quadrature Channel Modulation amplifier [10]. To mitigate this issue, the early-invented SC- QoS Quality-of-Service FDE scheme is still employed in some wireless applications QPSK Quadrature Phase Shift Keying for its lower PAPR, particularly in visible light communica- QSM Quadrature SM tion (VLC) systems [11], which are extremely sensitive to RF Radio Frequency the nonlinear characteristics of light emitting diode (LED) RX Receiver emitters. Furthermore, owing to the need for enlarging capac- SBIM Source-Based IM ity of wireless communications and ensuring satisfactory SC-FDE Single-Carrier Frequency-Domain quality-of-service (QoS) of mobile devices, multiple-input Equalization multiple-output (MIMO) technique [12] has attracted extensive SC-IM Single-Carrier-Based IM attention, which is capable of improving the system throughput SD Spatial Domain without the sacrifice of additional bandwidth usage or energy SD-IM Spatial-Domain IM consumption [13]. SIC Successive Interference Cancellation In 5G networks, the explosive growth in mobile data SIMO Single-Input Multiple-Output services and the popularisation of smart devices have necessi- SIMO-MBM MBM Combined with SIMO tated the requirement for high spectral and energy efficiency. SIM-OFDM Subcarrier-index modulated OFDM Following this trend, the novel concept of index modulation SISO Single-Input Single-Output (IM) has been promoted in wireless communications to meet SLM Selective Mapping the demand for high throughput and low energy consump- SM Spatial Modulation tion. More specifically, unlike conventional communication MAO et al.: NOVEL IM TECHNIQUES: SURVEY 317 schemes, only a fraction of certain indexed resource enti- applied to TD-IM [28], [29] to further enhance the system ties, e.g., subcarriers, antennas, time slots or channel states, performance. Furthermore, TD-IM can be combined with are activated for a data transmission, while the others are the space-time block code (STBC) system [30], [31], where kept unused by the associated transmission, where additional only subset of the dispersion matrices are selected for data information bits are conveyed implicitly by the index usage transmission, while their indices carry extra information or activation patterns. IM therefore can significantly enhance bits [32], [33]. the spectral and energy efficiency for the reason that, apart The aforementioned IM schemes define the so-called from information bits carried by usual amplitude/phase mod- source-based IM (SBIM), which embeds additional informa- ulation (APM) based transmission, additional index bits are tion bits into the indices of various TX or RX entities, such harvested without energy consumption. This makes an IM- as antennas, subcarriers or time-slots. Despite of their supe- aided system capable of employing only part of the resources rior energy efficiency and BER performance, SBIM systems to achieve the same throughput as its conventional counter- may suffer from severe interferences under the static fad- part, leading to a reduced system complexity, while consuming ing channel. Moreover, the achievable throughput of SBIM substantially less energy. Besides, due to the flexible struc- increases slowly, only proportional to the logarithm of the ture of IM-aided frame, considerable diversity gains can be number of TX entities. To address these issues whilst main- achieved from the activated pattern of the indexed entities, taining the diversity gain, CD-IM, also known as media-based types of the constellation alphabets, or the selection of chan- modulation (MBM) [34], has recently been introduced to nel states, etc., which contributes to significant performance radio frequency (RF) communications, which enjoys an inher- gain over the non-index-modulated counterparts. Therefore, ent diversity against static fading [34], [35]. Specifically, IM has been applied in various formats to diverse wire- the characteristics of tunable parasitic components external less communication applications, including millimeter-wave to the TX antennas, such as RF mirrors [36] or electronic (mmWave) transmission [14], [15], massive MIMO [16], [17] switches [37], are intentionally modified to change the RF and network coding [18]. Existing IM schemes can be clas- property consisting of permittivity, permeability and resistiv- sified into various signal domain IM schemes, which include ity. Even a small perturbation in a rich scattering environment frequency-domain IM (FD-IM), spatial-domain IM (SD-IM) can be dramatically augmented, leading to differentiable chan- and time-domain IM (TD-IM), as well as the channel-domain nel realizations. When mrf RF mirrors are employed, for IM (CD-IM) scheme. example, by controlling their on/off status, a total of 2mrf FD-IM is also referred to as IM-aided OFDM (IM-OFDM), channel states can be generated, which are unknown at the where IM is performed on the orthogonal subcarriers [19]. TX but available at the RX using pilots. Therefore, in addi- Explicitly, in addition to the binary bits carried by a classi- tion to the information carried by the conventional APM, cal APM scheme, such as pulse amplitude modulation (PAM), extra mrf bits are conveyed by the indices of the selected phase shift keying (PSK) and quadrature amplitude modulation channel states, leading to enhanced data rate. In compari- (QAM), additional information can be implicitly conveyed by son with SBIM, whose achievable throughput increases with the subcarrier activation pattern, that is, the indices of acti- the logarithm of the number of TX entities, the spectral effi- vated subcarriers [20]. Some IM-OFDM systems are capable ciency of MBM grows linearly with the number of used RF of achieving higher spectral efficiency than their non-index- mirrors. Moreover, for SM, the spacing between neighbour- modulated counterparts, by harvesting additional index bits. ing antennas is required to be sufficiently large in order to Moreover, the energy efficiency is enhanced, since transmis- achieve independent fading. On the other hand, for MBM, sion of index bits is energy-free. IM can be also conducted RF mirrors can be placed side-by-side [38]. These benefits on the spatial domain (SD) by applying the SD-IM technique, of MBM have motivated the relevant researches in the past also known as spatial modulation (SM) [21]Ð[23]. In SM, only few years. a fraction of TX or receiver (RX) antennas are activated for For clarity, Table I categorizes the existing IM tech- data transmission, while their indices convey additional infor- niques,1 and Fig. 1 illustrates the general structure of IM-aided mation bits in an implicit manner. Different from conventional systems. Compared to their non-index-modulated counterparts, MIMO schemes, such as spatial multiplexing schemes and rep- IM-aided systems convey additional energy-free bits, which etition codes, the antenna-activation pattern of SM is capable enhances the energy efficiency. Due to the flexible system of mitigating the inter-channel interference (ICI) as well as the structure of IM-aided systems, superior BER performance can inter-antenna synchronization (IAS) issue. Therefore, SM can be achieved by optimizing the system parameters. Moreover, achieve significant performance gains, in terms of bit error the use of SM contributes to low hardware complexity, robust- rate (BER) and energy efficiency, over the existent MIMO ness against ICI and static fading, as well as freeing from systems, such as the Bell Labs layered space-time (BLAST) IAS issue, since only a fraction of antennas are employed. system and the Alamouti system [24], [25]. IM can also be On the other hand, the introduction of MBM techniques carried out in the time domain (TD). Specifically, in each data offers the opportunity of dramatically increasing the system frame, only a fraction of the signaling time slots are activated throughput as well as provides inherent diversity gains. In for data transmission, and the corresponding indices carry information [26], [27], which leads to significant performance gain over its non-IM-aided counterpart. The multi-mode IM 1In this paper, we propose a new general MM-OFDM, and MM-OFDM philosophy and the faster-than-Nyquist signalling are also proposed in [49] is a simplified special case of our generic MM-OFDM. 318 IEEE COMMUNICATIONS SURVEYS & TUTORIALS, VOL. 21, NO. 1, FIRST QUARTER 2019
TABLE I SUMMARY OF REPRESENTATIVE IM-AIDED ARCHITECTURES
Fig. 1. The transmitter and receiver structure of generic IM-aided system. summary, some of the distinctive advantages of IM-aided • Superior BER performance. systems include: • Robust against ICI and static fading. • High energy efficiency. • Free of IAS issue. • Low hardware complexity. To the best of the authors’ knowledge, there exist lim- • Flexible system structure. ited literature surveying IM, including [20], [64]Ð[66]. MAO et al.: NOVEL IM TECHNIQUES: SURVEY 319
In [64] and [65], the design framework of SM as well as its pros and cons were comprehensively investigated, where the attention was particularly directed at the transceiver design, multi-dimensional constellation optimization, link adaptation methods, and network protocol design. By discussing many published technical papers, the book [20] reviewed the system models and the detection techniques of the existing SM, IM- OFDM and space-time-domain IM schemes. Some theoretical analysis, such as pairwise error probability (PEP) calculation, and simulation results were provided, while some possible challenges and open issues of IM were also forecasted. The recent paper [66] reviews IM techniques in different signal domains. However, only SM and IM-OFDM are investigated in detail. In particular, for applications and practical issues, only SM and IM-OFDM schemes are discussed in [66]. The organization of this survey paper is given in Fig. 2. Compared with the existing reviews on IM, our new contribu- tions are first summarized below. 1) We present a more comprehensive review and descrip- tion of FD-IM, by introducing more typical IM-OFDM schemes, such as DM-OFDM, GDM-OFDM, ZTM- OFDM and MM-OFDM, and providing the explicit descriptions of corresponding transceiver structures, constellation designs and performance evaluation, in terms of spectral efficiency, energy efficiency and BER. Moreover, a generic MM-OFDM structure is proposed in the paper for the first time to overcome the disadvantages of the existing MM-OFDM scheme. 2) Our survey includes the novel CD-IM techniques, namely, MBM, by introducing several typical MBM schemes. Limitations of these typical MBM schemes are revealed and possible solutions are suggested. 3) Our survey includes all the important space-time domain IM schemes, such as STSK as well as TD-IM schemes, which were not discussed in [20], and our review, which is much more explicitly than [66], includes the detailed descriptions of transceiver design strategy and com- prehensive performance evaluation based on spectral efficiency, energy efficiency and BER. 4) Applications of IM to VLC, not reviewed in most of the existing survey literature, are discussed in our survey paper. 5) Challenges and open issues missed in [20] and [66]are extensively discussed. Therefore, different from the existing overview on IM, our Fig. 2. Outline of the survey paper. presentation provides a more comprehensive investigation on the generalized concept of IM, and we review all the existing computational complexity analysis. The potential challenges IM techniques in the frequency domain (FD), SD, TD, and and future work are extensively discussed. channel domain (CD). State-of-the-art new researches, par- Before we proceed, we point out that placing an empha- ticularly the novel MBM and dual-mode (multi-mode) IM, sis on the FD-IM is because our research is mainly focusing are included in our paper, which offers a better illustration on FD-IM, and we would like to share our expertise and of the latest progress in the IM field. More specifically, in the lessons from our experience to help the readers avoiding this survey, after a comprehensive literature review, we detail pitfalls when embarking their own research in the IM field. the diverse IM frameworks in all the four FD, SD, TD and CD, with an emphasis on the FD-IM. This is followed by the performance evaluation of various typical IM techniques II. BASIC SYSTEM MODEL based on a range of performance metrics, including the min- In this section, we briefly introduce the basic commu- imum Euclidean distance (ED), the PEP analysis and the nication system models adopted by various IM techniques, 320 IEEE COMMUNICATIONS SURVEYS & TUTORIALS, VOL. 21, NO. 1, FIRST QUARTER 2019
capacity can be calculated according to [12], [71]
γ I HHH / / , CMIMO =log2 det Nr + [bit s Hz] (4) Nt
where I N denotes the N × N identity matrix and det is the matrix determinant. It can be seen from (3) and (4) that the capacities defined above are random variables, and are not suitable for performance evaluation. Hence, the ergodic capacity (the expectation of the system capacity) [71] and the Fig. 3. MIMO communication system diagram. capacity outage (the capacity supported 90% or 99% of the time period) [72], [73] are typically employed for performance investigation. including MIMO and single-input multiple-output (SIMO) as well as OFDM and SC-FDE. B. OFDM As shown in Fig. 4(a), binary bits are modulated by an APM A. MIMO and SIMO mapper, such as PAM, PSK or QAM, to generate the complex- T Fig. 3 presents the system diagram of spatial multiplexing valued FD signal block X =[X (0) X (1) ···X (N − 1)] , MIMO equipped with Nt TX antennas and Nr RX antennas. which is then passed through a serial-to-parallel converter s ··· T If the input signal vector is denoted as =[s1 s2 sNt ] , (S/P) before fed into the N-point inverse fast Fourier trans- where (·)T denotes the transpose operator, then the received form (IFFT) module to yield the TD signal block x = r ··· T ··· − T signal vector =[r1 r2 rNr ] can be represented by [x(0) x(1) x(N 1)] . Next cyclic prefix (CP) of length LCP is appended to x to combat the inter-block interference r Hs w, = + (1) (IBI). This is followed by the digital-to-analog conversion (D/A) and power amplification before transmission through where w ∈ CNr is the additive white Gaussian noise (AWGN) the single-input single-output (SISO) fading channel, whose vector, whose elements obey the circularly symmetric com- CN ,σ2 H ∈ CNr ×Nt channel impulse response (CIR) is defined by the channel coef- plex Gaussian distribution (0 w ), while T ficient vector h =[h0 h1 ···h −1] , where L is the length denotes the channel fading matrix, whose (i, j)th element Lh h of the CIR. The channel coefficients h for 0 ≤ i ≤ L − 1 h , stands for the channel coefficient between the jth TX i h i j areassumedtofollowCN(0, 1/L ). To remove completely antenna and the ith RX antenna, which can be modelled as an h theIBI,wemusthaveLCP ≥ L . independent variable obeying CN(0, 1) for the static fading h At the receiver, after the inverse operations, including the channel. analog-to-digital conversion (A/D), the CP removal and the At the receiver, the zero-forcing (ZF) detection is often N-point fast Fourier transform (FFT), the received FD signal employed for simplicity, which multiplies the received signal block X =[X (0) X (1) ···X (N − 1)]T is generated as vector r by the pseudo-inverse of H , formulated as r r r r −1 −1 X {X}H W, H H H H r =diag + (5) sZF = H H H r = s + H H H w, (2) where diag{X} stands for the diagonal matrix whose where (·)H denotes the conjugate transpose operator. It can be diagonal elements are the elements of X and H = T seen from (2) that the effect of the channel AWGN is ampli- [H (0) H (1) ···H (N − 1)] is the FD channel coefficient fied, which may cause performance degradation. To address vector obtained by the N-point FFT of h, while W = T this issue, several enhanced algorithms can be invoked, which [W (0) W (1) ···W (N − 1)] is the equivalent FD AWGN include the minimum mean-squared error (MMSE) detec- vector. Using channel estimation, h and hence H can be tion [67], [68] and the successive interference cancellation estimated to construct the one-tap FDE, and the equalized sig- (SIC) techniques [69], [70]. nals are fed into the corresponding constellation demapper for SIMO is a special case of MIMO with Nt =1.Apartfrom demodulation. spatial multiplexing MIMO, MIMO can also be designed to Owing to the IFFT at TX, OFDM signals suffer from high attain spatial diversity gains in order to enhance the achievable PAPR, which results in severe nonlinear distortions caused BER performance at the expense of reduced throughput. by the limited dynamic range and nonlinearities in the power To evaluate the performance of SIMO and MIMO systems, amplifier for RF communications [74] or in the LED emitter capacity analysis is often employed. For a memoryless SIMO for VLC [75]. Therefore, numerous PAPR reduction tech- system with Nr RX antennas, its capacity is given by [12] niques have been proposed, including hard clipping [76], companding [77], selective mapping (SLM) [78], partial trans- Nr 2 mit sequence (PTS) [79], and active constellation expansion CSIMO =log 1+γ h ,1 [bit/s/Hz], (3) 2 i (ACE) [80], etc., which present a trade-off between the PAPR =1 i and the spectral efficiency as well as the received SNR. where |·|is the modulo operator and γ denotes the system’s Alternatively, the digital predistorter [81], [82] or the non- signal-to-noise power ratio (SNR). As for MIMO systems, the linear detection scheme [83], [84] can be employed to address MAO et al.: NOVEL IM TECHNIQUES: SURVEY 321
Fig. 4. Transceiver models of OFDM and SC-FDE systems. the high PAPR issue, at the expense of increased TX or RX A. FD Index Modulation complexity. FD-IM, also known as IM-OFDM, is capable of embed- ding additional information bits on the indices of the acti- vated OFDM subcarriers without extra energy consumption, C. SC-FDE which enhances the energy efficiency. Below the IM-OFDM Fig. 4(b) illustrates the transceiver structure of SC-FDE, transceiver design is first illustrated. Then different IM-OFDM which transmits a single carrier modulated APM signal. schemes are classified into single-mode, multi-mode, and Effective one-tap FDE is implemented at RX with the aid non-RF classes, respectively. Afterwards, the signal detec- of FFT and IFFT operations [85], [86]. It has been shown tion algorithms for typical IM-OFDM schemes are introduced, that SC-FDE achieves similar BER performance, spectral which is followed by the performance analysis. and energy efficiencies as OFDM. Comparing Fig. 4(b) with 1) Transceiver Structure: The TX of IM-OFDM up to the Fig. 4(a), it is also clear that the total system complexity of creation of the FD signal block X is presented in Fig. 5. A total SC-FDE is similar to that of OFDM but the TX complexity of m information bits are divided equally into the G groups of of SC-FDE is lower than that of the OFDM TX. This makes p bits each, i.e., m = G · p. Each group is further split into the SC-FDE attractive for uplink transmission. Moreover, due to two subgroups of p1 and p2 bits, respectively, called index bits the use of single carrier, the PAPR of SC-FDE is much lower, and symbol bits. Correspondingly, the N OFDM subcarriers X which mitigates the need of power back-off [2] and helps to are also divided into the G subblocks reduce the nonlinear distortion of power amplifiers. For this (g) T aforementioned merit, SC-FDE has also been introduced to X =[X ((g − 1)L +1)X ((g − 1)L +2)···X (gL)] VLC [11], where the nonlinearities of LED are severe, and it for 1 ≤ g ≤ G with the subblock length of L = N/G.For outperforms other conventional optical modulation schemes, the gth OFDM subblock, the indices of the activated subcar- in terms of SNR gains. riers ig , referred to as index pattern, are determined by the corresponding index bits with the aid of an index selector, and the data symbols sg are generated by the constellation III. PRINCIPLES OF IM-AIDED SYSTEMS mapper according to the symbol bits. Afterwards, by using an IM can be performed in the SD on antennas, in the FD on OFDM block creator, all the G OFDM subblocks are concate- subcarriers, in the TD on time slots, or in the CD on channel nated together and fed into the subsequent stages which are state variations. In this section, based on this classification, the the same as in a conventional OFDM transmitter. frameworks of various IM-aided systems are illustrated, which At the RX, after the FFT operation, information bits can be are exemplified by the corresponding typical schemes. demodulated by ML detection subblock by subblock, where 322 IEEE COMMUNICATIONS SURVEYS & TUTORIALS, VOL. 21, NO. 1, FIRST QUARTER 2019
TABLE II ALOOK-UP TABLE OF GSIM-OFDM WITH p1 =2, L = 4 AND k = 2
empty. These operations are exemplified by Table II, where Si1 M and Si2 are arbitrary elements of . It is seen that for each OFDM subblock, the indices of the modulated subcarriers are Fig. 5. Transmitter diagram of IM-OFDM. determined by the two index bits, with the bit streams [0,0], [0,1], [1,0] and [1,1] corresponding to the index patterns [1,2], [2,3], [3,4] and [1,4], respectively. Hence, for GSIM-OFDM, all the possible realizations of the OFDM subblock, denoted p1 and p2 are formulated respectively as X X , X , ··· , X p } as = 1 2 2 1 , are considered to minimize the L L! p1 = log2 = log2 , (6) ED between the received subblock and its estimate. However, k (L − k)!k! since exponentially increasing number of subblock realizations p2 = k log2(M ), (7) have to be taken into account, the complexity of the optimal ML detection may be too large for practical implementa- where · denotes the integer floor operator. Hence the spectral tion. Therefore, sub-optimal strategies, such as log-likelihood efficiencies of ESIM-OFDM and GSIM-OFDM are given by ratio (LLR) detection, are proposed to reduce the computa- N (log2(M )+1) tional overhead at the expense of a slightly degradation in SEESIM−OFDM = , (8) 2(N + LCP) performance. Explicitly, the indices of the activated subcarriers and are firstly detected with the aid of LLR calculation subcarrier by subcarrier, and each data symbol is then demodulated by L N k log2(M )+ log2 k the corresponding demapper according to the estimated index SEGSIM−OFDM = , (9) pattern. Detection algorithms for typical IM-OFDM systems L(N + LCP) will be detailed in Section III-A5. respectively. From (9), it is seen that k and L in GSIM-OFDM 2) Single-Mode Class: In [39], subcarrier-index modulated can be flexibly adjusted to obtain a high spectral efficiency, OFDM (SIM-OFDM) was proposed, where part of the sub- which has been investigated in [87]Ð[89]. Specifically, in [87], carriers are modulated by QAM, and the indices of these the optimal subcarrier grouping strategy was proposed accord- activated subcarriers in each OFDM symbol or block are ing to the analytical expression of energy efficiency for determined by the corresponding majority bit-values of an on- GSIM-OFDM, while the optimal number of activated sub- off-keying (OOK) data stream. Since subcarrier grouping is carriers per subblock was deduced by maximizing the energy not applied, the transmitter of SIM-OFDM is equivalent to efficiency [88]. Furthermore, a closed-form approximated BER Fig. 5 with G = N. The data rate of SIM-OFDM, however, upper bound for GSIM-OFDM was derived [89]. is unstable due to the randomness of the OOK data stream, Recall that SIM-OFDM carries more index information than and this may impose potential error propagation, leading to ESIM-OFDM due to using the variable number of activated bursts of errors. To address this problem, Tsonev et al. [40] subcarriers. Exploiting this feature, an enhanced GSIM-OFDM proposed an enhanced SIM-OFDM (ESIM-OFDM) by par- (EGSIM-OFDM) version 1 (EGSIM-OFDM1)3 was proposed titioning the subcarriers into pairs. For each pair, only one by altering the number of activated subcarriers in each OFDM subcarrier is activated, whilst the other one remains empty, subblock [42]. Explicitly, the number of activated subcarriers where the index of the activated subcarrier carries one bit is selected from the set K = {k1, k2,...,kT }, where T is information. Although the BER performance of ESIM-OFDM the size of K. Therefore, the number of the index bits p1 for is better, it suffers the loss of half of the index bits, compared EGSIM-OFDM1 can be derived as with SIM-OFDM. Moreover, the system’s frequency resources T L 1 , are under-utilized, since only one half of the subcarriers are p = log2 =1 (10) i ki activated for data transmission. In [41], a generalized ESIM- OFDM (GSIM-OFDM)2 was proposed, where subcarriers are and its spectral efficiency is formulated as split into OFDM subblocks, and the subblock size is not con- T L ki N log2 i=1 ki M strained to be 2 as in ESIM-OFDM. Explicitly, in each OFDM SEEGSIM−OFDM1 = , (11) subblock, k out of L subcarriers (k < L) are mapped by the L(N + LCP) constellation alphabet M = {S1, S2,...,SM }, where M is which is enhanced significantly in comparison with the order of the APM constellation, and the others are kept GSIM-OFDM. To further improve the spectral efficiency,
2In [41], GSIM-OFDM is referred to as OFDM with IM (OFDM-IM). 3In [42], EGSIM-OFDM1 is referred to as OFDM-GIM1. MAO et al.: NOVEL IM TECHNIQUES: SURVEY 323
Fan et al. [42] also proposed an EGSIM-OFDM version 2 is because the index bits embedded in the subcarrier indices (EGSIM-OFDM2)4 by conducting IM on the in-phase and are only proportional to the logarithm of the subblock size L, quadrature (I/Q) components separately. Specifically, in each which are far less than the symbol bits embedded in high- OFDM subblock, a fraction of the I/Q parts of the subcarriers order APM constellation alphabet. This under-utilization of are selected for modulation using PAM separately. Let the subcarriers may even lead to performance degradation for high numbers of activated subcarriers for the I/Q components be throughput systems, compared to conventional OFDM. kI and kQ , which are modulated by MI - and MQ -PAM, To overcome this performance limitation of single-mode respectively. The spectral efficiency of EGSIM-OFDM2 is based schemes, dual-mode IM aided OFDM (DM-OFDM) given by was developed in [46], which fully utilizes the valuable spec- N tral resource while maintaining the diversity gain of IM. SEEGSIM−OFDM2 = L N L Explicitly, the subcarriers are partitioned into subblocks, and ( + CP) all the subblocks are utilized for data transmission. Within × kI log2(MI )+kQ log2 MQ each OFDM subblock, subcarriers are divided into two groups, A and B, modulated by two distinguishable constellation L L alphabets MA and MB with the sizes of MA and MB , respec- + log2 + log2 . kI kQ tively. Additional index information can be conveyed by the indices of the subcarriers in Group A, for example. Without (12) loss of generality, therefore, the indices of the subcarriers in Rather than conducting IM on I/Q components separately, Group A define index pattern, which are represented by IA,i Fan et al. [90] further improved EGSIM-OFDM2 by perform- for the ith subblock, with i =1, 2,...,G.Ifk subcarriers are ing IM jointly on I/Q components, achieving an even higher modulated by MA, and the other L − k subcarriers are mapped spectral efficiency due to an enlarged number of index pat- by MB , the spectral efficiency of DM-OFDM is expressed by terns. The spectral efficiency of this scheme, which we refer to as EGSIM-OFDM-JIQ, is formulated as [90] N N 2 log M k L SEDM−OFDM = 2 k L( N + LCP) SEEGSIM−OFDM−JIQ = , (13) L(N + LCP) × k log2(MA)+(L − k)log2(MB ) where the numbers of activated subcarriers are both equal to k for I/Q components, and both I/Q components are modulated L + log2 . (14) by M-PAM. A similar scheme, called OFDM-HIQ-IM, was k proposed in [91], where linear constellation precoding tech- nique is utilized to attain extra diversity gain. Furthermore, in addition to altering the number of activated subcarriers, dif- By comparing (9) with (14), it is readily seen that a significant ferent constellation alphabets can be employed for different throughput gain is achieved by DM-OFDM over GSIM- OFDM subblocks [43]. OFDM. Since the index pattern of each OFDM subblock needs M M Moreover, GSIM-OFDM can be combined with MIMO to be estimated at the RX, A and B must be differen- M ∧M ∅ to attain performance gain over conventional MIMO- tiable, i.e., A B = . Moreover, in order to achieve OFDM, leading to MIMO-OFDM-IM [44], [45]. Additionally, good BER performance, the minimum ED between two con- in [92] and [93], a subcarrier-level interleaving technique stellation points of the two alphabets should be equal to that was incorporated into GSIM-OFDM and MIMO-OFDM-IM, of two constellation points within each alphabet. Therefore, respectively, to enhance the system performance by increas- a feasible constellation design strategy is to divide a (MA + M ing the minimum ED between different symbols. Similarly, MB )-QAM alphabet into two subsets, employed as A and M a coordinate interleaved GSIM-OFDM was proposed in [94] B .Fig.6 illustrates an example of the two constellation by combining GSIM-OFDM with space-time codes and coor- alphabets in DM-OFDM, where the two quadrature phase shift M {− − , − , , − } dinate interleaving technique, in order to attain additional keying (QPSK)√ sets √ A = 1√ j 1 j √1+j 1+j and M { , , − − , − } diversity gain. Besides, exploiting the sparsity property of the B = 1+ 3 (1+ 3)j 1 3 (1+ 3)j are obtained GSIM-OFDM frame structure, the compressive sensing tech- from an 8-QAM constellation. nique was adopted in GSIM-OFDM [95], to increase both the By fully utilizing all the subcarriers for data transmission energy and spectral efficiencies. whilst maintaining the advantages of IM, DM-OFDM can 3) Multi-Mode Class: In the aforementioned single-mode achieve significant performance gain over other IM-OFDM schemes, such as GSIM-OFDM, only a fraction of subcar- schemes [46]. This motivates various works to extend DM- riers are modulated and, therefore, the precious frequency OFDM. By combining the ideas of EGSIM-OFDM1 and resources are unavoidably wasted. Moreover, as stated in [96], DM-OFDM, a generalized DM-OFDM (GDM-OFDM) [47] although GSIM-OFDM exhibits superior performance over was proposed to further enhance the spectral efficiency, where I conventional OFDM at low data rate, the gain disappears when the size of A,i is no longer constant but chosen from K { , ,..., } the system’s spectral efficiency is higher than 2 bit/s/Hz. This = k1 k2 kT . With this enhancement, additional diversity gain is achieved at the cost of higher detection com- 4In [42], EGSIM-OFDM2 is referred to as OFDM-GIM2. plexity. Similar to EGSIM-OFDM1, the spectral efficiency of 324 IEEE COMMUNICATIONS SURVEYS & TUTORIALS, VOL. 21, NO. 1, FIRST QUARTER 2019
OFDM subblock are split into nMM subsets modulated by nMM distinguishable constellation alphabets. Assuming that the ith subset consists of ki subcarriers and modulated by Mi with the size of Mi for i =1, 2,...,nMM, the spectral efficiency of MM-OFDM is given by i−1 nMM ki nMM L− j =0 kj log2 M + log2 i=1 i i=1 ki SEMM−OFDM = , L(1 + LCP/N ) (17)
where k0 =0.From(17), it can be seen that MM-OFDM achieves considerable throughput gain over other IM-OFDM schemes, while its energy efficiency is also enhanced signifi- cantly, which can be attributed to using multiple constellation
Fig. 6. An example of MA and MB in DM-OFDM with MA = MB = modes to convey more energy-free index bits. Owing to its 4 [46]. superior spectrum and energy efficiency, MM-OFDM outper- forms the other IM-OFDM counterparts, and can be widely applied to high-rate and low-power-consumption communica- GDM-OFDM can be derived as tion systems in 5G networks, VLC and Internet of Things T L kj L−kj (IoT). However, because of the enlarged number of alpha- N log2 j =1 kj MA MB SEGDM−OFDM = . bets, accurate detection of the index pattern for each OFDM L(N + LCP) subblock becomes difficult, and the multi-mode constellation (15) design is very challenging. GSIM-OFDM and DM-OFDM designs trade-off between Wen et al. [49] introduced a constellation mode selection energy efficiency and spectral efficiency. DM-OFDM, by uti- strategy based on the intra-mode distance and inter-mode dis- lizing all the subcarriers for data transmission, attains higher tance. The former is defined as the distance between any throughput at the cost of additional energy consumption. two subblocks with only one symbol error, while the latter is GSIM-OFDM, by keeping some subcarriers unmodulated, sac- defined as the distance between any two subblocks with two rifices spectral efficiency for higher energy efficiency and, symbol errors. At the high-SNR region, since the erroneous consequently, it may attain better BER performance. Based on detection is more likely to be caused by a single symbol error these observations, a zero-padded tri-mode IM aided OFDM between subblocks, the constellation design is to maximize the minimum intra-mode distance (MIAD), which is defined as (ZTM-OFDM) [48] was developed, which employs two differ- entiable constellation alphabets to modulate only a fraction of 2 dintra =min Xi − Xj , the subcarriers, leading to less energy consumption than DM- 1≤i of the data rate. Explicitly, ACO-OFDM only modulates the odd subcarriers, and PAM-DMT only activates the imagi- nary parts of subcarriers, both leading to anti-symmetric TD signals before clipping at zero. For U-OFDM, the absolute values of the positive and negative signals are transmitted in two OFDM symbols subsequently. These conventional optical OFDM schemes suffer from additional energy consumption or data rate loss. These drawbacks can be effectively addressed by the IM technique. In [104], an optical GSIM-OFDM (O-GSIM-OFDM) was proposed, which performs IM on the subblocks of DCO- OFDM or ACO-OFDM symbols before Hermitian symmetry operation. More explicitly, in each OFDM subblock, k out of the L subcarriers are modulated by the M-ary APM constel- lation, where the indices of the activated subcarriers convey additional information bits. With the CP length LCP, the spec- =4 Fig. 7. An example of MM-OFDM constellation design with M and tral efficiencies of O-GSIM-OFDM based on ACO-OFDM and nMM =8[49]. DCO-OFDM can be formulated respectively as − L k (BPSK), a natural choice for the constellation order M = 2, (N 2) log2 k M is employed as the first constellation mode to generates a set SEO−GSIM−OFDM,DCO = , 2(N + LCP)L of possible solutions with phase rotation by maximizing the (21) MIAD. This is followed by selecting the rotation angles as L k (j − 1)π/nMM for 2 ≤ j ≤ 8 to maximize the MIRD. The N log2 k M SEO−GSIM−OFDM,ACO = . (22) final 8-mode constellations are depicted in Fig. 7. 4(N + LCP)L Note that the design of [49] is only capable of designing constellation modes in certain SNR area with certain mod- Then, Mao et al. [105] developed optical DM-OFDM ulation constellation. In order to achieve a globally-optimal (O-DM-OFDM) by combining DM-OFDM with DCO-OFDM constellation design with more general APM, there remain or U-OFDM. In O-DM-OFDM, all the useful subcarriers are numerous challenges to be addressed. partitioned into subblocks, and all the subcarriers within each 4) Non-RF Class: GSIM-OFDM was adopted in under- OFDM subblock are modulated by two different constellation water acoustic communications in [97], where the negative alphabets. Specifically, k subcarriers are mapped by MA with impacts of ICI on the system performance are illustrated. To size of MA, and the other (L − k) are mapped by MB with address this issue, two adjacent subcarriers in each OFDM size of MB . Additional information bits are harvested from the subblock are employed for data transmission with opposite indices of subcarriers modulated by MA and MB . Hence, the polarity in order to combat ICI [97]. Furthermore, in [98], spectral efficiencies of the O-DM-OFDM schemes based on existent literature on ICI self-cancellation were reviewed, and DCO-OFDM and U-OFDM can be derived respectively as a novel ICI reduction scheme was proposed for the application − L k L−k of IM-OFDM in underwater acoustic communications. (N 2) log2 k MAMB SEO−DM−OFDM,DCO = , The IM technique was also introduced to VLC. Different 2(N + LCP)L from RF communications, intensity modulation with direct (23) detection (ItM/DD) is usually employed in VLC, and thus only − L k L−k real-valued non-negative signals can be used for data transmis- (N 2) log2 k MAMB SEO−DM−OFDM,U = . sion [1]. To achieve real-valued signals, Hermitian symmetry 4(N + LCP)L is imposed on the FD signal block X =[X (0) X (1) ··· (24) X (N − 1)]T before IFFT operation as: ∗ O-DM-OFDM schemes achieve higher spectral efficiency than X (k)=X (N − k), k =1, 2,...,N /2 − 1, (20) O-GSIM-OFDM counterparts, which leads to throughput gain. where (·)∗ is the conjugate operator, and X(0) = X(N/2) = 0. When the nonlinear transfer characteristics of LEDs are taken In order to generate unipolar signals, several optical into account, simulation results have demonstrated the supe- OFDM schemes were proposed, including DC-biased opti- riority of O-DM-OFDM over conventional optical OFDM cal OFDM (DCO-OFDM) [99], asymmetrically clipped schemes, in terms of practical implementation. optical OFDM (ACO-OFDM) [100], PAM discrete multi-tone 5) Signal Detection for Typical IM-OFDM Schemes: At the (PAM-DMT) [101], and unipolar OFDM (U-OFDM) [102] RX, the optimal ML detection can often be employed. Since or Flip OFDM [103]. In DCO-OFDM, certain DC-bias is ESIM-OFDM can be seen as the special case of GSIM-OFDM imposed on the bipolar signals to make them non-negative. with L = 2 and k = 1, while GSIM-OFDM can be consid- Unlike DCO-OFDM, ACO-OFDM, PAM-DMT and U-OFDM ered as the special case of DM-OFDM with either MA or generate unipolar signals without DC-bias by sacrificing half MB set to {0}, the ML detectors for these three IM-OFDM 326 IEEE COMMUNICATIONS SURVEYS & TUTORIALS, VOL. 21, NO. 1, FIRST QUARTER 2019 ( ) Pr X ((β − 1)L + i ) ∈Mj |Xr ((β − 1)L + i ) ( ) γ j =ln l l , ∀M ∈Ml (33) il β − ∈M | β − j all q=j ,q∈Q(l) Pr X (( 1)L + il ) q Xr (( 1)L + il ) schemes are similar. Specifically, by considering all the possi- index patterns whose numbers of subcarriers with positive ble realizations of OFDM subblock, the data symbols and the LLRs do not equal to k. Therefore, instead of hard decision corresponding index pattern of the βth OFDM subblock can with zero threshold, in each OFDM subblock, the largest k be obtained by: LLR values are used to determine which k subcarriers are M (β) (β) modulated by A, whilst the others are considered to be X , I =arg min M X (β)∈X ,I(β) modulated by B . After the estimation of index pattern for each OFDM subblock, the data symbols can be demod- L 2 (β) (β) (β) ulated straightforwardly by the corresponding constellation X (i) − H (i)X (i) , (25) r demappers. i=1 LLR detection for GDM-OFDM [47] is more complicated, (β) (β) (β) where I is the index pattern of X , Xr (i) is the ith since the number of activated subcarriers in each OFDM sub- (β) element of the βth received OFDM subblock and H (i)= block is alterable, which is chosen from K = {k1, k2,...,kT }. H (βL + i). The ML detection for EGSIM-OFDM, GDM- Therefore, the computational complexity of the LLR detec- OFDM, ZTM-OFDM and MM-OFDM-IM are more compli- tion is T times of the complexity required by DM-OFDM. cated, since larger sets of OFDM subblock realizations have to Specifically, for each OFDM subblock, LLR detection is be considered due to alterable number of activated subcarriers conducted assuming that the number of subcarriers modu- and/or multiple constellation modes. lated by MA is ki for 1 ≤ i ≤ T. Then the data symbols The ML detector maximizes the minimum ED between are demodulated according to the corresponding estimated (β, ) the received OFDM subblock with different subblock realiza- index patterns, yielding the T possible solutions X ki = (β, ) (β, ) (β, ) tions by exhaustive search, and its computational complexity [X ki (1) X ki (2) ···X ki (L)] for 1 ≤ i ≤ T . increases significantly with the sizes of constellation alpha- Afterwards, the ML estimate of the data symbols and cor- bets, the numbers of activated subcarriers per subblock and responding index pattern for the ith OFDM subblock can be the number of constellation modes. Therefore, for systems determined based on these T potential solutions as with large sizes of constellation alphabets and/or high number β,k β,k of activated subcarriers, the log-likelihood ratio (LLR) algo- I , X =argmin k∈K rithm [46] is invoked for reduced-complexity detection at the L 2 cost of slight performance degradation. For the ith OFDM (β) (β) β,k X (i) − H (i)X (i) . subcarrier of DM-OFDM, where 0 ≤ i ≤ N − 1, the loga- r =1 rithm of the ratio between the a posteriori probabilities for the i (28) events whether the subcarrier is modulated by MA or MB is calculated as LLR detection for ZTM-OFDM [48] can be partitioned into MA two steps: 1) perform LLR detection to find the indices of Pr X (i)=S , |X (i) q=1 A q r I I ∨I γi =ln . (26) activated subcarriers, denoted as C = A B ; 2) perform MB | j =1 Pr X (i)=SB,j Xr (i) LLR detection again on the subcarriers corresponding to IC M From (26), it is seen that the ith subcarrier is more likely to be to distinguish the subcarriers modulated by A from those M M γ > modulated by B . activated by A if the LLRi 0, and vice versa. Noting MA Since the LLR detection algorithm of [49] cannot be applied the two aprioriprobabilities =1 Pr(X (i)=S , )=k/L q A q to the MM-OFDM presented in this paper, we detail our MB − / and j =1 Pr(X (i)=SB,j )=(L k) L as well as the fact LLR detection for this MM-OFDM system. Denote the initial σ2 of the channel AWGN having average energy w =No,(26) detection constellation set and its corresponding index set by can be simplified by applying Bayes’ formula as M(0) {M , M ,...,M }, all = 1 2 nMM (29) MA − 2 MB k Xr (i) H (i)SA,q Q(0) { , ,..., }, γi =ln +ln exp − = 1 2 nMM (30) M (L − k) No A q=1 (0) (0) respectively. The size of Q is denoted by |Q |.Fortheβth MB 2 β − Xr (i) − H (i)SB,j subblock, the corresponding FD channel coefficients [H (( − ln exp − . (27) β − ··· β T No 1)L +1) H (( 1)L +2) H ( L)] are first sorted in j =1 descending order according to their moduli, yielding, |H ((β − After the LLR calculation of the N subcarriers using (27), 1)L + i1)|≥|H ((β − 1)L + i2)|≥···≥|H ((β − 1)L + iL)|. for each OFDM subblock, there should be k subcarriers with An L-stage LLR calculation procedure is invoked to determine positive LLR values and the other (L − k) subcarriers with neg- by which constellation mode the il th subcarrier is modulated ative LLRs, which define a legitimate index pattern. However, for l =1, 2,...,L. Since the number of subcarriers modulated under extremely noisy conditions, there may exist illegitimate by Mj is kj for 1 ≤ j ≤ nMM in each subblock, during the MAO et al.: NOVEL IM TECHNIQUES: SURVEY 327 Fig. 8. BER performance comparison between DM-OFDM of 1.33 bits/s/Hz Fig. 9. BER performance comparison between the ML and LLR detectors and conventional OFDM of 0.89 bits/s/Hz [46]. for EGSIM-OFDM and DM-OFDM under both AWGN and frequency- selective Rayleigh fading channel conditions. The system’s spectral efficiency is 2.22 bit/s/Hz. iteration procedure, if the number of the estimated subcarriers M M modulated by j reach kj , the constellation mode j should the frequency-selective Rayleigh fading channel and given be removed from further consideration. Therefore, we define SNR ≥ 17 dB, the DM-OFDM outperforms the conventional the constellation set and its corresponding index set at the lth OFDM. More specifically, at the BER level of 5 × 10−4,the iteration respectively as DM-OFDM attains around 2 dB SNR gain over the conven- (l−1) tional OFDM. Under the AWGN channel with SNR > 5dB, (l) M \M, k reached at (l − 1)th iteration, M = all j j 0.44 bit/s/Hz spectral efficiency gain is attained by the DM- all M(l−1), , all otherwise OFDM over the conventional OFDM without suffering from (31) a BER performance degradation. (l−1) Q \ j , k reached at (l − 1)th iteration, The detection complexities per subblock of various IM- Q(l) = j Q(l−1), otherwise. OFDM schemes using ML detection are compared in Table III, in terms of the number of complex multiplications required, (32) where the operator ζ2 outputs the largest power-of-2 inte- ( ) At the lth iteration, where 1 ≤ l ≤ L,the|Q l | LLRs are ger smaller than ζ, and O(M ) stands for on the order of M. calculated for the il th subcarriers, as given in (33)asshown From Table III, it can be seen that except for SIM-OFDM and at the top the previous page. Assume that the index of the ESIM-OFDM which suffer from the drawback of low spec- (l) largest LLR value among these |Q | LLRs is jl . Then the tral efficiency, all the other IM-OFDM schemes impose high i th subcarrier is considered to be modulated by M .The computational complexity when employing ML detection. l jl iterative procedure is continued until l = L, and all the L Specifically, the computational complexities of these schemes subcarriers are classified. After obtaining the index pattern, increase significantly with the systems’ parameters, such as the the index bits can be recovered with the aid of look-up table, subblock size, the number of activated subcarriers, and/or the and the symbol bits for each subcarrier are easily demodulated constellation size. Therefore, the sub-optimal LLR detectors using ML detection. play an important role in realizing low-complexity IM-OFDM 6) Performance Analysis: With their superior spectrum systems. For example, for the LLR-based GSIM-OFDM and and energy efficiency, IM-OFDM schemes, especially, multi- DM-OFDM systems, the detection computational complex- mode IM-OFDM schemes, are capable of achieving better ities, in terms of the number of complex multiplications BER performance over the conventional OFDM of the same required, are on the orders of O(LM ) and O(L(MA + MB )), throughput. In other words, IM-OFDM is capable of attain- respectively, which are dramatically lower than those imposed ing a spectral efficiency gain over the conventional OFDM, by ML detection. Moreover, as demonstrated by the simula- while achieving a similar BER performance as the latter. tion results given in [41] and [46], the LLR-based detectors Taking DM-OFDM for instance, Fig. 8 compares the BER for GSIM-OFDM and DM-OFDM only suffer from slight performance of the DM-OFDM at 1.33 bit/s/Hz with those of performance loss, compared to their optimal ML counterparts, the conventional OFDM at 0.89 bit/s/Hz under both the AWGN which are also illustrated in Fig. 9. Specifically, given the same and the frequency-selective Rayleigh fading channel environ- system’s spectral efficiency of 2.22 bit/s/Hz, Fig. 9 compares ments, where the ML detection is employed [46]. The system’s the BER performance attained by the ML and LLR detec- SNR is defined as SNR = Eb/N0, where Eb denotes the tors for GSIM-OFDM and DM-OFDM under both AWGN and σ2 average energy per bit and N0 = w is the power spectral frequency-selective Rayleigh fading channel conditions. It can density of the channel’s AWGN. In addition to the spectral be seen that for both GSIM-OFDM and DM-OFDM, there is efficiency gain of 0.44 bit/s/Hz, it can be observed that under only marginal performance gap between the LLR detection 328 IEEE COMMUNICATIONS SURVEYS & TUTORIALS, VOL. 21, NO. 1, FIRST QUARTER 2019 TABLE III PERFORMANCE COMPARISON OF EXISTING IM-OFDM SCHEMES and the ML detection, and this gap becomes negligible in high-SNR region. Table III also compares the spectral efficiencies and power consumptions of different IM-OFDM schemes. As expected, two trade-offs are witnessed. It can be seen that spectrum more efficient DM-OFDM, GDM-OFDM and MM-OFDM are capable of enhancing the achievable system’s through- put significantly in comparison with GSIM-OFDM and its generalized versions. However, the former schemes tend to consume more energy than the latter schemes. This is the well understood trade-off between spectral efficiency and energy efficiency. Furthermore, the systems, which fully exploit the diversities in I/Q components of subcarriers, the number of constellation modes, and/or the number of activated subcarriers in each OFDM subblock, can attain considerable performance gain but inevitably suffer from complexity increase. This is the well-known trade-off between system performance and Fig. 10. BER performance comparison between MM-OFDM, GSIM-OFDM, computational complexity. A well engineered communication DM-OFDM and conventional OFDM under the frequency-selective Rayleigh system requires careful consideration of these two trad-offs. fading channel [49]. The BER performance, an effective QoS indicator for communication systems, is commonly adopted to investigate DM-OFDM and GSIM-OFDM, with that of the conventional IM-OFDM systems based on Monte Carlo simulation or the- OFDM under the Rayleigh fading channel condition based oretical analysis. Using Monte Carlo simulations, the BER on Monte Carlo simulations [49]. The system parameters performance of various IM-OFDM schemes can be eval- are set as follows to provide similar spectral efficiency for uated in a straight-forward manner. Fig. 10 compares the different systems. Conventional OFDM: 32-QAM is used; BER performance of three IM-OFDM systems, MM-OFDM, GSIM-OFDM: 3 out of 4 subcarriers in each subblock are MAO et al.: NOVEL IM TECHNIQUES: SURVEY 329 modulated by 64-QAM; DM-OFDM: 2 out of 4 subcarri- The approximation (39) is considered to be a tight upper ers in each subblock are modulated by 16-PSK; MM-OFDM: bound for x > 0.5, and it is widely adopted in IM-OFDM 4 subcarriers in each subblock are modulated by 4 different schemes for its simplicity [41], [46]. To enhance the approxi- PSK or QAM constellation alphabets. Firstly, from Fig. 10,it mation accuracy, two more expressions of the Q-function were is seen that IM-OFDM schemes are capable of attaining the proposed in [109] based on Prony approximation to the sum SNR gain over the conventional OFDM, at the BER level of of exponential terms, which are given respectively by −3 2 2 10 . Secondly, MM-OFDM is capable of achieving signif- Q(x) ≈ 0.208e−0.971x +0.147e−0.525x , (40) icant performance gain over GSIM-OFDM and DM-OFDM, −0.876x 2 −0.525x 2 −0.603x 2 due to its superior spectral efficiency. Thirdly, it can be seen Q(x) ≈ 0.168e +0.144e +0.002e , that the MM-OFDM with PSK constellations suffers from (41) serious performance loss compared to its QAM counterpart, where x > 0. In addition, to enhance the tightness of the which indicates that appropriate constellation design is par- approximation in the region of small x, a novel approximation ticularly crucial for MM-OFDM to achieve superior BER of the erfc function, which is the derivative of the Q-function, performance. was proposed in [110]as For IM-OFDM schemes with ML detection in a subblock- 2 − −1.98x −x by-subblock manner, their BER performances are mainly 1 e e√ , erfc(x)= . π (42) dependant on the minimum ED dmin between the different 1 135 x possible realizations of OFDM subblock, normalized by the for x ∈ [0, 20]. For a comprehensive literature review on Q- function approximation, the reader is referred to [111]. square root of Eb, given by Assuming that Pr(X(β) → X(β)|H(β)) is approximated as 1 |H(β) dmin =min Xi − Xj , (34) f (x ), we can calculate the unconditional PEP (UPEP) 1≤ < ≤2p1 i j Eb according to where the average bit energy Eb can be calculated as X(β) → X(β) |H(β) , (N + LCP)Es Pr = EHβ) f x (43) Eb = , (35) pG where EH{·} stands for the expectation with respect to H. in which Es denotes the average symbol energy. Since After obtaining the UPEP of any two possible realizations of a reduced-complexity LLR detector suffers from negligible OFDM subblock, the estimated BER, which is referred to as performance loss compared to its optimal ML counterpart at average bit error probability (ABEP), can be derived as [46] high SNRs, the minimum ED metric dmin is also capable of 1 (β) (β) (β) (β) characterizing the performance of LLR detection. ABEP = Pr X → X E X , X , p · 2p Furthermore, PEP is also widely used to evaluate IM-OFDM X(β)=X (β) systems, which is defined as the probability that one transmit- (44) ted OFDM subblock is mistakenly detected as another at RX. To estimate the BER, it is sufficient to investigate only a sin- where E(X(β), X(β)) denotes the number of bit errors for the gle subblock, since the PEP events are identical for different event that X(β) is mistakenly detected as X(β). OFDM subblocks [41], [46]. The conditional PEP (CPEP) of Remark: Empirically, there exist inevitable and non- (β) (β) X being wrongly detected as X given the knowledge of negligible estimation errors between the ABEP (44) and the (β) the channel state information (CSI) H is defined by Monte Carlo simulated BER at low SNRs, because of the ! approximation in deriving this ABEP. However, at the high- (β) (β) (β) Esρ Pr X → X |H = Q , (36) SNR region, the ABEP is a tight upper bound of the actual 2No BER. In fact, for IM-OFDM systems with lower spectral effi- (β) ciency, tighter BER bound is more likely to be achieved using where Q(·) is the standard Gaussian Q-function, X and (β) PEP calculation, for the reason that there are less possible real- X are arbitrary elements of X , while ρ is calculated by izations of OFDM subblock, yielding reduced operations for (β) (β) (β) ρ = diag X − X H . (37) the UPEP calculation with less approximations. This empiri- cal observation is also demonstrated by the simulation results Since there is no closed-form solution for the CPEP given in [41] and [46]. in (36), several schemes were proposed to approximate the To validate the accuracy of our PEP analysis, we consider Q-function [106]Ð[110]. In [106], a tight but complicated the ZTM-OFDM [48]. Fig. 11 compares its simulated BER approximation of the Gaussian Q-function is formulated as performance with the corresponding ABEP results under the 1 − 2/2 frequency-selective Rayleigh fading channel at the spectral Q(x) ≈ √ √ e x , (38) 2π 0.661x +0.339 x 2 +5.510 efficiency of 2.22 bit/s/Hz and 1.33 bit/s/Hz, respectively. It is observed that, at low SNRs, there inevitably exists notice- for x > 0. To simplify the expression, the works [107], [108] able difference between the simulated results and analytical propose an exponential bound of the Q-function less accurate ABEP results, because of the approximation in the ABEP devi- than (38) in general, which is expressed as ations. However, at high-SNR region, the difference between 1 − 2/2 1 −2 2/3 the ABEP results and the simulated BER disappears, which Q(x) ≈ e x + e x . (39) 12 4 demonstrates the accuracy of the PEP analysis. 330 IEEE COMMUNICATIONS SURVEYS & TUTORIALS, VOL. 21, NO. 1, FIRST QUARTER 2019 including [20], [64], [65]. Therefore, this paper will focus on typical SM schemes to help the reader better understand the principles and potentials of SM. 1) SSK or SM: The SM structure was first introduced in [50], in which the authors proposed the space shift key- ing (SSK) scheme to convey information bits by the index of single activated TX antenna. For example, when two antennas are employed at the TX, bits “0” and “1” can be transmitted by activating the 1st and 2nd antennas, respec- tively. Afterwards, generalized SSK (GSSK) was proposed in [51], where multiple antennas are activated to convey infor- mation bits, leading to considerable spectral efficiency gain but also causing severe IAS issue. Since then the interests in SSK grew, and many studies were conducted, includ- ing channel-coded and feedback-based design, performance evaluation via theoretical analysis, and system parameter Fig. 11. Comparison between the analytical ABEP results and the simu- optimization [37], [116]Ð[122]. lated BER performance for the ZTM-OFDM at 2.22 bit/s/Hz and 1.33 bit/s/Hz, At first, the difference between SSK and SM was ambigu- respectively, under the frequency-selective Rayleigh fading channel [48]. ous until 2009 when the concepts of SSK and SM were clearly classified [123]. It is now generally understood that in SSK, information bits are only conveyed by the index of Before we close the discussion on FD based IM tech- single activated antenna and the actual transmitted signal does niques, we point out IM-OFDM schemes have been applied not carry information bits. By contrast, in SM, in addition in practical communication systems, owing to their advan- to information bits conveyed by the index of single activated tages of low energy consumption and additional spectral antenna, the actual transmitted signal is modulated by APM efficiency gain as well as additional diversity gain in the and, therefore, it carries information bits. According to this subcarrier-index domain, over the conventional OFDM. For classification, SSK is viewed as a special case of SM. Unlike example, IM-OFDM was invoked in vehicle-to-vehicle and SSK, since both APM and IM are employed for data transmis- vehicle-to-infrastructure communications, where the interleav- sion in SM, it is more suitable for high-rate data transmission ing technique was incorporated [112], and independent IM was and has attracted great attentions from the research commu- performed on I/Q components to increase the index bits [113]. nity. For instance, in [52], the combined scheme of SM and Physical-layer security techniques can be applied to FD-IM OFDM (SM-OFDM), was proposed, in which only one TX systems to enhance the systems’ data secrecy [114], [115]. antenna is activated during each OFDM symbol transmission Specifically, for time division duplexing (TDD) protocol based with extra information bits conveyed by the index of activated systems, the CSI of the legitimate link can be utilized as antenna. the secret key by exploiting the channel reciprocity property. With the help of this legitimate CSI based secret key, the 2) Typical SM Based Systems: Compared with BLAST- study [114] adopted joint optical subcarrier index selection and type OFDM and Alamouti-type OFDM, SM-OFDM achieves adaptive interleaving to enhance the secrecy, while maintaining dramatic reduction in computational complexity while attain- reliable data transmission. The work [115] applied random- ing significant BER performance gain [52]. However, there ized mapping rules between the data symbol bits/index bits exists a trade-off by only activating single TX antenna, very and the symbol/index pattern, resulting in a high BER at the similar to the case of GSIM-OFDM. Specifically, although eavesdropper. SM-OFDM achieve considerable reduction in system com- plexity and is free from ICI, the additional index bits conveyed by the index of activated antenna cannot compensate for the B. SD Index Modulation throughput loss due to empty TX antennas, particularly for SD-IM, also known as SM, is capable of providing high- high spectral-efficiency systems. In general, the design of an rate and reliable data transmission with much lower system SM-based system is a careful trade-off between the system’s complexity compared to other MIMO systems. In SM, only complexity and achievable throughput or BER performance. a single TX antenna is employed for data transmission for Two improved SM schemes, generalized SM (GSM) [53] each signaling time slot, where the activated antenna index and multiple active-spatial modulation (MA-SM) [54], both carries additional log2 Nt bits information. Since only one employing multiple nrf TX antennas for data transmission, antenna is activated all the time, ICI is avoided, leading which enlarges the possible realizations of antenna activation to reduced detection complexity. Furthermore, unlike stan- pattern and attains higher diversity ‘gain’ over the classical dard spatial multiplexing MIMO using multiple antennas for SM.6 By activating nrf TX antennas simultaneously, rather simultaneous data transmission, which may require multiple than a single TX antenna, the antenna activation pattern of expensive RF chains [65], only a single RF chain is required in SM, leading to low-hardware-complexity implementation. 6The concept of diversity here is not a classical one. SM systems have There already exist comprehensive literature reviewing SM, inherently capability of spatial diversity against the spatial channel fading. MAO et al.: NOVEL IM TECHNIQUES: SURVEY 331 components separately. More explicitly, for each signaling time instant, one M-QAM symbol is generated as usual but its real and imaginary parts are transmitted by two differ- ent activated antennas. By this arrangement, QSM is capable of doubling the diversity gain. Moreover, the ICI is com- pletely avoided since the signals on two activated antennas are orthogonal. The data rate of QSM is formulated as RQSM =2log2 Nt +log2 M [bpcu]. (47) It can be seen that the idea of QSM is very similar to the aforementioned EGSIM-OFDM2 [42], where IM is per- formed on the I/Q components of each subcarrier separately. It is also worth pointing out that the idea of the improved EGSIM-OFDM2, namely, EGSIM-OFDM-JIQ [90], can also Fig. 12. Transmitter structure of MA-SM. be applied to QSM in order to further enhance its data rate. An interesting SM system design called precoded or pre- processed SM (PSM) was proposed in [58] and [59]. Unlike GSM and MA-SM is capable of conveying log Nt index 2 nrf the aforementioned SM schemes which perform IM on TX bits, compared to log2 Nt bits for classical SM. The differ- antennas, RX antennas are considered in PSM, whose indices ence between GSM [53] and MA-SM [54] is that for GSM, carry additional information bits. Specifically, a preprocess- all the activated antennas are modulated by the same symbol, P p p ···p ing matrix =[ 1 2 Mp ] containing the Mp different whilst for MA-SM, different symbols are transmitted by dif- preprocessing vectors is pre-stored at the TX and RX. For ferent activated antennas. Fig. 12 presents the TX of MA-SM, each signaling time instant, an M-ary transmitted symbol xt where m binary bits are firstly divided into m1 index bits and p is multiplied by the chosen vector i from the preprocessing m2 symbol bits with the aid of a bit splitter. The m1 index bits matrix, where the index of the chosen preprocessing vector are fed into an antenna index selector to activate nrf antennas conveys log2 Mp binary bits. The optimization of P can be for data transmission, while the m2 symbol bits are divided carried out by maximizing the throughput whilst minimizing m2 equally into nrf parallel streams of bits each, which are nrf the interferences on the other antennas [58], which is very modulated by nrf M-ary constellation mappers, respectively, complicated. One feasible and simple design of PSM is to to generate a nrf -dimensional transmit symbol vector. The ele- apply precoding targeting at only single RX antenna, where ments of this transmit symbol vector are then allocated to the Mp = log2 Nr , so that the received vector only has one non- nrf activated antennas according to the antenna activation pat- zero element for each signaling time instance, and its index tern. Clearly, the index bits m1 and the number of activated TX Nt carries additional information. This is equivalent to perform- antennas nrf is related by the relationship m1 = log . 2 nrf ing IM on the RX antennas. This simplified system design is The TX of GSM is similar to that of MA-SM except that the adopted in our description. Inspired by the idea of MA-SM, m2 symbol bits are modulated by a single M-ary constella- generalized PSM (GPSM) was proposed in [60] by activat- tion mapper and the resulting transmit symbol is allocated to ing multiple nrf RX antennas for data transmission, where the nrf activated antennas according to the antenna activation two practical issues, negative effects of imperfect CSI at the pattern. Thus, the data rates of GSM and MA-SM, in terms TX (CSIT) and the low-rank approximation employed for of bits per channel use (bpcu), are given respectively by large-dimensional MIMO systems, were investigated, and a reinforcement matrix was applied to attain further performance Nt , RGSM =log2 M + log2 [bpcu] (45) gain. Clearly, PSM can be viewed as a special case of GPSM n rf with nrf =1. The TX structure of GPSM is shown in Fig. 13. nrf Nt RMA−SM =log2 M + log2 [bpcu]. (46) Similar to MA-SM, at each signaling instant, m binary bits nrf are mapped onto nrf M-ary symbols and the corresponding Since in general 2m1 < Nt , only a subset of 2m1 activated index pattern. The nrf resultant symbols are preprocessed to nrf t produce an N × 1 signal vector with the aid of the nrf × N antenna combinations, out of the total of N combinations, r r nrf RF switch, where the indices of non-zero elements correspond are used for data transmission. A feasible solution of select- to the input index pattern, and additional information bits are ing 2m1 antenna activation patterns was proposed in [53], conveyed by the activation pattern of the RX antennas. After where the BER value is approximated using the union bound- an N × N precoding operation, the N × 1 vector is fed to ing technique [124], and the selection of activated antenna r t t the TX antennas for data transmission. If M-ary constellation combinations is attained by minimizing the BER expression. is employed for modulation, the data rate of GPSM is Attracted by its distinctive merits, MA-SM was applied to Nr STBC systems [125] in order to attain extra spectral efficiency RGPSM = log2 + nrf log2 M [bpcu]. (48) gain as well as to optimize the diversity and coding gains. In nrf 2015, quadrature spatial modulation (QSM) was proposed to Moreover, inspired by QSM, generalized precoded QSM fully exploit both the in-phase and quadrature dimensions [55], (GPQSM) was proposed in [126], where both the I/Q in which SM is conducted on both the in-phase and quadrature components of the RX antennas are employed for separate 332 IEEE COMMUNICATIONS SURVEYS & TUTORIALS, VOL. 21, NO. 1, FIRST QUARTER 2019 TABLE IV ALOOK-UP TABLE OF ESM-2TX WITH QPSK PRIMARY CONSTELLATION AND TWO DIFFERENT BPSK SECONDARY CONSTELLATIONS Fig. 13. Transmitter structure of GPSM. is activated, and two secondary alphabets M1 and M2 when both TX antennas are activated, where the size of M0 is M IM. GPQSM doubles the index bits, compared to GPSM, and while the size of M1 and M2 is M/2 so that information bits its data rate is formulated as carried by different subblocks are equal. Table IV illustrates Nr an ESM system with Nt =2(ESM-2TX), where QPSK pri- RGPQSM =2 log2 + nrf log2 M [bpcu]. (49) nrf mary constellation, M0 = {1+j, 1 − j, −1 − j, −1+j}, and two different BPSK secondary constellations, M1 = {1, −1} Remark: In comparison with the other SM schemes which and M2 = {j, −j}, are employed. The four possible antenna perform IM on the TX antenna domain, the PSM-based patterns are listed in the left column of Table IV, which con- schemes convey index information in the RX antenna domain. vey two index bits, while the corresponding transmitted signal IM on the RX antenna domain is totally independent from IM vectors are given in the right column of Table IV. More specifi- on the TX antenna domain. Therefore, there is considerable cally, when only one antenna is activated for data transmission, scope for further research to perform IM simultaneously on QPSK is employed with data symbol S4 ∈M0 to gener- the TX and RX antennas, which is capable of further enhance ate two activation patterns. By contrast, when both antennas the achievable system’s performance significantly, in terms of are used, two BPSK constellations are used, respectively, with both throughput and diversity enhancements. (1) (2) S ∈M1 and S ∈M2 to produce two more activation Although the data rates of the aforementioned modified SM 2 2 patterns. In general, for ESM-2TX with the size of primary systems have been enhanced in comparison with the standard constellation equal to M, its data rate is given by SM, there still exists a throughput gap between these schemes and classical spatial multiplexing MIMO. For instance, given RESM−2TX =log2 M +2 [bpcu]. (50) Nt = Nr =4and 16-QAM modulation, the data rate of spatial multiplexing MIMO is 16 [bpcu], whereas for MA-SM Clearly, the three constellations, M0, M1 and M2,must and GPSM with nrf =2, the data rate equals to 10 [bpcu]. be mutually distinguishable in order to facilitate accurate Even combined with QSM, the data rate of GPQSM can only demodulation at the RX. be raised to 12 [bpcu]. It can be seen that this is similar to The ESM technique can further be generalized by employ- the case of GSIM-OFDM. Specifically, when constellations of ing more TX antennas and more constellations, which is lower order are utilized, the SM-based schemes are capable of detailed in [56]. Moreover, in order to achieve higher through- achieving throughput gain over spatial multiplexing MIMO. put and better BER performance, novel design strategies were However, for high-order constellations, spatial multiplexing proposed to ESM in [57]. Since ESM signals are transmit- MIMO provides higher-rate data transmission than its SM ted in a vector manner, the system BER is determined by counterparts. This is because for high spectral efficiency the normalized minimum ED between the different possi- systems, extra information bits conveyed by antenna activa- ble realizations of the transmitted vector similar to (34). To tion index are insufficient to compensate for the throughput attain SNR gain, therefore, one needs to enlarge the normal- loss due to empty antennas. ized minimum ED. To achieve this objective, a constellation To mitigate this inherent throughput loss of SM-based design needs to ensure that the minimum ED between differ- schemes, an enhanced SM (ESM) scheme with multiple ent transmitted vectors is no smaller than the minimum ED antenna patterns and signal constellations was proposed between the constellation points within each employed alpha- in [56], where information bits are carried by different com- bet, and at the same time, to enable that more realizations of bination of antenna activation patterns and symbol constella- transmitted vector are generated to convey more index bits, tions. Explicitly, for each signaling time instant, the number which is equivalent to enlarge the normalized minimum ED. of activated antennas is variable and different constellation In the work [57], three designs were developed, namely, ESM- alphabets are employed, which considerably increases the pos- Type 1 and ESM-Type 2 as well as their combination called sible realizations of the transmitted signal vector, leading ESM-Type 3. In ESM-Type 1, a 4-TX-antenna ESM system to an enhanced throughput. For instance, for systems with is considered, where one M-QAM primary constellation and Nt =2TX antennas, a possible antenna and constellation a distinguishable M/2-size secondary constellation are used combination, referred to as a subblock, is designed by employ- for modulation. For each signaling time instant, only nrf =2 ing a primary constellation alphabet M0 when one TX antenna antennas are activated, which are modulated by one primary MAO et al.: NOVEL IM TECHNIQUES: SURVEY 333 constellation symbol and one secondary constellation point, respectively. With this arrangement, each transmitted vector is capable of doubling index bits in comparison with GSM with nrf =2. ESM-Type 2 attains even higher throughput gain by expanding the transmitted signal space. Specifically, for systems with Nt =4, and nrf =2, a union of 4 subspaces L = {L1, L2, L3, L4} (51) is designed from which the transmitted vector s ∈Lis selected [57]. Each of the subspaces L1, L2 and L3 consists of 4 different activation patterns. For each of these activation patterns, the two activated antennas are modulated by two dif- P S ferentiable constellation constellations M /2 and M /2, both having the size of M/2. Thus log2 M symbol bits are con- veyed by each of these three subspaces, and additional 2 prefix bits are conveyed by the index of selected subspace. As for Fig. 14. Transceiver structure of FDE-aided SC-IM. the subspace L4, it contains 8 activation patterns, and two different constellations used for modulating L4 should also the secrecy of SM systems [134]Ð[136]. Explicitly, jamming convey log2 M symbol bits. Moreover, the activation patterns signals were used in [134] and [135], while the randomized in L4 should be specially designed, so that the minimum ED mapping rule between the antenna activation pattern and index between transmitted vectors is unchanged. It can be seen that bits was utilized in [136], both approaches utilizing the CSI the design of this ‘expanded’ subspace L4 is complicated, of the legitimate link as the secret key. which can be found in [57]. Before concluding our presentation for typical SM-based C. TD Index Modulation systems, we briefly comment on their RX designs. Since the signals are transmitted in a vector form for almost all the Various TD-IM schemes can be classified into two classes: SM-based systems, the optimal ML detection can be directly schemes performing IM on time slots of signaling frame applied, similar to the ML detector for IM-OFDM schemes. and schemes conducting IM on dispersion matrices of STBC Nevertheless, due to the significantly increased detection system. According to this classification, below typical TD-IM complexity, the optimal ML detector may not be suitable schemes are briefly illustrated, in terms of their principles as for practical implementation, and several reduced-complexity well as the achievable system performance. sub-optimal detectors were proposed as a trade-off [54], [125]. 1) IM Carried Out on Time Slots: As mentioned previously, 3) Discussion: Because of its promising performance as in the uplink of many current wireless standards, SC-FDE well as high energy efficiency, SM has been introduced to dif- is usually employed for data transmission over SISO dis- ferent applications, including wireless networking [127], [128] persive channel for its low PAPR and low TX complex- and VLC [129]Ð[133], etc. In various existing SM-based ity [2], [137], [138]. To enhance the energy efficiency of systems, IM is performed on different entities, such as the conventional SC-FDE, a pure TD-IM scheme called single- indices of TX and RX antennas, the I/Q components of carrier IM (SC-IM) was proposed by performing IM on time transmitted signals, and the selection of used precoding vec- slots of each transmit frame [26], where only part of the time tors, etc. All these IM designs achieve significant diversity slots are occupied for data transmission, and the others are gains over classical spatial multiplexing MIMO. However, kept empty. With this arrangement, in addition to the conven- due to intentional empty TX antennas, the spatial resources tional APM bits, extra information bits are conveyed by the are under-utilized in SM based systems, which may lead to indices of the activated time slots with no energy consumption. inevitable throughput loss. To address this issue, consider- The transceiver structure of the FDE-aided SC-IM system is able research efforts have been directed towards designing depicted in Fig. 14. A total of l × p binary bits are parti- ESM systems, which attain considerable throughput gain at tioned into l × p1 bits for the index selector and l × p2 bits the cost of increasing design complexity and detection com- fed to the M-ary constellation mapper to generate the l sub- s(i) (i) (i) ··· (i) T ≤ ≤ plexity. This in turn demands more effective system design frames =[s1 s2 sls ] for 1 i l. Since only and low-complexity detector design. In this survey, we have afractionofthels time slots in each subframe are utilized (i) concentrated on a few typical SM based systems, with the for data transmission, sj of the jth time slot can either be an aim of promoting the understanding of SM principle. In the M-ary symbol or 0, where 1 ≤ j ≤ ls . The overall transmis- literature, there exist numerous researches focusing on vari- sion frame of length Ns = l × ls is obtained by concatenating ous aspects of SM based systems, including enhanced system the l subframes as s =[(s(1))T (s(2))T ···(s(l))T]T.After design, performance evaluation and system optimization. The adding the CP of length LCP, the resultant signals are trans- reader is referred to the existing survey papers [20], [64], [65] mitted through the fading channel, and the received signals are and the references therein for more details. equalized by the one-tap FDE based on the MMSE criterion. Data confidentiality is clearly an important issue for practi- Finally, the data symbols and corresponding index pattern are cal SM systems. Several works have been proposed to enhance jointly estimated with ML detection. Assuming that k time 334 IEEE COMMUNICATIONS SURVEYS & TUTORIALS, VOL. 21, NO. 1, FIRST QUARTER 2019 slots are activated in each subframe, the data rate of SC-IM is formulated by ls Ns k log2 M + log2 k RSC−IM = [bit/frame]. (52) (Ns + LCP)ls It can be seen that TD-IM is equivalent to FD-IM, where time slots are analogous to subcarriers. The dual-mode IM technique used in DM-OFDM can also be applied to SC-IM, yielding the dual-mode SC-IM (DM- SCIM) scheme [28], where the ls time slots of each subframe are activated by two distinguishable constellation alphabets. By assuming that k time slots of each subframe are modu- Fig. 15. Transmitter diagram of GSTSK. lated by MA-ary constellation, and the others are modulated by MB -ary constellation, then its data rate can be calculated as ST-IM can be represented by k ls −k ls Ns log2 MAMB + log2 k Nns RDM−SCIM = Nns k log2 Nt + log2 + k log2 M (N + LCP)l k s s RST−IM = [bits/frame]. (53) Nns + LCP [bpcu], (55) Additionally, the faster-than-Nyquist (FTN) rate sampling technique is incorporated to SC-IM and DM-SCIM, respec- in which klog2Nt is the number of the bits transmitted by Nns tively, in [28] and [29] to enhance the data rate over the SM, log2 k is the number of the TD index bits, and standard SC-IM and DM-SCIM, at the cost of higher k log2 M bits are transmitted by kM-ary symbols. At the RX, intersymbol interference (ISI). For instance, unlike the the optimal ML detector with high complexity can be used for conventional time-orthogonal transmission scheme based joint detection. To reduce the detection complexity, a subop- on Nyquist criterion, where the minimum symbol interval timal 2-stage ST-IM detector was proposed in [30], which is 1 is T0 = 2 W with W denoting the signal bandwidth, the quite similar to the two-stage LLR detector for GDM-OFDM FTN-IM of [29] shortens the symbol interval as T = αT0 systems. At the first stage, a MMSE estimator is employed in which α<1. By using a root raised cosine filter with to obtain the indices of the activated antennas, yielding the a roll-off factor of β, the data rate of FTN-IM can be estimated index bits conveyed by SM. Afterwards, a message derived as passing algorithm is applied in an iterative manner to find the a posteriori probabilities of the activated time slots, which are ls Ns k log2 M + log2 k utilized to recover the data symbols of activated time slots RFTN−IM = [bit/frame]. α(1 + β)(Ns + LCP)ls and their corresponding TD index pattern. Jacob et al. [30] (54) further proposed a 3-stage detector with message passing over a bipartite graph to improve the system reliability. It is worth pointing out that the concept of TD-IM can be 2) IM Carried Out on Dispersion Matrices: Instead of traced back to a much earlier modulation scheme called pulse- using time slots, IM on the TD can be carried out in a position modulation (PPM) [139], which is widely adopted very different but equivalent manner, leading to space-time in optical communications. Specifically, in the Np-PPM, each shift keying (STSK) for MIMO [32]. Unlike SM, STSK is of the symbol duration is partitioned into the Np time slots, capable of striking a flexible trade-off of diversity gain and where only one slot is employed to transmit a pulse, and multiplexing gain. Moreover, like SM, the ICI is completely the others are kept unused. Thus, instead of using the sig- avoided in STSK based systems. Explicitly, for each signaling nal intensity to convey information, log2 Np information bits block, one out of the Q dispersion matrices is selected for data are conveyed by the position of the pulse. In other words, transmission, whose index carries additional information bits. log2 Np bits are embedded in the index of the activated To further enhance the achievable system throughput, general- time slot. ized STSK (GSTSK) [33] was developed by activating P > 1 SM and TD-IM can be combined, resulting in space-time dispersion matrices simultaneously, at the expense of increased IM (ST-IM) for MIMO [30]. More specifically, based on a detection complexity. Since STSK is a special case of GSTSK standard SM system, each signaling frame is partitioned into with P = 1, here only GSTSK is described in detail. Nns time slots, and only k slots are activated for each RF The TX structure of GSTSK employing Nt TX antennas chain, and the others remain empty. Therefore, in ST-IM, in and Nr RX antennas is illustrated in Fig. 15. For each block addition to the information bits conveyed by data symbol and transmission, which is lasting for the duration of Nns time spatial indexing of SM, extra information bits can be carried slots, the p information bits are partitioned into the p1 index by the activation index of time slots. If we assume that M-ary bits and p2 symbol bits. The index bits are employed to deter- constellation is used for modulation and LCP CP symbols are mine the activation pattern of the dispersion matrices, namely, added to each data stream at the TX, then the data rate of selecting the P dispersion matrices {A(1), A(2),...,A(P)} MAO et al.: NOVEL IM TECHNIQUES: SURVEY 335 from the set of the Q pre-designed dispersion matrices " A = A1, A2,...,AQ , (56) where Ai for 1 ≤ i ≤ Q are complex-valued Nt × Nns matri- ces. On the other hand, the p2 symbol bits are further split equally into the P sub-groups, which are modulated by the P M-ary constellation mappers to generate the symbol sequence {s(1), s(2),...,s(P)}. The resultant symbols are multiplied by the corresponding activated dispersion matrices to generate the coded signal matrix S ∈ CNt ×Nns , which is given by P ( ) ( ) S = s i A i . (57) i=1 The signal matrix S is transmitted through the Nt TX antennas over the block duration of Nns time slots, and the received signal matrix Y ∈ CNr ×Nns is represented by Y = HS + W , (58) Fig. 16. BER performance comparison between the conventional SC system, SC-IM and DM-SCIM with two RX antennas under the frequency-selective Nr ×Nt where H ∈ C is the MIMO channel matrix and Rayleigh fading channel [28]. W ∈ CNr ×Nns is the channel AWGN matrix. Given the esti- mated H , ML detector can be employed to detect all the p transmitted bits by considering all the possible combinations and proposed the layered multi-group steered STSK (LMG- of the activated dispersion matrices and data symbols [33]. SSTSK) for MIMO downlink, which combines the multi-user From the aforementioned description, p1 and p2 are given by TX beamforming, STSK and OFDM techniques for simul- taneous data transmission to multiple users. Furthermore, Q p1 = log2 , (59) multi-set STSK (MS-STSK) was proposed in [146]. In MS- P STSK, in addition to the bits transmitted by the STSK . p2 = P log2 M (60) codeword, at each subcarrier, a unique selection of TX Then the data rate for GSTSK is derived as antennas are activated for data transmission, and their indices carry extra information bits. Then, MS-STSK was Q p1 + p2 log2 P + P log2 M extended to include the FD, resulting in multi-space-frequency RGSTSK = = [bpcu]. Nns Nns STSK (MSF-STSK) [146]. Both MS-STSK and MSF- (61) STSK achieve throughput and performance gains over the conventional STSK. The structure of GSTSK is highly flexible and it includes 3) Discussion: IM can be conducted alone in the TD, and a all the existing MIMO structures, such as STBC, BLAST, pure TD-IM scheme is SC-IM. Inspired by the dual-mode IM SSK and SM, as its special cases [33], [140], [141]. Because philosophy of FD-IM, DM-SCIM is proposed to enhance the of its unveiling advantages, the STSK technique has drawn achievable throughput of SC-IM. FTN signaling can also be much attention from the research community. In [142], a soft- incorporated with SC-IM for further performance gain. Fig. 16 decision-aided detector was proposed for STSK and GSTSK, compares the BER performance of the conventional SC system which significantly reduces the detection complexity with only with those of the two typical TD-IM schemes, SC-IM and DM- slight performance degradation in comparison with the optimal SCIM, under the frequency-selective Rayleigh fading channel maximum a posteriori detector. STSK was further extended at the spectral efficiency of 2.59 bit/s/Hz [28]. To achieve this to include the FD, leading to the space-time-frequency shift high spectral efficiency, the SC system adopts 8-PSK. For the keying (STFSK) scheme [143], where information bits are SC-IM and DM-SCIM, the subblock length is 2, where a sin- also modulated with frequency shift keying (FSK) on the gle subcarrier is activated by 32-ary constellation in SC-IM, FD. Unlike other SD-IM based schemes, which can only be while the two subcarriers are modulated by QPSK and 8-PSK applied to the narrow-bank MIMO channel of (1), STFSK is in each subblock of DM-SCIM. Since a fraction of time slots designed for the frequency-selective MIMO channel. In [32], in SC-IM are intentionally unused to convey index bits infor- the differential STSK was also proposed, where the signals mation, higher-order constellation alphabet has to be adopted are differentially encoded at TX with the aid of Cayley uni- to reach the same data rate as the conventional SC system and tary transform, and hence the CSI is not required at the RX. As DM-SCIM, leading to inevitable high performance penalty. a continuous work, in [144], OFDM was amalgamated with Consequently, SC-IM suffers from severe performance loss in differential STSK, and the iterative soft multiple-symbol dif- comparison with the other two schemes, as can be seen from ferential sphere decoder was employed to obtain the SNR gain Fig. 16. Similar to GSIM-OFDM, SC-IM can outperform its over the conventional soft-decision-aided differential detec- non-IM-aided counterpart only at low data rate. By contrast, tion method. More recently, Hemadeh et al. [145] generalized DM-SCIM can outperform the conventional SC system at high the concept of STSK to the multi-user MIMO scenario, data rate, as can be observed from Fig. 16. Specifically, at the 336 IEEE COMMUNICATIONS SURVEYS & TUTORIALS, VOL. 21, NO. 1, FIRST QUARTER 2019 TABLE V PERFORMANCE COMPARISON OF TYPICAL TD-IM SCHEMES BER level of 10−3, DM-SCIM attains 1 dB SNR gain over the conventional SC system. IM can also be performed in both the SD and TD, and two examples are ST-IM and STSK or its generalized version GSTSK. However, the IM operations are carried out very dif- ferently by ST-IM and GSTSK. ST-IM can be viewed as the combined SM and SC-IM, where IM operations in the TD and in the SD are independent. This enables multi-stage detectors Fig. 17. Transmitter diagram of SIMO-MBM. to reduce the detection complexity. By contrast, GSTSK sig- nals are transmitted in a space-time block manner, where the indices of the activated dispersion matrices convey additional logarithm of the TX antenna number, whilst for a MBM information, and IM operations in the SD and in the TD are based system, the extra information bits that can be conveyed correlated. This gives the high flexibility to GSTSK systems. increase linearly with the number of RF mirrors. Since no For these three typical TD-IM schemes, Table V summarizes energy is consumed for transmitting larger number of CD their achieved data rates and the ML detection complexities index bits, the system’s energy efficiency is also naturally per frame or block, in terms of multiplications required. From improved. Moreover, the RF mirrors can be closely placed the aforementioned descriptions, it is observed that STSK and thus no space constraint is imposed on CD-IM. By con- technique can be extended from single carrier system to mul- trast, for SD-IM schemes, such as SM and STSK, the distance ticarrier system by including IM on the FD. Apart from between neighbouring antennas has to be sufficiently large. throughput and performance gains, these STFSK designs are There also exist several challenges in realizing MBM [34]. particularly applicable to frequency-selective MIMO channel An obvious difficulty is that since the number of possible chan- environments. For a comprehensive review of these STFSK nel realizations should be large in order to attain high spectral based schemes, the reader is referred to the survey paper [147] and energy efficiency, training overhead for acquiring these and the references therein. channel states at the RX can be huge. Other difficulties include the possible outage due to unavailability of CSIT and the ran- domness of the states, although MBM is reasonably robust to D. CD Index Modulation channel fading as deep fading does not have permanent effect The concept of CD-IM, also known as MBM, was firstly on variable channel states [35]. proposed in [34]. In MBM, IM operations are not performed Because the advantages clearly outweigh the disadvantages, on the TX or RX entities, such as antennas, subcarriers or MBM has become a promising novel technique to enhance time slots, but on the variable channel states for conveying the BER performance and the system throughput [148]. We additional information [34]. Specifically, by placing special classify various CD-IM systems into two groups: those employ parasitic components, such as RF mirror [36] and electronic single TX antenna, i.e., SIMO based systems, and those utilize switches [37], close to the TX to perturb the rich scattering multiple TX antennas, i.e., MIMO based systems. environment, numerous independent channel realizations are 1) Single-TX-Antenna Based MBM: We use SIMO- produced. These channel states, although unknown to the TX, MBM [34] and differential MBM (DMBM) [61] to illustrate can be made available to the RX through training. Therefore, the basic concept of single-TX-antenna based MBM. the index of the used channel state can be utilize to convey a) SIMO-MBM: The TX of SIMO-MBM system is char- additional information bits. acterized in Fig. 17, where a single RF chain is presented. A Compared to its SBIM counterparts, MBM can significantly block of p binary bits are divided into two sub-groups of p1 enhances spectral and energy efficiency [34], [38]. For exam- and p2 bits, respectively. The block of p1 information bits ple, for SM based systems, the index bits increases with the are fed into the index selector to generate the index pattern I, MAO et al.: NOVEL IM TECHNIQUES: SURVEY 337 differentially encoded DMBM signals are transmitted block- by-block with the block size of n, i.e., each block consists of n time slots. Moreover, RF mirrors are repeatedly switched from state 1 to n sequentially, so that the channel matrix experienced over the ith block can be represented by8 (i) (i) (i) (i) Nr ×n Fig. 18. Transmitter diagram for DMBM. H = h1 h2 ···hn ∈ C . (65) The ith coded transmission block, represented by an n × n which serves as the control signal to determine the on-off sta- matrix, is generated as follows. First, the block of p1 infor- mation bits are utilized by the mirror activation pattern (MAP) tus of the mrf RF mirrors. This selects one used channel state rf n × n P out of the total of 2m possible realizations. The block of p2 generator to produce the permutation matrix i which information bits are modulated as usual by an M-ary constel- has only one non-zero value in each column and in each 9 P lation mapper, and the resultant signal s is then sent to the TX row. There are total of n! permutations of the MAP i , antenna for data transmission. which represent the n! possible channel states that may be Denote the set of all the 2mrf possible channel states by experienced. On the other hand, the block of p2 informa- tion bits are mapped onto the nM-PSK symbols, denoted by H(c) h(c), h(c),...,h(c) , s ··· T ∈ Cn×1 = 1 2 2mrf (62) i =[si (1) si (2) si (n)] . Then the ith uncoded signal block is represented by the n × n diagonal matrix ( ) h c ∈ CNr ×1 D {s } where i is the ith SIMO channel realization, for i =diag i . Thus, the differentially encoded ith signal i ∈{1, 2,...,2mrf }. Further assume that the index pattern block for transmission over the n time slots is given by h(c) corresponds to the nth channel state n . Then the received I n , i =0, y ∈ CNr ×1 X i = (66) signal vector can be expressed as X i−1Pi Di , i ≥ 1, (c) I × X y = hn s + w, (63) where n denotes the n n identity matrix. Clearly, i has only one non-zero value in each column and in each row, and where w ∈ CNr ×1 denotes the channel AWGN vector. In there are total of the n! possible permutations of X i in this order to demodulate the MBM signal, including the index bits sense. Since p1 = log2(n!) index bits and p2 = n log2 M and symbol bits, the RX must have the CSI. That is, it must symbol bits are transmitted over the n time slots, the data rate know which channel state is ‘activated’ or used for the cur- of DMBM is given by rent data transmission. In other words, the RX must have the H(c) 1 knowledge of the channel state set . Therefore, pilots or RDMBM =log2 M + log2(n!) [bpcu]. (67) training sequences are utilized for channel estimation. It can n be seen that since the size of H(c) increases exponentially with At the RX, the received signals are differentially demod- the number of RF mirrors mrf , training overhead imposes a ulated block by block, without the need of CSI. Explicitly, × Y Y practical limitation on mrf , i.e., mrf cannot be too large. The two subsequent Nr n received blocks i−1 and i can data rate of SIMO-MBM is clearly given by be written respectively as Y H (i−1)X W , RSIMO−MBM = mrf +log2 M [bpcu]. (64) i−1 = i−1 + i−1 (68) Y H (i)X W , It was demonstrated in [38] that SIMO-MBM is capable of i = i + i (69) Nr ×n converting the SIMO channel into multiple parallel AWGN where W i ∈ C denotes the corresponding channel channels and, therefore, it is capable of approaching the AWGN matrix. Under the same classical assumption for con- capacity of random coding over an AWGN channel. ventional differential demodulation, namely, if the fading is b) DMBM: It is seen that for the aforementioned SIMO- sufficiently slow, we may have MBM, the CSI is required at the RX for demodulation, H (i−1) H (i). which is usually estimated by training. However, perfect CSI = (70) is impossible to acquire, since estimation errors inevitably Consequently, we have occur during training. Moreover, for MBM systems employ- Y Y P D W# , ing a large number of RF mirrors, training overhead becomes i = i−1 i i + i (71) impractically large. Inspired by differential SM [149], differ- # where W i = W i − W i−1Pi Di also follows a white ential MBM (DMBM) was proposed in [61], so that CSI may Gaussian distribution. Therefore, the ML criterion can be not be required for demodulation at the RX. Fig. 18 illustrates the TX of DMBM system equipped with 8At the lth time slot of every block, although the RF mirrors are placed single TX antenna and a number of RF mirrors or elec- in the same lth state, the SIMO channel vectors experienced in the lth slot 7 of two different blocks will generally be different owing to channel fading. tronic switches. The operations of DMBM is very different Therefore, the block index should be indicated in the channel matrix H. from other MBM schemes, such as SIMO-MBM. Specifically, 9The term ‘mirror activation pattern’ originated from [61] is somewhat misleading, since the MAP Pi has nothing to do with the generation of the (i) 7The TX structure of the DMBM system presented in [61] is incor- ith channel matrix H . In fact, it is the single no-zero value of each column rect. Moreover, [61] did not correctly describe the operations of DMBM, of Pi , in other words, the index pattern, that determines the single channel specifically, how to generate the channel matrix over the transmission block. coefficient experience in the corresponding time slot. 338 IEEE COMMUNICATIONS SURVEYS & TUTORIALS, VOL. 21, NO. 1, FIRST QUARTER 2019 applied to estimate the transmitted data symbols and the the Nt 1×Nr SIMO-MBM systems. Clearly, the data rate for corresponding index pattern, which is formulated as LMIMO-MBM is given by a P , D Y − Y P D , RLMIMO−MBM = Nt log2 M + Nt mrf [bpcu]. (75) i i =arg min i i−1 i i F (72) ∀P i ,Di At the RX, ML detection can naturally be employed for s ··· T where · F stands for the matrix Frobenius norm. With Pi , signal demodulation. By denoting =[s1 s2 sNt ] and (1) (2) (Nt ) the index bits for the ith block are recovered with the aid of H c =[hc hc ···hc ], the received signal vector (74) look-up table, while the symbol bits can be demodulated with can be written as the demapper given D . Furthermore, to reduce the computa- i y H s w, tional overhead, a low-complexity ML detector based on the = c + (76) trace of matrix was also derived in [61]. and the optimal ML detection is carried out according to It is worth pointing out that if fading is fast, the assump- $ 2 tion (70) is no longer valid, and the ML detector (72) will H c, s =argmin y − H cs . (77) suffer from serious performance degradation, leading to BER ∀H c ,s floor, just as classical differential detection systems. We further $ Afterwards, the index bits can be recovered based on H c with point out that the optimal multiple-symbol differential detec- the aid of look-up table, and the symbol bits are demodulated tion and the reduced-complexity multiple-symbol differential from s using the corresponding demapper. The computational sphere detection [150]Ð[152] can be adopted to overcome the complexity of the optimal ML detector (77) increases sig- difficulty caused by fast fading channel, at the expense of a nificantly with the system’s parameters Nt , M and mrf .An increased detection complexity. suboptimal detector based on greedy search was also given 2) Multiple-TX-Antenna Based MBM: After the initial pro- in [35], which largely reduces the detection complexity but posal of SIMO-MBM in [34] and [38], it has drawn con- suffers from inevitable performance loss. Moreover, from the siderable attention from researchers. It can be seen that to information security perspective, artificial noise can be added attain high throughput and diversity gains, the number of RF to the transmitted signals to impose the interference only to mirrors mrf must be large. However, even under the static the eavesdropper, leading to secrecy rate enhancement [153]. channel environment, training overhead is huge, since the pos- b) STCM: By combining Alamouti-STBC and MBM, mrf sible channel states 2 is huge. Moreover, huge storage space space-time channel modulation (STCM) was proposed in [63], is required in RX to store these CSIs for signal detection. which can be viewed as a special case of LMIMO-MBM. a) LMIMO-MBM: To mitigate the aforementioned diffi- Specifically, as in classical Alamouti-STBC, two complex culties, MIMO, i.e., multiple TX antennas, can be applied to symbols, denoted by s1 and s2, are transmitted through 2 split the mrf mirrors equally into the Nt groups for each TX TX antennas in two time slots, and the Alamouti 2 × 2 antenna. Thus, given the same data rate, the training task can transmission matrix is given by N be divided into the t smaller tasks, reducing the overall train- ∗ s1 −s2 ing overhead significantly, and moreover, the detection com- S = ∗ , (78) plexity may be reduced considerably. Explicitly exploiting the s2 s1 desirable merits of combining the spatial multiplexing MIMO where (·)∗ denotes the conjugate operation. Both TX anten- and the idea of MBM, layered MIMO-MBM (LMIMO-MBM) a nas are equipped with mrf RF mirrors, and different channel was proposed in [35]. states can be selected in each time slot. Hence, additional index Let the number of RF mirrors per TX antenna be ma , and a rf bits are conveyed by the corresponding MAPs. Given M-QAM m denote the set of all the 2 rf possible SIMO channel states symbol constellation, the data rate of STCM is given by related to the ith TX antenna by a RSTCM =log2 M + mrf [bpcu]. (79) H(i) h(i), h(i),...,h(i) , = 1 2 ma (73) 2 rf At the RX, similar to the more general case of LMIMO-MBM, ( ) the transmitted symbols and the corresponding index pattern h i ∈CNr ×1 where l denotes the lth realization of the ith can be demodulated using the ML detection [63]. ≤ ≤ SIMO channel vector. Further denote si for 1 i Nt as c) GSM-MBM: As discussed previously, SM based the M-ary symbol transmitted through the ith TX antenna. schemes have low hardware overhead and lower energy con- y ∈CNr ×1 Then the received signal vector can be sumption as well as are robust to ICI. In [36] and [62], the expressed as GSM scheme is combined with the MBM, leading to the Nt (i) GSM-MBM, where IM is performed on both the SD and CD. y = si hc + w, (74) i=1 To achieve even higher performance gain in MIMO-MBM schemes, MAP selection based on ED metric, feedback-based (i) (i) where hc ∈H for 1 ≤ i ≤ Nt denote the SIMO CSIs phase compensation and constellation rotation were applied. actually used for the current transmission, i.e., they corre- Fig. 19 depicts the TX of an Nt × Nr GSM-MBM system Nr ×1 a spond to the current index pattern, while w ∈C is the with mrf RF mirrors per TX antenna. The block of m informa- MIMO channel AWGN vector. It can be seen that an Nt ×Nr tion bits is split into three subblocks of m1, m2 and m3 bits, LMIMO-MBM system can be viewed as the superposition of respectively. The first subblock of m1 bits is further divided MAO et al.: NOVEL IM TECHNIQUES: SURVEY 339 TABLE VI PERFORMANCE COMPARISON OF TYPICAL MBM SCHEMES h(j ) h(j ) ···h(j ) [ 1 2 ma ] denotes the matrix containing all the pos- 2 rf sible channel state realizations for the jth TX antenna, and emj a stands for the 2mrf × 1 vector with all zero elements except e for the mj th element which is equal to 1. Note that mj picks up the mj th channel realization from all the possible realiza- tions of H (j ), which is the currently used CSI as indicated by the MAP. On the other hand, the indices or positions of the nrf nonzero elements in s are specified by the antenna activa- tion pattern. Due to the similar structures of LMIMO-MBM and GSM-MBM, the ML detection (77) can be also applied to GSM-MBM to estimate the antenna and RF mirror index patterns as well as the M-ary symbols. Similar to the derivation of GSM-MBM, by combining QSM and MBM technique, the quadrature channel modulation (QCM) scheme was formed [154], [155], which is capable of improving the performance over both QSM and MBM alone. Fig. 19. Transmitter diagram for GSM-MBM. Here, we only detail the GSM-MBM to demonstrate how to combine SM techniques with MBM. For the QCM, the reader a is referred to [154], [155] for detail. into nrf = m1/mrf parallel streams to determine the index pattern of the RF mirrors for each TX antenna, with the aid 3) Discussion: For the aforementioned five MBM schemes, Table VI summarize their data rates and ML-based detection of an nrf × Nt switching controller. The second subblock of m2 bits is fed into an index selector to generate the antenna complexities, in terms of complex multiplications required. Compared to SBIM, MBM is capable of enhancing the achiev- activation pattern, which determines which nrf TX antennas, able system’s throughput significantly, since the index bits out of the total of Nt TX antennas, are activated for data trans- mission. The third subblock of m3 bits is partitioned equally increase linearly with the number of RF mirrors. Except for the DMBM system, however, the aprioriMBM constella- into nrf parts, and each part is modulated by an M-ary con- stellation before loaded onto the activated antennas. Clearly, tion alphabet or the set of all the channel realizations must m1, m2 and m3 are given respectively by be available at the RX of a MBM system. This set of all the channel realizations is typically acquired by training before a , m1 = nrf mrf (80) data transmission, which imposes huge training overhead, par- Nt ticularly when a large number of RF mirrors are employed. m2 = log2 , (81) nrf Moreover, during the data transmission, when the MAP indi- cates a particular channel state, the actual channel may be m3 = nrf log2 M . (82) different from this channel state acquired in training, unless Therefore, the data rate of GSM-MBM is given by the channel is static. Thus, channel fading seriously affects the performance of MBM systems. This does not seem to be rec- a Nt ognized fully in the existing literature, which often choose to RGSM−MBM = nrf mrf + log2 + nrf log2 M [bpcu]. nrf emphasize the advantage of throughput enhancing capability (83) of MBM. Thus, DMBM is a promising technique for the rea- son that no CSI is required at the RX for demodulation, and ×1 The received signal y ∈ CNr can be modeled by it only suffers from 2 to 4 dB SNR loss, compared to SIMO- MBM with unrealistic assumption of perfect knowledge of the y Nt H (j )e w, = sj mj + (84) j =1 MBM channel state set at the RX [61]. It is worth emphasizing again that even for DMBM, channel fading must be sufficiently s ··· T where =[s1 s2 sNt ] consists of only nrf non-zero slow so that the channels in two consecutive frames remain elements which are M-ary modulated symbols, H (j ) = unchanged. 340 IEEE COMMUNICATIONS SURVEYS & TUTORIALS, VOL. 21, NO. 1, FIRST QUARTER 2019 TABLE VII CLASSIFICATION OF TYPICAL SBIM-AIDED SCHEMES Before concluding the discussion on CD-IM systems, we multiple subcarriers (FD-IM), antennas (SD-IM) or time-slots discuss the issue of MBM constellation design or MAP selec- (TD-IM). IM can activate a single subset of the transmission tion. It is well known that the channel gains can be modelled resources (subcarriers, antennas or time-slots) for transmis- as circularly symmetric complex Gaussian variables. Thus, the sion, leading to ‘single-mode’ class of IM-aided schemes, or Nr -dimensional MBM constellation points or channel states IM can activate multiple subsets of the transmission resources are randomly located, and the distances between any two con- (subcarriers, antennas or time-slots) for transmission, result- stellation points are irregular. In order to improve the system ing in ‘multi-mode’ class of IM-aided schemes. According performance, it is highly desired to only use ‘good’ channel to the modes of IM, most of the IM-aided schemes in FD, states or MBM constellation points. An effective approach to SD and TD can be classified into the single-mode class and do so is to employ a larger number of Mrf (> mrf ) RF mir- multi-mode class, which is illustrated in Table VII. Note that mrf rors, and to choose a subset of msub =2 good channel the transmission resources (subcarriers, antennas or time-slots) Mrf states from the full set of mall =2 possible channel states. are all available physically for data transmission, and by using Two selection strategies were considered in [62], namely, or activating all the available transmit entities, we have the mutual-information (MI) based MAP selection and ED based corresponding traditional non-IM systems. MAP selection. Let the full set of all the mall possible chan- In single-mode class, only a fraction of the transmit entities, H {h , h ,...,h } nel realizations be denoted by all = 1 2 mall . i.e., subcarriers, TX antennas, time slots, or dispersion matri- By arranging all these MBM constellation points in the ces, are activated for data transmission, which are modulated descending order of their energy by a single constellation alphabet, whilst the other subcar- riers remain empty. With the single-mode IM arrangement, h ≥ h ≥···≥h ≥···≥h , (85) l1 l2 lmsub lmall index bits are conveyed by the indices of the activated trans- the MI-based MAP selection, originally proposed in [38], mit entities or resources. By contrast, in multi-mode class, multiple subsets of the transmit entities are activated using chooses the subset Hsub = {h , h ,...,h }, consist- l1 L2 lmsub multiple distinguishable constellation alphabets, and additional ing of the msub largest energy MBM constellation points in order to attain the largest MI. By contrast, the ED-based MAP information bits are also conveyed by the index pattern. selection is based on maximizing the minimum ED between CD-IM systems are physically very different from SBIM different constellation points, and it is capable of achieving the systems discussed above. True, IM can be performed by ‘selecting’ or ‘activating’ a specific channel state from the optimal BER performance. Specifically, let H sub denote the set of potential channel states, and hence it conveys extra bits. channel matrix consisting of msub elements of Hall, and fur- ther denote an arbitrary transmitted signal vector by s. Then But the transmission entity or resource is a single channel state the optimally selected subset channel matrix is given by and, therefore, the single-mode/multi-mode classification does not apply. Physically, there exists no non-IM counterpart of a opt 2 CD-IM system. H sub =argmax min H sub(s − s ) . (86) ∀H sub s=s This optimal ED-based MAP selection scheme is based IV. POTENTIAL CHALLENGES AND OPEN ISSUES on exhaustive search, and it suffers from the drawback of extremely high computational complexity. On the other hand, Based on our comprehensive review of the existing litera- the MI-based MAP selection scheme enjoys the advantage of ture for IM, we now outline the potential challenges and open very low complexity, but suffers from severe performance loss issues that require solutions and further research. compared to the optimal ED-based counterpart [62]. In [156], a greedy iterative algorithm was implemented to find a sub- A. Balance Between Spectral and Energy Efficiency optimal solution of the optimization problem (86), which As underpinned by Shannon’s fundamental capacity, in significantly reduces the computational complexity, while only designing an IM-aided system, there exists a trade-off between suffering from negligible performance loss. the spectral efficiency and energy efficiency. For instance, GSIM-OFDM is more energy efficient than DM-OFDM for the E. Classification of Typical SBIM-Aided Schemes reason that only a fraction of all the subcarriers are employed From the detailed presentations of Sections III-AÐC, it can in GSIM-OFDM, leading to a reduced power consumption. be seen that transmission resources for SBIM systems are However, since all the subcarriers are utilized in DM-OFDM, MAO et al.: NOVEL IM TECHNIQUES: SURVEY 341 it utilizes the frequency resources more efficiently than GSIM- the assumption of the unchanged CSI during two consecu- OFDM. Because the system’s BER performance is mainly tive frames is invalid, further reseach efforts are warranted to determined by the received SNR, to optimize the system’s investigate how to apply multiple-symbol differential detec- performance, it is essential to maximize the received SNR tion and the reduced-complexity multiple-symbol differential by adjusting the system’s critical parameters, such as the sphere detection [150]Ð[152] to differentially encoded MBM number of activated subcarriers in each subblock, the sub- systems. In such a multiple-symbol differential detection based block size, and the employed constellation alphabets, etc. This MBM system, the detection is based on multiple observed optimization is equivalent to balancing the system’s spectral frames. The higher the number of frames considered, the bet- efficiency and energy efficiency. ter the achievable system performance and more robust to From the viewpoint of balancing the system’s spectral effi- the fast fading channel, but the detection complexity may ciency and energy efficiency, the ‘optimal’ FD-IM system may become unacceptably high. It can be seen that this is a clas- take the form between DM-OFDM and GSIM-OFDM, which sical trade-off optimization between detection accuracy and can simply be exemplified by combining some DM-OFDM complexity. and GSIM-OFDM subblocks together for data transmission. The optimization involved, however, is extremely compli- cated, since the received SNR is an implicit function of C. Channel Coding for IM-Aided Systems many system’s critical parameters, where joint optimization Channel coding is a critical technique to achieve a reli- is required. Several existing works, including [87], [88], con- able communication over hostile environment. Representative sidered to optimize a few key parameters for GSIM-OFDM, channel coding methods include Hamming codes [157], where the number of activated subcarriers or the constellations turbo codes [158], low-density parity check (LDPC) are constrained to be the same for each OFDM subblock. In the codes [159], block Markov superposition transmission existing literature, there certainly exists no research addressing (BMST) codes [160], and polar codes [161], which can be the above-mentioned joint optimization design, which is chal- applied to both the APM symbol bits and the index bits in lenging but the gain will be very significant and, therefore, it IM-aided schemes. Although channel-coded systems suffers warrants further research efforts. from inevitable data rate loss and additional computational complexity due to the need of channel encoding and decod- ing, the system performance becomes significantly enhanced B. Trade-off Between Detection Accuracy and Complexity by coding protection of both the symbol bits and index bits, For most IM-aided systems, ML detection is often employed which is a necessary requirement for practical implementa- to detect the transmit symbol vector, such as subblock for tion. However, channel coding is not employed in most of IM-OFDM and transmit frame for TD-IM, which consid- the researches on IM. Some preliminary work has been con- ers all the possible realizations of the transmit signal vector ducted for SD-IM [162]Ð[164]. In [162], polar codes are and minimizes the ED between the candidates and received implemented to protect both the symbol bits and index bits signals. Although attaining the optimal detection accuracy, in SM. The works [163] and [165] apply turbo codes to the the computational complexity of the optimal ML detector trellis coded spatial modulation (TCSM) system, while the increases significantly with the system ’s critical parameters, study [164] utilizes BMST codes to enhance the reliability such as the OFDM subblock length and the size of MBM of SM. Moreover, there have been studies on channel coding constellation alphabet. Therefore, ML detection is unsuitable for FD-IM [166]Ð[168], where LDPC and BMST codes are for large-scale systems. For IM-OFDM and TD-IM schemes, applied to GSIM-OFDM for different applications, including reduced-complexity LLR detection has been employed at the VLC, highly mobile scenarios and power line communica- cost of only marginal performance loss at low SNRs. For tions (PLC), leading to superior BER performance. Recently, SM and TD-IM systems, however, ML detection is mainly LDPC codes have also been employed to protect both the adopted, and there exists very limited literature discussing low- symbol bits and index bits of GDM-OFDM [47], which finds complexity RX design. Moreover, several greedy-based low- that the calculation of soft information for each bit is very complexity detectors for MBM systems suffer from inevitable complicated, and totally different from conventional OFDM. performance degradation. Therefore, it is necessary to develop Since IM is performed on FD signals, conventional methods low-complexity detector with reliable performance, where bet- cannot be applied to obtain the bit soft information, and the ter or even optimal trade-off between the detection accuracy LLR for each subcarrier indicating the index pattern has to and computational overhead can be made. be taken into account. Therefore, the design of channel-coded As mentioned previously, most of MBM based designs suf- IM-aided systems is challenging but necessary for real-world fer from the drawback of high training overhead and can application. To reduce the complexity, a feasible trade-off can only be applied under a static channel environment. DMBM be made by only encoding the symbol bits while leaving the by contrast is a promising design for practical implemen- index bits uncoded or vice versa. tation of MBM, since it does not require the CSI at the More importantly, turbo detection/decoding, in which soft RX. However, DMBM still requires that the channel fad- detection and soft channel decoding operations are carried ing is sufficiently slow, in order to ensure that the CSIs at out iteratively, is the enabling technology to operate near- two consecutive frames remain the same. In order to extend capacity communication systems with affordable complex- the application to the fast fading channel environment where ity [169]Ð[171]. These iterative detection/decoding designs 342 IEEE COMMUNICATIONS SURVEYS & TUTORIALS, VOL. 21, NO. 1, FIRST QUARTER 2019 also do not require accurate CSI and, consequently, can sig- E. PAPR Reduction in IM-Aided OFDM Schemes nificantly reduce training overhead for large-scale MIMO Conventional OFDM signals are notoriously known to have systems, since errors caused by the CSI estimation error can high PAPR, which causes severe nonlinear distortions due to also be corrected by the iterative detection/decoding proce- the nonlinear transfer characteristics of TX devices, such as dure. Future research is therefore warranted to investigate power amplifiers and LEDs. IM-OFDM schemes also suf- how to design turbo detection/decoding for IM-aided systems, fer from the high PAPR problem. Although ESIM-OFDM in order to fully realize their performance potential with and GSIM-OFDM have slightly lower PAPRs, compared to affordable computational complexity. One example is to com- conventional OFDM, their PAPRs are still much higher than bine bit-interleaved coded modulation with iterative decoding other non-OFDM systems, and will cause serious performance (BICM-ID) [172] and IM-OFDM by exchanging soft informa- degradation. For DM-OFDM and MM-OFDM, where all the tion between the index pattern demodulator and the channel subcarriers are modulated, the system’s PAPR is almost the decoder. same as conventional OFDM. Therefore, PAPR reduction techniques must be adopted to IM-OFDM based systems to mitigate the detrimental effects of high PAPR. Some classical D. Multi-Mode Index Modulation PAPR reduction methods, such as clipping [76], SLM [78] and For IM-OFDM, the multi-mode schemes, including DM- PTS [79], can be directly applied to IM-OFDM based systems. OFDM [46], ZTM-OFDM [48] and MM-OFDM [49], achieve But other PAPR reduction techniques need modifications by superior performance over the single-mode counterparts. This taking the signal property of IM-OFDM into consideration in is because when multiple distinguishable constellations are order to achieve better overall performance. For instance, when employed for IM, the number of possible realizations of the ACE algorithm [80] is adopted, the constellation extension OFDM subblock becomes much larger, leading to spectral strategy is correlated to the high-dimensional constellation efficiency enhancement. Furthermore, additional diversity is design of IM-OFDM, which requires joint optimization in harvested by the use of different constellation sets, resulting in order to harvest maximum performance gain. significant performance gain over the single-mode schemes. In All the above-mentioned PAPR reduction techniques trade this paper, we have proposed the generic MM-OFDM scheme, off the system’s PAPR with the spectral efficiency and/or the and have pointed out that the MM-OFDM scheme presented received SNR. It is highly desired to combat the high PAPR in [49] is only a very special case of our MM-OFDM scheme. issue without the need to make such a compromise. For con- Because of its distinctive merits, there is a scope to extend this ventional OFDM downlink, the digital predistorter [81], [82] multi-mode IM approach in the FD to other IM-aided systems can alternatively be adopted to compensate the nonlinear dis- in other domains, such as SM and TD-IM. tortions of the TX power amplifier, while for conventional Multiple constellation design is crucial to ensure good OFDM uplink, the nonlinear detection scheme [83], [84] can performance for multi-mode IM based systems. In [49], the be employed to address the nonlinear distortions at TX. For multi-mode constellation design is carried out based on the optical wireless, the work [173] presented a RX-side predis- MIAD and MIRD criteria for a given spectral efficiency value. tortion scheme to compensate for the nonlinear distortions of It is claimed in [49] that the MIAD criterion ensures good LEDs at TX. These novel techniques are attractive, because performance of the constellations at high SNR, whilst the they are capable of overcoming the problem caused by high MIRD criterion filters the solutions produced by the MIAD PAPR, without sacrificing the system’s spectral efficiency or criterion in order to guarantee the medium-SNR performance. received SNR. Rather they achieve the desired goal at the However, the resultant solutions may not be optimal for the expense of increased TX or RX complexity. There exists following reason. It is well known that for different constella- no work yet to apply these techniques to IM-OFDM based tion orders, the required SNR values are different for reaching systems, which is worth considering in future research. certain level of BER performance, e.g., 10−3. Therefore, both the constellation orders and the received SNR values should jointly be taken into account in the multiple constel- lation design. Moreover, the scheme of [49] is a very special F. Hybrid IM-Aided Schemes and simplified case of the generic MM-OFDM proposed in As discussed previously, IM can be performed on dif- this paper. The design strategy of [49] may not be directly ferent domains, including FD, SD, TD and CD. Moreover, applicable to our generic MM-OFDM, which includes sev- in the SD based IM systems, IM operation can be car- eral additional critical factors to consider, e.g., the types of ried out on TX antennas or RX antennas. By performing constellation and the number of constellation modes. For IM operation simultaneously on several domains, the system example, in Fig. 10, we have compared two MM-OFDM performance can be enhanced significantly, in comparison systems with the same design except that one adopts PSK with performing IM on single domain. For instance, in the constellations and the other employs QAM constellations. The ST-IM system, a fraction of the TX antennas are activated MM-OFDM with PSK constellations is observed to suffer for data transmission, where binary bits can be conveyed by from serious performance loss, compared to the MM-OFDM their indices, while on each activated antenna, symbols are with QAM constellations. Therefore, effective multiple con- transmitted on part of the time slots, whose indices carry stellation design for the generic MM-OFDM is an urgent issue additional information bits. This leads to significant through- that have to be addressed. put gain over the pure SM and TD-IM schemes. It can be MAO et al.: NOVEL IM TECHNIQUES: SURVEY 343 seen that by combining multiple IM operations together, con- IM. By applying the zero-padded IM technique, energy con- siderable diversity gain can be achieved, which enhances the sumption is reduced, which compensates for the low energy system’s throughput and performance. Currently, there exist a efficiency caused by the addition of DC-bias, as in DCO- few works [30], [36], [62], [174], which consider hybrid IM- OFDM system. Furthermore, since illumination and commu- aided systems. However, the design strategy to combine three nication are the dual purposes of many LED based lighting types or even four types of IM-aided schemes has not been systems, dimming control is essential for VLC system design, properly investigated yet. Because of the enlarged multiple which may be also realized with the aid of IM by adjusting different signal sets in such a hybrid IM-aided system, jointly the number of activated TX entities. optimal constellation design is required and, moreover, low- Additionally, coherent optical communications, originated complexity detection algorithm is also a potential issue for the in optical fiber transmission, plays an important role in free- hybrid architecture. space optical (FSO) systems [181]. FSO signals suffer from severe attenuation and interferences due to atmosphere turbu- G. Applications to Mobile Communications lence or complex climate conditions such as fog or haze [181]. Although IM offers an attractive and effective means of Rapid proliferation of smart mobile devices and explo- enhancing the energy efficiency and the received SNR for VLC sive increase in mobile data traffic have imposed the urgent systems, it is challenging to apply IM to coherent optical com- need of speedily upgrading the current 3G and 4G mobile munications. This is because in coherent optical communica- networks to the future-generation mobile network known as tions, due to the use of coherent detection, both the amplitude 5G. Andrews et al. [175] list the ‘big three’ key technologies and phase of the incoming light can be detected, which means for 5G networks: ultra-densification, mmWave, and massive that transmitted signals are complex-valued. Moreover, two MIMO. In a nutshell, 5G networks must be capable of offer- independent data streams with orthogonal polarization can be ing much higher data rate, lower latency and less cost as well transmitted simultaneously, harvesting additional diversities. as consuming less energy than the current 3G and 4G com- Therefore, strategies of employing IM in VLC and RF archi- munications. The IM technique provides an ideal enabling tectures cannot be applied in coherent optical communications. technology to address these engineering challenges. To be Further research is warranted to address this critical issue of more specific, as discussed in this survey paper, some IM- how to apply IM to coherent optical communications. aided schemes, such as multi-mode IM-aided systems, are capable of significantly enhancing the data rate by conveying additional energy-free bits, which leads to considerable energy V. C ONCLUSION efficiency gain in comparison with non-index-modulated coun- Index modulation, which is capable of enhancing the terparts. Moreover, some IM-aided schemes can be utilized to system’s energy efficiency and providing high-rate data trans- simplify the transceiver structures. This contributes to lower mission, has become a promising technique for wireless cost and reduces computational complexity, which in turn communications. In IM-aided systems, in addition to the leads to lower latency. For instance, SM is capable of reducing symbol bits carried by conventional APM, extra informa- the number of required RF chains and the detection complex- tion bits are conveyed by the indices of activated transmit ity. Due to the aforementioned merits, preliminary work has entities, without extra energy consumption. Transmit enti- been conducted to adopt the IM technique in mmWave trans- ties that can be exploited for IM include the subcarriers of missions [14], [15], massive MIMO [16], [17], and network OFDM, TX antennas of MIMO, time slots of single-carrier coding [18]. It is believed that the IM technique can be incor- systems, and channel states of MBM, etc. With the aid of IM, porated with different critical technologies in 5G networks, considerable diversity gains can be achieved, leading to signif- where further research is needed. icant performance enhancement over the non-index-modulated counterparts. Thus, IM technique has attracted the full atten- H. Applications to Optical Communications tion from the academia and industry, and numerous relevant Due to the shortage of frequency resources and the researches have been proposed in the past few years. ever-increasing demand for high-rate communication, optical This paper has provided a comprehensive survey on IM- communication has become as a promising complementary aided systems by classifying various IM based schemes in technique to RF communication, which provides additional terms of indexing domains, which include frequency domain, advantages of unlicensed spectrum, robustness to the elec- spatial domain, time domain and channel domain. This gen- tromagnetic interferences, information security and safety to eral classification yields the four categories of IM schemes: human health [176]. Optical communications can be generally IM-OFDM, SM, TD-IM and MBM. For each category of IM classified into VLC [177] and coherent optical communica- based systems, we have provided the corresponding system tions [178]Ð[180]. At present, there exists limited literature model followed by the transceiver design of the typical applying the IM technique to optical communicating systems. IM-aided systems, to help the reader to better understand Indeed, enormous benefits can be obtained by applying IM IM principles. Performance evaluation, in terms of spectral to optical communications. In VLC, due to Hermitian sym- efficiency/throughput, energy efficiency, BER and detection metry and the unique frame structures, as in ACO-OFDM and complexity, have been presented, along with a brief introduc- PAM-DMT systems, optical OFDM suffers from inevitable tion to performance analysis methods, including the minimum data rate loss, which can be recovered at least partially by ED calculation and PEP approximation. 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Theory, vol. 55, no. 7, pp. 3051Ð3073, Jul. 2009. the Excellent Master Dissertation of Tsinghua University, and National [162] P. Akuon and H. Xu, “Polar coded spatial modulation,” IET Commun., Scholarship. vol. 8, no. 9, pp. 1459Ð1466, Jun. 2014. [163] C. Vladeanu, “Turbo trellis-coded spatial modulation,” in Proc. GLOBECOM, Anaheim, CA, USA, Dec. 2012, pp. 4024Ð4029. [164] L. Wang, C. Liang, Z. Yang, and X. Ma, “Two-layer coded spatial mod- Qi Wang (S’15–M’16) received the B.E. and ulation with block Markov superposition transmission,” IEEE Trans. Ph.D. degrees (with Highest Hons.) in electronic Commun., vol. 64, no. 2, pp. 643Ð653, Feb. 2016. engineering from Tsinghua University, Beijing, [165] R. Mesleh, M. Di Renzo, H. Haas, and P. M. Grant, “Trellis coded China, in 2011 and 2016, respectively. From 2014 spatial modulation,” IEEE Trans. Wireless Commun., vol. 9, no. 7, to 2015, he was a Visiting Scholar with the pp. 2349Ð2361, Jul. 2010. Electrical Engineering Division, Centre for Photonic [166] S. Alaka, T. L. Narasimhan, and A. Chockalingam, “Coded index Systems, Department of Engineering, University modulation for non-DC-biased OFDM in multiple LED visible light of Cambridge. From 2016 to 2017, he was a communication,” in Proc. VTC Spring, Nanjing, China, May 2016, Research Fellow with Southampton Wireless Group, pp. 1Ð5. University of Southampton. Since 2017, he has [167] L. Wang and X. Ma, “Coded index modulation with block Markov been a Senior Engineer with Huawei Technologies, superposition transmission for highly mobile OFDM systems,” in Proc. China. VTC Spring, Nanjing, China, May 2016, pp. 1Ð5. He has authored over 30 IEEE/OSA journal papers and several con- [168] H. Zhang, L.-L. Yang, and L. Hanzo, “LDPC-coded index-modulation ference papers. He has also co-authored a book entitled Visible Light aided OFDM for in-vehicle power line communications,” in Proc. VTC Communications: Modulation and Signal Processing (Wiley-IEEE Press). Spring, Nanjing, China, May 2016, pp. 1Ð5. His research interests include modulation and signal processing for wireless [169] P. Zhang, S. Chen, and L. Hanzo, “Reduced-complexity near-capacity communication and visible light communication. He was a recipient of the joint channel estimation and three-stage turbo detection for coher- Excellent Doctoral Dissertation of the Chinese Institute of Electronics, the ent space-time shift keying,” IEEE Trans. Commun., vol. 61, no. 5, Outstanding Ph.D. Graduate of Tsinghua University, the Excellent Doctoral pp. 1902Ð1913, May 2013. Dissertation of Tsinghua University, National Scholarship, and the Academic [170] P. Zhang, S. Chen, and L. Hanzo, “Embedded iterative semi-blind chan- Star of Electronic Engineering Department in Tsinghua University. He was nel estimation for three-stage-concatenated MIMO-aided QAM turbo selected by the IEEE Series on Digital and Mobile Communication. He serves transceivers,” IEEE Trans. Veh. Technol., vol. 63, no. 1, pp. 439Ð446, as an Associate Editor for IEEE ACCESS and a TPC member for many IEEE Jan. 2014. conferences, including Globecom, GlobalSIP, CSNDSP, and IWCMC. 348 IEEE COMMUNICATIONS SURVEYS & TUTORIALS, VOL. 21, NO. 1, FIRST QUARTER 2019 Zhaocheng Wang (M’09–SM’11) received the B.S., Sheng Chen (M’90–SM’97–F’08) received the M.S., and Ph.D. degrees from Tsinghua University, B.Eng. degree in control engineering from East Beijing, China, in 1991, 1993, and 1996, respec- China Petroleum Institute, Dongying, China, in tively. From 1996 to 1997, he was a Post-Doctoral 1982, the Ph.D. degree in control engineering from Fellow with Nanyang Technological University, the City University, London, in 1986, and the Singapore. From 1997 to 1999, he was with OKI Higher Doctoral degree (Doctor of Science) from the Techno Centre (Singapore) Pte. Ltd., Singapore, University of Southampton, Southampton, U.K., in where he was first a Research Engineer and later 2005. From 1986 to 1999, he held research and aca- became a Senior Engineer. From 1999 to 2009, demic appointments with the University of Sheffield, he was with Sony Deutschland GmbH, where he U.K., the University of Edinburgh, U.K., and the was first a Senior Engineer and later became a University of Portsmouth, U.K. Since 1999, he has Principal Engineer. He is currently a Professor of electronic engineering with been with Electronics and Computer Science, University of Southampton, Tsinghua University and serves as the Director of Broadband Communication where he holds the post of a Professor in intelligent systems and signal Key Laboratory, Tsinghua National Laboratory for Information Science and processing. Technology. He is a Distinguished Adjunct Professor with King Abdulaziz University, He has authored or co-authored over 100 journal papers (SCI indexed). Jeddah, Saudi Arabia. His research interests include adaptive signal pro- He holds 34 granted U.S./EU patents. He has co-authored two books, one cessing, wireless communications, modeling and identification of nonlinear of which entitled Millimeter Wave Communication Systems, was selected by systems, neural network and machine learning, intelligent control system IEEE Series on Digital and Mobile Communication (WileyÐIEEE Press). His design, evolutionary computation methods, and optimization. He has published research interests include wireless communications, visible light communica- over 600 research papers. He was a recipient of ISI Highly Cited Researcher tions, millimeterwave communications, and digital broadcasting. He currently Award in engineering in 2004. He is a fellow of the United Kingdom Royal serves as an Associate Editor for the IEEE TRANSACTIONS ON WIRELESS Academy of Engineering and a fellow of IET. COMMUNICATIONS and the IEEE COMMUNICATIONS LETTERS, and has also served as the technical program committee co-chair of various inter- national conferences. He is a fellow of the Institution of Engineering and Technology.