A Survey on Spatial Modulation in Emerging Wireless Systems: Research Progresses and Applications <s> A. Single-RF SM <s> Spatial modulation (SM) is a recently developed transmission technique that uses multiple antennas. The basic idea is to map a block of information bits to two information carrying units: 1) a symbol that was chosen from a constellation diagram and 2) a unique transmit antenna number that was chosen from a set of transmit antennas. The use of the transmit antenna number as an information-bearing unit increases the overall spectral efficiency by the base-two logarithm of the number of transmit antennas. At the receiver, a maximum receive ratio combining algorithm is used to retrieve the transmitted block of information bits. Here, we apply SM to orthogonal frequency division multiplexing (OFDM) transmission. We develop an analytical approach for symbol error ratio (SER) analysis of the SM algorithm in independent identically distributed (i.i.d.) Rayleigh channels. The analytical and simulation results closely match. The performance and the receiver complexity of the SM-OFDM technique are compared to those of the vertical Bell Labs layered space-time (V-BLAST-OFDM) and Alamouti-OFDM algorithms. V-BLAST uses minimum mean square error (MMSE) detection with ordered successive interference cancellation. The combined effect of spatial correlation, mutual antenna coupling, and Rician fading on both coded and uncoded systems are presented. It is shown that, for the same spectral efficiency, SM results in a reduction of around 90% in receiver complexity as compared to V-BLAST and nearly the same receiver complexity as Alamouti. In addition, we show that SM achieves better performance in all studied channel conditions, as compared with other techniques. It is also shown to efficiently work for any configuration of transmit and receive antennas, even for the case of fewer receive antennas than transmit antennas. <s> BIB001 </s> A Survey on Spatial Modulation in Emerging Wireless Systems: Research Progresses and Applications <s> A. Single-RF SM <s> In this letter, we derive the optimal detector for the so-called spatial modulation (SM) system introduced by Mesleh et al. in (Mesleh, 2006). The new detector performs significantly better than the original (~ 4 dB gain), and we support our results by deriving a closed form expression for the average bit error probability. As well, we show that SM with the optimal detector achieves performance gains (~ 1.5 - 3 dB) over popular multiple antenna systems, making it an excellent candidate for future wireless communication standards. <s> BIB002 </s> A Survey on Spatial Modulation in Emerging Wireless Systems: Research Progresses and Applications <s> A. Single-RF SM <s> In this Letter, we introduce fractional bit encoded (FBE)-spatial modulation (SM), which is a novel and more versatile SM scheme that allows the transmitter to be equipped with an arbitrary number of antennas. The solution is based on the theory of modulus conversion, and is especially useful for compact mobile devices where cost and space constraints pose fundamental limits on the achievable bit rate. Numerical results will show that FBE-SM can offer design flexibility and the desired trade-off in terms of attainable performance and capacity. <s> BIB003 </s> A Survey on Spatial Modulation in Emerging Wireless Systems: Research Progresses and Applications <s> A. Single-RF SM <s> Spatial modulation (SM) is a recent multiple-input multiple-output transmission technique, which entirely avoids inter-channel interference as well as the need for transmit antenna synchronisation. The first objective of this study is to present an asymptotic bound to quantify the average bit error rate (BER) performance of M-ary quadrature amplitude modulation (M-QAM) SM with optimal-based detection over independent and identically distributed Rayleigh flat fading channels. The analytical frameworks are validated by Monte Carlo simulation results, which show that the derived lower bounds are increasingly tight for large signal-to-noise ratio values. The second objective is to introduce a novel SM detection scheme, termed multiple-stage (MS) detection. Performance and complexity comparisons with existing SM detectors show two main benefits of MS detection: near-optimal BER performance and up to a 35% reduction in receiver complexity as compared to the maximum likelihood-based SM detector. <s> BIB004 </s> A Survey on Spatial Modulation in Emerging Wireless Systems: Research Progresses and Applications <s> A. Single-RF SM <s> In the context of multiple-input multiple-output (MIMO) communications, we propose a bit-padding information guided channel hopping (BP-IGCH) scheme which breaks the limitation that the number of transmit antennas has to be a power of two based on the IGCH concept. The proposed scheme prescribes different bit-lengths to be mapped onto the indices of the transmit antennas and then uses padding technique to avoid error propagation. Numerical results and comparisons, on both the capacity and the bit error rate performances, are provided and show the advantage of the proposed scheme. The BP-IGCH scheme not only offers lower complexity to realize the design flexibility, but also achieves better performance. <s> BIB005 </s> A Survey on Spatial Modulation in Emerging Wireless Systems: Research Progresses and Applications <s> A. Single-RF SM <s> Space shift keying (SSK) modulation and its extension, the generalized SSK (GSSK), present an attractive framework for the emerging large-scale MIMO systems in reducing hardware costs. In SSK, the maximum likelihood (ML) detector incurs considerable computational complexities. We propose a compressed sensing based detector, NCS, by formulating the SSK-type detection criterion as a convex optimization problem. The proposed NCS requires only O(ntNrNt) complexity, outperforming the O(NrNtnt) complexity in the ML detector, at the cost of slight fidelity degradation. Simulations are conducted to substantiate the analytical derivation and the detection accuracy. <s> BIB006 </s> A Survey on Spatial Modulation in Emerging Wireless Systems: Research Progresses and Applications <s> A. Single-RF SM <s> In this paper, we study the performance of spatial modulation (SM) multiple-input-multiple-output (MIMO) wireless systems over generic fading channels. More precisely, a comprehensive analytical framework to compute the average bit error probability (ABEP) is introduced, which can be used for any MIMO setup, for arbitrary correlated fading channels, and for generic modulation schemes. It is shown that, when compared with state-of-the-art literature, our framework 1) has more general applicability over generalized fading channels, 2) is, in general, more accurate as it exploits an improved union-bound method, and, 3) more importantly, clearly highlights interesting fundamental trends about the performance of SM, which are difficult to capture with available frameworks. For example, by focusing on the canonical reference scenario with independent identically distributed Rayleigh fading, we introduce very simple formulas that yield insightful design information on the optimal modulation scheme to be used for the signal constellation diagram, as well as highlight the different roles played by the bit mapping on the signal and spatial constellation diagrams. Numerical results show that, for many MIMO setups, SM with phase-shift-keying (PSK) modulation outperforms SM with quadrature-amplitude modulation (QAM), which is a result never reported in the literature. In addition, by exploiting asymptotic analysis, closed-form formulas of the performance gain of SM over other single-antenna transmission technologies are provided. Numerical results show that SM can outperform many single-antenna systems and that, for any transmission rate, there is an optimal allocation of the information bits onto spatial and signal constellation diagrams. Furthermore, by focusing on the Nakagami-fading scenario with generically correlated fading, we show that fading severity plays a very important role in determining the diversity gain of SM. In particular, the performance gain over single-antenna systems increases for fading channels less severe than Rayleigh fading, whereas it gets smaller for more severe fading channels. In addition, it is shown that the impact of fading correlation at the transmitter is reduced for less severe fading. Finally, analytical frameworks and claims are substantiated through extensive Monte Carlo simulations. <s> BIB007 </s> A Survey on Spatial Modulation in Emerging Wireless Systems: Research Progresses and Applications <s> A. Single-RF SM <s> In order to realize the information guided channel hopping, also known as spatial modulation, with more design flexibility, in this paper we propose a novel scheme that allows operation with an arbitrary number of transmit antennas. Once the number of transmit antennas is not a power of two, the antennas' symbols are mapped by different numbers of bits. Subsequently, constellations with different orders are exploited for the modulation of radiated symbols so as to guarantee that the total number of bits transmitted at each time slot remains the same. Furthermore, we introduce a decoding algorithm with low complexity for this design. Numerical results on bit error rate performance are provided and substantiate that the proposed scheme turns out to be a promising alternative to the design of information guided channel hopping. <s> BIB008 </s> A Survey on Spatial Modulation in Emerging Wireless Systems: Research Progresses and Applications <s> A. Single-RF SM <s> In this Letter, a low-complexity Euclidean distance-based method for antenna subset selection in Spatial Modulation systems is presented. The proposed method avoids the high complexity of both the optimal exhaustive search and of a recently proposed Euclidean distance-based algorithm for performing the selection. Moreover, as the number of receive antennas increases and for practical signal-to-noise ratio (SNR) values, it offers better error performance than the conventional transmit antenna selection (TAS) algorithm. In addition, the benefits of the proposed selection scheme, as the number of receive antennas increases, are further substantiated by comparing its relative energy gain over the TAS method for a target uncoded Symbol Error Rate (SER). <s> BIB009 </s> A Survey on Spatial Modulation in Emerging Wireless Systems: Research Progresses and Applications <s> A. Single-RF SM <s> Most of the studies on spatial modulation (SM) signal detection assume perfect channel state information (CSI) and ignore the channel's time-spatial correlation. Performance degradation incurs in the presence of imperfect CSI and channel correlations when estimating or predicting channel state based on periodic pilots. Detector structures that take into account both the channel estimation error and time-spatial correlation are investigated in this paper. We propose the CSI error and channel correlation aware ML detectors in conjunction with two channel estimation methods and present numerical results to quantify the associated performance improvements. <s> BIB010 </s> A Survey on Spatial Modulation in Emerging Wireless Systems: Research Progresses and Applications <s> A. Single-RF SM <s> In this paper, for the first time real--world channel measurements are used to analyse the performance of spatial modulation (SM), where a full analysis of the average bit error rate performance (ABER) of SM using measured urban correlated and uncorrelated Rayleigh fading channels is provided. The channel measurements are taken from an outdoor urban multiple input multiple output (MIMO) measurement campaign. Moreover, ABER performance results using simulated Rayleigh fading channels are provided and compared with a derived analytical bound for the ABER of SM, and the ABER results for SM using the measured urban channels. The ABER results using the measured urban channels validate the derived analytical bound and the ABER results using the simulated channels. Finally, the ABER of SM is compared with the performance of spatial multiplexing (SMX) using the measured urban channels for small and large scale MIMO. It is shown that SM offers nearly the same or a slightly better performance than SMX for small scale MIMO. However, SM offers large reduction in ABER for large scale MIMO. <s> BIB011 </s> A Survey on Spatial Modulation in Emerging Wireless Systems: Research Progresses and Applications <s> A. Single-RF SM <s> In this letter, we propose a distance-based ordered detection (DBD) algorithm for spatial modulation (SM) to reduce the receiver complexity and achieve a near maximum likelihood (ML) performance. The proposed algorithm firstly compensates the channel attenuation and obtains the estimated symbols with transmit antenna indices, then orders the indices based on the distances between these symbols and their demodulation constellations. A searching method is developed to obtain the final decision through a trade-off between performance and complexity. The equivalence between DBD and ML algorithms is also proved by theoretical analysis. Furthermore, a new low-complexity soft output DBD (SODBD) algorithm is developed for coded SM systems. The simulation results show that DBD algorithm has a close performance to ML algorithm while effectively reducing the complexity compared to conventional near-ML algorithms. <s> BIB012 </s> A Survey on Spatial Modulation in Emerging Wireless Systems: Research Progresses and Applications <s> A. Single-RF SM <s> A key challenge of future mobile communication research is to strike an attractive compromise between wire- less network's area spectral efficiency and energy efficiency. This necessitates a clean-slate approach to wireless system design, embracing the rich body of existing knowledge, espe- cially on multiple-input-multiple-ouput (MIMO) technologies. This motivates the proposal of an emerging wireless commu- nications concept conceived for single-radio-frequency (RF) large-scale MIMO communications, which is termed as SM. The concept of SM has established itself as a beneficial transmission paradigm, subsuming numerous members of the MIMO system family. The research of SM has reached sufficient maturity to motivate its comparison to state-of-the-art MIMO communica- tions, as well as to inspire its application to other emerging wireless systems such as relay-aided, cooperative, small-cell, optical wireless, and power-efficient communications. Further- more, it has received sufficient research attention to be im- plemented in testbeds, and it holds the promise of stimulating further vigorous interdisciplinary research in the years to come. This tutorial paper is intended to offer a comprehensive state-of-the-art survey on SM-MIMO research, to provide a critical appraisal of its potential advantages, and to promote the discussion of its beneficial application areas and their research challenges leading to the analysis of the technological issues associated with the implementation of SM-MIMO. The paper is concluded with the description of the world's first experimental activities in this vibrant research field. <s> BIB013 </s> A Survey on Spatial Modulation in Emerging Wireless Systems: Research Progresses and Applications <s> A. Single-RF SM <s> In this letter, we investigate the effects of antenna switching on band-limited spatial modulation (SM), where the employment of an SM-specific practical time-limited shaping filter is taken into account. More specifically, we evaluate the SM scheme's performance penalty imposed on a bandwidth efficiency, which arises due to the time-limited pulse transmissions. Furthermore, to combat this limitation while maintaining lower RF chains than transmit antenna elements, we propose a multiple-RF antenna switching operation that allows us to exploit a longer pulse shape than that enabled by a single-RF SM scheme. It is demonstrated in our simulations that upon increasing the number of transmit antenna elements, the SM scheme is capable of outperforming the classic MIMO systems, under the assumptions of a low number of RF chains and realistic pulse shaping. <s> BIB014 </s> A Survey on Spatial Modulation in Emerging Wireless Systems: Research Progresses and Applications <s> A. Single-RF SM <s> Spatial Modulation (SM) is a recently developed low-complexity Multiple-Input Multiple-Output scheme that jointly uses antenna indices and a conventional signal set to convey information. It has been shown that the Maximum-Likelihood (ML) detector of an SM system involves joint detection of the transmit antenna index and of the transmitted symbol, hence, the ML search complexity grows linearly with the number of transmit antennas and the size of the signal set. To circumvent the problem, we show that the ML search complexity of an SM system may be rendered independent of the constellation size, provided that the signal set employed is a square- or a rectangular-QAM. Furthermore, we derive bounds for the capacity of the SM system and derive the optimal power allocation between the data and the training sequences by maximizing the worst-case capacity bound of the SM system operating with imperfect channel state information. We show, with the aid of our simulation results, that the proposed detector is ML-optimal, despite its lowest complexity amongst the existing detectors. Furthermore, we show that employing the proposed optimal power allocation provides a substantial gain in terms of the SM system's capacity as well as signal-to-noise ratio compared to its equal-power-allocation counterpart. Finally, we compare the performance of the SM system to that of the conventional Multiple-Input Multiple-Output (MIMO) system and show that the SM system is capable of outperforming the conventional MIMO system by a significant margin, when both the systems are employing optimal power splitting. <s> BIB015 </s> A Survey on Spatial Modulation in Emerging Wireless Systems: Research Progresses and Applications <s> A. Single-RF SM <s> In this paper, a novel channel estimation (CE) method is proposed for spatial modulation (SM), a unique single-stream multiple-input-multiple-output transmission technique. In SM, there is only one transmit antenna being active at any time instance. While this property completely avoids inter-channel interference, it results in a challenge to estimate the channel information. In conventional CE (CCE) methods for SM, all transmit antennas have to be sequentially activated for sending pilots. Therefore, the time consumed in CE is proportional to the number of transmit antennas, which significantly compromises the throughput. By exploiting channel correlation, the proposed method, named transmission cross CE (TCCE), has the following characteristics: i) the entire channel is estimated by sending pilots through one transmit antenna; ii) it requires no overhead or feedback; and iii) it achieves a low computational complexity at the receiver. In addition, we propose an analytical framework to compute the distribution of the CE errors over time-varying fading channels. The corresponding average bit error probability (ABEP) bound of SM is also derived for the proposed method. Results show that the proposed ABEP bound matches with the simulations very well. When compared with CCE, the new method obtains a signal-to-noise ratio gain of up to 7.5 dB for medium and high correlations between the transmit antennas. Moreover, an adaptive CE technique can be readily implemented for SM via switching between CCE and TCCE. <s> BIB016 </s> A Survey on Spatial Modulation in Emerging Wireless Systems: Research Progresses and Applications <s> A. Single-RF SM <s> This letter proposes spatial modulated full duplex (SMFD), which applies spatial modulation to a point-to-point full-duplex communication system. The spatial modulation transmits its information bits by transmit antenna selection in addition to symbol modulation, whereas the full-duplex (FD) technique suppresses self-interference leaking from the transmitter to the receiver in an adaptive fashion. A closed-form solution is derived for the instantaneous maximum mutual information possible with a 2 $\times$ 2 antenna configuration. The results show higher efficiencies in terms of outage and ergodic maximum mutual information in comparison with conventional FD. Simulations also compare this technique with multiple-input–multiple-output half duplex, where further potential is demonstrated. <s> BIB017 </s> A Survey on Spatial Modulation in Emerging Wireless Systems: Research Progresses and Applications <s> A. Single-RF SM <s> In this paper, we propose a detector, based on the compressive sensing (CS) principles, for multiple-access spatial modulation (SM) channels with a large-scale antenna base station (BS). Particularly, we exploit the use of a large number of antennas at the BSs and the structure and sparsity of the SM transmitted signals to improve the performance of conventional detection algorithms. Based on the above, we design a CS-based detector that allows the reduction of the signal processing load at the BSs particularly pronounced for SM in large-scale multiple-input–multiple-output (MIMO) systems. We further carry out analytical performance and complexity studies of the proposed scheme to evaluate its usefulness. The theoretical and simulation results presented in this paper show that the proposed strategy constitutes a low-complexity alternative to significantly improve the system's energy efficiency against conventional MIMO detection in the multiple-access channel. <s> BIB018 </s> A Survey on Spatial Modulation in Emerging Wireless Systems: Research Progresses and Applications <s> A. Single-RF SM <s> In this paper, the performance of suboptimal detection of spatial modulation (SM) based on the so-called maximum ratio combining (MRC) isinvestigated. In this detection scheme, in contrast to maximum likelihood (ML) detection, transmit antenna index and amplitude-phase modulation(APM) symbols are detected separately in two stages. Therefore, the detection complexity of SM can be significantly reduced. We analyze theinstantaneous and average symbol error rate (SER) of such a detection scheme and compare it with that of the optimal ML detection. Also, we proposean adaptive space modulation scheme to minimize the SER of MRC detection by utilizing the channel state information. Finally, the problem of constellationbreakdown of SM in the presence of the MRC detection for the special case of the phase-shift keying (PSK)-modulated SM is investigated. The derivedanalytical results are further validated using extensive simulations. <s> BIB019 </s> A Survey on Spatial Modulation in Emerging Wireless Systems: Research Progresses and Applications <s> A. Single-RF SM <s> In this paper, distributed spatial modulation (DSM) is introduced. DSM is a cooperative diversity protocol for multirelay wireless networks, which is based on the concept of spatial modulation (SM). The distinguishable feature of DSM lies in improving the reliability of the source via distributed diversity and by increasing the aggregate throughput of the network since new data is transmitted during each transmission phase. This is achieved by encoding the data transmitted from the source into the spatial positions of the available relays and by exploiting the signal domain to transmit the data of the relays. At the destination, a diversity combiner that is robust to demodulation errors at the relays is proposed, and its end-to-end error probability and achievable diversity are studied. It is mathematically proved that DSM allows the source to achieve second-order diversity. With the aid of Monte Carlo simulations, DSM is compared against state-of-the-art cooperative protocols, and it is shown to provide a better error probability. <s> BIB020 </s> A Survey on Spatial Modulation in Emerging Wireless Systems: Research Progresses and Applications <s> A. Single-RF SM <s> In this paper, the concept of spatial modulation is exploited in two-way relay channels, where two single-antenna source terminals exchange information through an assisting multi-antenna relay node, and thereby two novel transmission strategies are proposed based on the decode-and-forward protocol, aiming to achieve high throughput. One strategy is to simply engage spatial modulation in the transmissions of the relay node, whereas the other is to develop transmit diversity with spatial modulation for further benefiting from the feature of two-way relaying. Neither of the strategies requires channel state information at the transmitter and, therefore, the assumption of channel reciprocity that is commonly used in two-way relay channels can be released herein. To evaluate the performance of both proposed strategies, their capacity behaviors are analyzed and numerical comparisons are established in the metrics of achievable rate region and sum-rate. Subsequently, the first strategy, simple spatial modulation, is generalized into the two-way relaying with multi-antenna source terminals to improve the flexibility in system design and demonstrate the tractability of spatial modulation. Illustrative discussions on bit error rate not only substantiate the validity of the proposed strategies but also provide useful tools for the two-way relaying layout without the restriction of channel reciprocity. <s> BIB021 </s> A Survey on Spatial Modulation in Emerging Wireless Systems: Research Progresses and Applications <s> A. Single-RF SM <s> Spatial modulation (SM) is a promising multiple-input multiple-output (MIMO) transmission technology, which exploits the indices of transmit antennas to encode information into the spatial dimension and needs less radio frequency chains. To detect the transmitted information, the maximum likelihood (ML) algorithm is often adopted which has high computational complexity. Some low-complexity detection algorithms only consider hard-decision cases with no channel coding. In this paper, a low-complexity soft output detection algorithm is proposed for coded spatial modulation systems. Its computational complexity doesn't increase with the modulation order and hence much lower than the soft output ML detection algorithm. Simulation results demonstrate that the bit error rate (BER) performance is near to the ML detection with obvious complexity reduction. By sorting the detection metrics and selecting less transmit antenna indices as search candidates to compute soft bit information, further reduction of computational complexity could be obtained. <s> BIB022 </s> A Survey on Spatial Modulation in Emerging Wireless Systems: Research Progresses and Applications <s> A. Single-RF SM <s> In this letter, we investigate the effects of pulse shaping on the bandwidth-versus-energy-efficiency tradeoff of band-limited spatial modulation (SM) massive multiple-input multiple-output (MIMO) systems. Although single-RF SM schemes have the merit of achieving high energy and bandwidth efficiencies, owing to the benefits of its antenna-activation principle, most of the previous studies assumed the use of a time-orthogonal shaping filter, which is unrealistic for a single-RF SM transmitter. To this end, we consider the use of time-limited shaping filters, such as a truncated root-raised cosine filter and a truncated Gaussian filter, for the single-RF SM transmitter. Our information-theoretic results demonstrate that, unlike in the previous studies, single-RF SM schemes do not exhibit any substantial advantages over the conventional full-RF MIMO schemes for a low number of transmit antennas, while for a large-scale antenna array, single-RF SM schemes outperform the conventional full-RF MIMO schemes. <s> BIB023
At the beginning of this century, SM has emerged as a novel MIMO technology that works with a single RF chain and exploits the active antenna index to convey additional information based on the antenna-switching mechanism BIB001 , BIB013 , BIB009 . As a result, the information of SM is not only explicitly transmitted as one phase-shift keying (PSK)/quadrature amplitude modulation (QAM) symbol, but also implicitly transmitted by selecting the index of one active antenna for each channel use. Given the number of transmit antennas N T and the modulation order of the signal constellation M , the spectral efficiency of SM is where [bpcu] stands for bits per channel use. Specifically, the first part of log 2 N T bits determines the index of the active antenna j and the second part of log 2 M bits is used to modulate the constellation symbol s. Consequently, as the constellation symbol s is carried by the j-th antenna, the transmit vector of SM can be expressed as where all elements of x except the j-th one are zeros. As shown in Fig. 1 , using the antenna-switching mechanism at the transmitter, the index of active antenna changes randomly for each channel use according to the incoming information bits. Specially, when M = 1, the SM system degenerates into the SSK system, in which the overall information bits are mapped into the index of active antenna in the space domain and the corresponding spectral efficiency is At the receiver side, both the index of active antenna and the corresponding constellation symbols must be detected for information recovery. Various detection algorithms have been developed for SM systems, which can be divided into two main categories: joint detection and decoupled/separate detection. For example, the maximum-likelihood (ML) detector is the most typical representative of joint detection, which searches jointly over all possible transmit antennas and constellation symbols to achieve optimal detection performance BIB002 . However, the ML detector has relatively high complexity which linearly scales with the number of transmit antennas and the size of the constellation. On the other hand, various suboptimal lower-complexity detectors were also developed, which typically involve a two-step decoupled process, i.e., first determine the index of the active transmit antenna and then demodulate the constellation symbol carried on the active transmit antenna BIB004 - BIB019 . As a result, the size of the search space is reduced from O(N T * M ) to O(N T + M ). Although the two-step decoupled/separate detectors have smaller search complexity, they usually suffer from performance degradation compared with the optimal detector. Therefore, it is an essential and challenging problem to design low-complexity detection algorithms to achieve optimal or near-optimal performance for the SM receiver. It is noted that by exploiting the sparsity of the SM signal, the implementations of low-complexity detection algorithms based on CS theory are developed to achieve near-optimal performance BIB006 , BIB018 . On the other hand, the practical shaping filter is employed to evaluate the impact of antenna switching for band-limited SM and a multiple-RF antenna switching mechanism is developed to overcome the shortage of single-RF SM scheme in BIB014 . Moreover, the authors of BIB023 evaluate the impact of pulse shaping on the bandwidth-versus-energy-efficiency tradeoff for band-limited SM and emphasize the advantage of single-RF SM in large-scale antenna array implementation. Moreover, the design of SM detection algorithms taking into account of channel correlation  , BIB010 , imperfect channel estimation BIB015 - BIB016 , performance analysis BIB007 - BIB011 , cooperative protocol BIB020 - BIB021 , and coded systems BIB012 , BIB022 - BIB003 are also extensively investigated in the literature. It is also worth pointing out that the concept of SM provides a multiple-antenna full-duplex node additional freedom to decide which antennas for signal transmission and which antennas for reception simultaneously, increasing the spectral efficiency while remaining the RF chains advantages. The authors of BIB017 for the first time proposed this idea, which was later extended to full-duplex relaying, such as in  . Note that in the above introduction the number of transmit antennas N T has been assumed to be a power of 2. When this assumption cannot be satisfied, effective schemes such as fractional bit encoding BIB003 , bit padding BIB005 , and constellation order varying BIB008 can be applied to improve the spectral efficiency of the SM system. The investment for the benefit is the increased susceptibility to error propagation.