A Survey on Spatial Modulation in Emerging Wireless Systems: Research Progresses and Applications <s> C. Differential (D)SM <s> Motivated by the recent concept of Spatial Modulation (SM), we propose a novel Space-Time Shift Keying (STSK) modulation scheme for Multiple-Input Multiple-Output (MIMO) communication systems, where the concept of SM is extended to include both the space and time dimensions, in order to provide a general shift-keying framework. More specifically, in the proposed STSK scheme one out of Q dispersion matrices is activated during each transmitted block, which enables us to strike a flexible diversity and multiplexing tradeoff. This is achieved by optimizing both the space-time block duration as well as the number of the dispersion matrices in addition to the number of transmit and receive antennas. We will demonstrate that the resultant equivalent system model does not impose any Inter-Channel Interference (ICI), and hence the employment of single-stream Maximum Likelihood (ML) detection becomes realistic at a low-complexity. Furthermore, we propose a Differential STSK (DSTSK) scheme, assisted by the Cayley unitary transform, which does not require any Channel State Information (CSI) at the receiver. Here, the usual error-doubling, caused by the differential decoding, gives rise to 3-dB performance penalty in comparison to Coherent STSK (CSTSK). Additionally, we introduce an enhanced CSTSK scheme, which avoids the requirement of Inter-Antenna Synchronization (IAS) between the RF chains associated with the transmit Antenna Elements (AEs) by imposing a certain constraint on the dispersion matrix design, where each column of the dispersion matrices includes only a single non-zero component. Moreover, according to the turbo-coding principle, the proposed CSTSK and DSTSK schemes are combined with multiple serially concatenated codes and an iterative bit-to-symbol soft-demapper. More specifically, the associated STSK parameters are optimized with the aid of Extrinsic Information Transfer (EXIT) charts, for the sake of achieving a near-capacity performance. <s> BIB001 </s> A Survey on Spatial Modulation in Emerging Wireless Systems: Research Progresses and Applications <s> C. Differential (D)SM <s> A novel reduced-complexity near-optimal detection algorithm is proposed for enhancing the recent Coherently-detected Space-Time Shift Keying (CSTSK) scheme employing arbitrary constellations, such as {\cal L}-point Phase-Shift Keying (PSK) and Quadrature Amplitude Modulation (QAM). The proposed detector relies on a modified Matched Filter (MF) concept. More specifically, we exploit both the constellation diagram of the modulation scheme employed as well as the Inter-Element-Interference (IEI)-free STSK architecture. Furthermore, we generalize the Pulse Amplitude Modulation (PAM)- or PSK-aided Differentially-encoded STSK (DSTSK) concept and conceive its more bandwidth-efficient QAM-aided counterpart. Then, the proposed reduced-complexity CSTSK detector is applied to the QAM-aided DSTSK scheme, which enables us to carry out low-complexity non-coherent detection, while dispensing with channel estimation. It is revealed that the proposed detector is capable of approaching the optimal Maximum Likelihood (ML) detector's performance, while avoiding the exhaustive ML search. Interestingly, our simulation results also demonstrate that the reduced-complexity detector advocated may achieve the same performance as that of the optimal ML detector for the specific STSK scheme's parameters. Another novelty of this paper is that the star-QAM STSK scheme tends to outperform its square-QAM counterpart, especially for high number of dispersion matrices. Furthermore, we provided both the theoretical analysis and the simulations, in order to support this unexpected fact. <s> BIB002 </s> A Survey on Spatial Modulation in Emerging Wireless Systems: Research Progresses and Applications <s> C. Differential (D)SM <s> Differential spatial modulation (DSM) is favorable in practice since it can offer a better tradeoff between reception reliability and system complexity in comparison with coherent spatial modulation (SM). In this letter, the bit error probability (BEP) performance of a point-to-point communication system, in which DSM is adopted at a transmitter equipped with two antennas, is analyzed. A general expression for an upper bound on the average BEP (ABEP) achieved by the system under Rayleigh fading channels is derived. Moreover, a closed-form ABEP and an asymptotic analysis are provided for BPSK signaling. The derived analytical results verify that DSM leads to a less than 3dB signal-to-noise power ratio penalty with respect to coherent SM while maintaining the same data rate of 2bit/s/Hz. <s> BIB003 </s> A Survey on Spatial Modulation in Emerging Wireless Systems: Research Progresses and Applications <s> C. Differential (D)SM <s> Motivated by the recent generalized spatial modulation (GSM)-multiple input multiple-output (MIMO) concept, in this paper we conceive a non- coherently detected GSM architecture, which is achieved with the aid of Cayley unitary differential encoding. More specifically, the proposed differentially-encoded transmitter structure enables us to eliminate any limitations imposed by pilot insertions and channel state information (CSI) estimation, while attaining the GSM scheme's increased transmission rate as well as reduced number of RF chains at the transmitter. Furthermore, we extend the proposed non-coherent GSM scheme to operate in a single-antenna transmitter structure. Our performance results reveal that a high transmission rate is achieved, while attaining reduced-RF branches and dispensing with the channel estimation at the receiver. <s> BIB004 </s> A Survey on Spatial Modulation in Emerging Wireless Systems: Research Progresses and Applications <s> C. Differential (D)SM <s> Spatial modulation (SM) is a newly emerging multiple-input–multiple-output technique that activates only a single antenna for transmission at any time instant and uses the index of the active antenna as an additional information-carrying mechanism. However, by its nature, SM decoding is coherent in that channel state information (CSI) is required at the receiver. In fact, coherent SM decoding can be very complex due to the heavily entangled channel estimation and symbol detection. In this correspondence, a differential SM scheme that completely bypasses any CSI at the transmitter or receiver, while preserving the single active transmit antenna property, is developed. The proposed scheme can be applied to any constant energy constellation such as phase-shift keying (PSK) and to systems with arbitrary numbers of transmit and receive antennas. Simulation results are presented under various system configurations. With the same spectral efficiency, the proposed scheme is capable of paying no more than 3 dB of signal-to-noise ratio penalty compared with coherent SM and outperforming the single-antenna differential PSK and differential space–time coding schemes. <s> BIB005 </s> A Survey on Spatial Modulation in Emerging Wireless Systems: Research Progresses and Applications <s> C. Differential (D)SM <s> Differential spatial modulation (DSM) is a newly-emerging differential scheme tailored to the spatial modulation technique, which selects only one among a group of antennas for transmission at any time instant. DSM, however, gives rise to prohibitive search complexity when the number of transmit antennas is large. In this letter, a low-complexity suboptimal detector is proposed for DSM. It is designed based on the maximum-likelihood criterion but takes more candidates for the antenna activation orders into account. The detection is performed in two steps: the first step is to confine the number of candidates for the modulated symbols to a small portion by exploiting the symmetry of the signal constellation; the second step is to select the most likely modulated symbols from the output of the first step according to the determined antenna activation order via a Viterbi-like algorithm. Analyses and simulations show that the proposed detector achieves near-optimal performance yet largely reduces the search complexity. <s> BIB006 </s> A Survey on Spatial Modulation in Emerging Wireless Systems: Research Progresses and Applications <s> C. Differential (D)SM <s> We develop a novel differential spatial modulation (DSM) scheme for amplitude phase shift keying (APSK) modulation, which can either improve throughput or performance over DSM for PSK. Then we investigate the impact of time-varying fading on DSM. We find performance degrades if the fading is too fast due to differential detection. The impact of a long outer error control code (ECC) is also considered. Its performance is limited by the slowly varying channel required for differential detection. We consider using reconfigurable antennas to periodically change the channel conditions and hence significantly improve coded performance for DSM systems. <s> BIB007 </s> A Survey on Spatial Modulation in Emerging Wireless Systems: Research Progresses and Applications <s> C. Differential (D)SM <s> In this letter, we propose a new differential spatial modulation (DSM) scheme for two transmit antennas. The proposed scheme employs the same architecture as the existing block-based DSM scheme, but with a new cyclic signal constellation. We also provide the asymptotic decoding performance analysis for the proposed DSM scheme, based on which the design criteria are further developed to attain full transmit diversity as well as better decoding performance. The numerical results validate the analytical error rate framework and verify the superiority of the proposed scheme. <s> BIB008 </s> A Survey on Spatial Modulation in Emerging Wireless Systems: Research Progresses and Applications <s> C. Differential (D)SM <s> In this paper, we propose a novel virtual multi-input-multi-output (VMIMO) architecture to convey information from the source node (SN) to the destination node (DN) via multiple relay nodes (RNs). As it is built on dual-hop networks with differential spatial modulation (DSM), we call it dual-hop hybrid DSM (DH-HDSM). In order to harvest the diversity provided by the SN and reduce the complexity at the RNs, DH-HDSM forms a precoding aided DSM pattern in the first hop and applies incoherent detection in a centralized or distributed manner at the RNs. Based on the decode-and-forward protocol, DSM transmission is carried out in the second hop and achieves high energy efficiency via statistical single RN activation at any time instant. We analyze the performance of DH-HDSM in terms of the average bit error probability and make comparisons with dual-hop hybrid spatial modulation (DH-HSM) and differential VMIMO systems with either a single relay or best relay selection. Theoretical results and Monte Carlo simulations confirm that DH-HDSM outperforms DH-HSM and other differential relay schemes in terms of error performance when the DN is equipped with multiple antennas. <s> BIB009 </s> A Survey on Spatial Modulation in Emerging Wireless Systems: Research Progresses and Applications <s> C. Differential (D)SM <s> Differential spatial modulation (DSM) was recently proposed to overcome the challenge of channel estimation in spatial modulation (SM). In this letter, we propose a gray code order of antenna index permutations for DSM. To facilitate the implementation, the well-known Trotter-Johnson ranking and unranking algorithms are adopted, which results in similar computational complexity to the existing DSM that uses the lexicographic order. The coding gain achieved by the proposed gray code order over the existing lexicographic order is also analyzed and verified via simulations, which reveals a maximum of about 1.2dB for the case of four transmit antennas. Based on the gray coding framework, we further propose a diversity-enhancing scheme named intersected gray (I-gray) code order for DSM, where the permutations of active antenna indices are selected directly from the odd (even) positions of the full permutations in the gray code order. From analysis and simulations, it is shown that the I-gray code order can harvests an additional diversity order at the expense of only one information bit loss for each transmission with respect to the gray code order. <s> BIB010 </s> A Survey on Spatial Modulation in Emerging Wireless Systems: Research Progresses and Applications <s> C. Differential (D)SM <s> Differential spatial modulation (DSM) is a novel multiple-input multiple-output wireless transmission technique, which relies on a single radio-frequency transmit structure without the need of the channel state information. In this letter, a novel high-rate design scheme relying on the amplitude phase shift keying (APSK) is proposed for DSM schemes. Moreover, a simplified upper bound of the average bit error probability (ABEP) of the proposed APSK-aided DSM scheme is derived and the ring ratio of the designed DSM constellation is optimized based on our theoretical ABEP results. Simulation results show that, at the same throughputs, the proposed scheme is capable of providing considerable bit error rate performance improvement over conventional DSM schemes. <s> BIB011 </s> A Survey on Spatial Modulation in Emerging Wireless Systems: Research Progresses and Applications <s> C. Differential (D)SM <s> In this paper, a novel differential space-time coding scheme is conceived for open-loop noncoherent multiple-input multiple-output (MIMO) downlink scenarios, where the transmission rate increases logarithmically in a scalable manner upon increasing the number of transmit antennas. More specifically, the proposed scheme relies on the projection of a differentially encoded square matrix to its rectangular counterpart and so is capable of reducing the number of symbol intervals needed for block transmission. This is especially beneficial for massive MIMO scenarios, in which the number of transmit antennas is very high. Another advantage exclusive to the presented scheme is that no channel state information (CSI) is required at either the transmitter or the receiver, which eliminates pilot overhead, CSI estimation, CSI feedback, and time-division duplex reciprocity. Furthermore, the rectangular transmission matrix of the proposed scheme contains only a single non-zero element per column, and hence, the transmitter may rely on only a single RF chain, similar to the conventional coherent spatial modulation scheme. <s> BIB012 </s> A Survey on Spatial Modulation in Emerging Wireless Systems: Research Progresses and Applications <s> C. Differential (D)SM <s> We consider differential spatial modulation (DSM) operating in a block fading environment and propose sparse unitary dispersion matrices (DMs) using algebraic field extensions. The proposed DM sets are capable of exploiting full transmit diversity and, in contrast to the existing schemes, can be constructed for systems having an arbitrary number of transmit antennas. More specifically, two schemes are proposed: 1) field-extension-based DSM (FE-DSM), where only a single conventional symbol is transmitted per space–time block; and 2) FE-DSM striking a diversity–rate tradeoff (FE-DSM-DR), where multiple symbols are transmitted in each space–time block at the cost of a reduced transmit diversity gain. Furthermore, the FE-DSM scheme is analytically shown to achieve full transmit diversity, and both proposed schemes are shown to impose decoding complexity, which is independent of the size of the signal set. It is observed from our simulation results that the proposed FE-DSM scheme suffers no performance loss compared with the existing DM-based DSM (DM-DSM) scheme, whereas FE-DSM-DR is observed to give a better bit-error-ratio performance at higher data rates than its DM-DSM counterpart. Specifically, at data rates of 2.25 and 2.75 bits per channel use, FE-DSM-DR is observed to achieve about 1- and 2-dB signal-to-noise ratio (SNR) gain with respect to its DM-DSM counterpart. <s> BIB013 </s> A Survey on Spatial Modulation in Emerging Wireless Systems: Research Progresses and Applications <s> C. Differential (D)SM <s> We design a differential transmission scheme based on a novel temporally and spatially modulated space-time block coding codebook. Our proposed design is the first differential transmission scheme for spatial modulation with multiple active transmit antennas. Our numerical results demonstrate the significant performance gains of our proposed differential transmission scheme over the state-of-the-art schemes. <s> BIB014 </s> A Survey on Spatial Modulation in Emerging Wireless Systems: Research Progresses and Applications <s> C. Differential (D)SM <s> In this paper, we propose a simple yet powerful mapping scheme that converts any conventional square-matrix-based differential space-time coding (DSTC) into a nonsquare-matrix-based DSTC. This allows DSTC schemes to be used practically in open-loop large-scale multiple-input multiple-output scenarios. Our proposed scheme may be viewed as the differential counterpart of coherent spatial modulation (SM), of the generalized SM, of Bell Laboratories layered space-time architecture, and of subcarrier-index modulation. The fundamental impediment of the existing DSTC schemes is the excessive complexity imposed by the unitary constraint. Specifically, the transmission rate of conventional DSTC schemes decays as the number of transmit antennas increases. Our proposed scheme eliminates this impediment and thus achieves a significantly higher transmission rate. We introduce four novel construction methods for the nonsquare codewords, some of which include an arbitrary number of nonzero elements in each codeword column. Our analysis shows that the proposed encoding technique reduces the complexity of both the inverse Fourier transform and the detection processes. Our proposed scheme is shown to approach the performance of its coherent counterpart for low-mobility scenarios, where the number of transmit antennas is increased up to 256. <s> BIB015
Since the SM transmitter embeds the spatial information in the active antenna implicitly, the SM receiver has to detect such spatial information by distinguishing different channel fading states associated with different transmit antennas, which requires the CSI for coherent detection. However, the CSI requirement at the receiver increases the deployment cost due to the pilot overhead and channel estimation complexity. Alternatively, differential encoding of the SM symbols, which dispenses with any CSI at the transceiver while inheriting the advantages of SM, emerges as an attractive solution with low deployment cost. A differentially encoded space-time shift keying (STSK) modulation scheme is presented in BIB001 as the primitive idea of (D)SM, which employs the Cayley unitary transform and conveys information via the activation state of the space-time dispersion matrix. To overcome limitation on the real-valued constellation of BIB001 , the authors of BIB002 further develop a differentially STSK scheme with QAM to achieve higher bandwidth-efficiency. On the other hand, a permutation-based (D)SM scheme is developed in BIB005 , which conveys information via the antenna activation order and is applicable to an arbitrary number of transmit antennas. Specifically, as the original SM of N T antennas has N T activation states, the (D)SM will transmit an N T ×N T space-time block, which is one permutation of block activation states. As a result, we have N ! different permutations for the space-time block and the transmitter of (D)SM selects one out of N T ! permutations according to the previous space-time block and the incoming spatial information bits, which is illustrated in Fig. 5 . For each (D)SM block, the first part with p 1 = log 2 (N T !) bits is applied to the permutation selector to determine a permutation P(i), while the second part with p 2 = N T log 2 M bits is then applied to the symbol modulator for generating N T constellation symbols in the form of the diagonal matrix diag{s 1 (i) · · · s NT (i)}, resulting in the information block where diag(·) denotes the diagonal operation. Finally, the (D)SM block matrix is calculated by where the initial block matrix of (11) can be assumed to be the identity matrix, i.e., S(0) = I NT . As it can be seen, the N T × N T space-time block is a full-rank matrix and has only one non-zero entry in each row or column. By leveraging the time-coherent property for non-coherent detection, the (D)SM can successfully avoid the requirement of pilot insertion at the transmitter and channel estimation at the receiver to achieve low deployment cost. Fig. 6 shows the BER comparison results between non-coherent detection (D)SM and coherent detection SM with N T = 4, targeting at the spectral efficiency of 3 bps/Hz. It can be observed that compared with coherent detection SM, the performance loss in terms of BER for the non-coherent detection (D)SM is less than 3 dB. Fig. 7 shows the BER performance results of (D)SM under different parameter settings, targeting at the spectral efficiency of 3 bps/Hz. By showing the single-antenna differential PSK (DPSK) as a benchmark, it can be observed that the performance gain of (D)SM increases as the number of receive antennas grows. A reduced complexity detector is investigated for (D)SM in BIB006 to achieve near-optimal performance, which is derived from the ML principle and adopts a two-step operation. The introduction of amplitude phase shift keying (APSK) modulation to (D)SM is investigated in BIB007 and BIB011 to enhance the transmission efficiency and performance. In BIB003 , the performance of (D)SM with two transmit antennas over Rayleigh fading channels is analyzed in terms of the average bit error probability, which shows a less than 3 dB performance loss compared with the coherent SM. To fill the performance gap between the DSM and the coherent SM, the state-ofthe-art in rectangular DSM concept is extensively investigated in BIB012 - BIB015 . On the other hand, DSM also has various applications. For example, the concept of (D)SM is then implemented in dual-hop networks BIB009 , which reaps the transmit-diversity and reduces the receive complexity by using precoding. To achieve the improved BER performance of (D)SM, the concept of Gray coding is applied, where the Trotter-Johnson ranking and unranking theory is adopted to perform index permutations BIB010 . To capture the full transmit-diversity of (D)SM, schemes that use cyclic signal constellation and algebraic field extensions are developed in BIB008 and BIB013 , respectively. Inspired by the (G)SM concept, the authors of BIB004 generalize the differential STSK scheme by allowing a subset of space-time dispersion matrices to carry more than one real-valued constellations. Furthermore, the differential transmission scheme for (G)SM with multiple active transmit antennas is described in BIB014 , which strikes a more flexible trade-off between the diversity gain and transmission rate.