A Survey on Spatial Modulation in Emerging Wireless Systems: Research Progresses and Applications <s> A. Compressed-Sensing (CS) Theory for 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> BIB001 </s> A Survey on Spatial Modulation in Emerging Wireless Systems: Research Progresses and Applications <s> A. Compressed-Sensing (CS) Theory for SM <s> Generalized spatial modulation (GSM) is a novel scheme developed from the conventional single-active antenna spatial modulation (SA-SM). The challenge of the GSM lies at the receiving end. Since more than one antenna is activated, the complexity of ML detection for GSM is much higher than that for SA-SM, especially if the number of antennas is large. Low complexity sub-optimal detections, such as ZF detection or MMSE detection, can be used to detect GSM. However, the performance of these detections is poor and cannot yet be applied in an underdetermined system. Spatial modulation has an inherent property of sparsity. However, to the best of our knowledge, this property has not been used for GSM. In this paper, we exploit this property and propose a sub-optimal detection algorithm. The traditional algorithm using sparsity is sensitive to noise and not suitable for the application to communication systems. Therefore, we employ a denoising scheme to counter the effect of the background noise. <s> BIB002 </s> A Survey on Spatial Modulation in Emerging Wireless Systems: Research Progresses and Applications <s> A. Compressed-Sensing (CS) Theory for SM <s> Generalised spatial modulation (GSM) is extended from the concept of spatial modulation (SM). Due to its superior energy efficiency to classical multiple-input multiple-output (MIMO) techniques, GSM has attracted plenty of interest under the study of large-scale MIMO systems. In this paper, we propose a low-complexity symbol detector for GSM based on the framework of sparse Bayesian learning (SBL), which effectively recovers the GSM symbols by exploiting the inherent sparsity property of GSM. Compared to other sparsity-based symbol detectors, e.g., detectors based on the basis pursuit (BP) method and the orthogonal matching pursuit (OMP), the SBL-based detector is capable of achieving a superior reconstruction accuracy using less receive antennas. Numerical simulations are performed to substantiate the performance of the proposed detector. <s> BIB003 </s> A Survey on Spatial Modulation in Emerging Wireless Systems: Research Progresses and Applications <s> A. Compressed-Sensing (CS) Theory for 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> BIB004 </s> A Survey on Spatial Modulation in Emerging Wireless Systems: Research Progresses and Applications <s> A. Compressed-Sensing (CS) Theory for SM <s> Generalized spatial modulation (GSM) is a spectral and energy efficient multiple-input–multiple-output transmission technique. The low-complexity detection algorithm design with near maximum likelihood (ML) performance at the receiver is very challenging, and is the focus of this letter. In specific, we exploit the fixed sparsity constraint in the transmitted GSM signals, and take advantage of Bayesian compressive sensing (BCS) in sparse signal recovery. A new detection algorithm, referred to as enhanced Bayesian compressive sensing (EBCS), is proposed. It features more than 75% complexity reduction at high signal-to-noise ratios compared with the ordered-blocked minimum-mean-squared-error algorithm. Furthermore, it is shown by simulation that its error performance is comparable to the ML algorithm, and the performance gap is negligible in many cases. <s> BIB005 </s> A Survey on Spatial Modulation in Emerging Wireless Systems: Research Progresses and Applications <s> A. Compressed-Sensing (CS) Theory for SM <s> Generalized spatial modulation (GSM) is a novel multiple-input–multiple-output (MIMO) technique, which relies on a sparse use of radio-frequency (RF) front ends at the transmitter. In this paper, low-complexity and compressive-sensing (CS)-based detectors for GSM systems are proposed. First, an extension of the normalized CS detector (E-NCS) based on the orthogonal matching pursuit (OMP) algorithm is proposed, which is shown to be suitable for large-scale GSM implementations, due to its low complexity. Furthermore, to mitigate the error floor effect of the E-NCS detector, two efficient CS (ECS) detectors based on the OMP algorithm are designed with the aid of a preset threshold. Specifically, different searching algorithms are designed, whose objective is to balance computational complexity and system performance. An upper bound for the average bit error probability (ABEP) of the first ECS detector is derived and used to optimize the preset threshold. Simulation results show that the proposed ECS detectors are capable of achieving a considerable reduction in computational complexity, compared with other near-optimal algorithms, with a negligible performance loss. <s> BIB006 </s> A Survey on Spatial Modulation in Emerging Wireless Systems: Research Progresses and Applications <s> A. Compressed-Sensing (CS) Theory for SM <s> In the practical radar with multiple antennas, the antenna imperfections degrade the system performance. In this paper, the problem of estimating the direction of arrival (DOA) in a multiple-input and multiple-output (MIMO) radar system with unknown mutual coupling effect between antennas is investigated. To exploit the target sparsity in the spatial domain, the compressed sensing based methods have been proposed by discretizing the detection area and formulating the dictionary matrix, so an off-grid gap is caused by the discretization processes. In this paper, different from the present DOA estimation methods, both the off-grid gap due to the sparse sampling and the unknown mutual coupling effect between antennas are considered at the same time, and a novel sparse system model for DOA estimation is formulated. Then, a novel sparse Bayesian learning (SBL)-based method named sparse Bayesian learning with the mutual coupling (SBLMC) is proposed, where an expectation-maximum-based method is established to estimate all the unknown parameters including the noise variance, the mutual coupling vectors, the off-grid vector, and the variance vector of scattering coefficients. Additionally, the prior distributions for all the unknown parameters are theoretically derived. With regard to the DOA estimation performance, the proposed SBLMC method can outperform state-of-the-art methods in the MIMO radar with unknown mutual coupling effect, while keeping the acceptable computational complexity. <s> BIB007 </s> A Survey on Spatial Modulation in Emerging Wireless Systems: Research Progresses and Applications <s> A. Compressed-Sensing (CS) Theory for SM <s> The terrestrial return channel provides interactive services in digital television terrestrial broadcasting systems to meet various consumers’ demands around the world. The extension of non-orthogonal multiple access and generalized spatial modulation multiple-input multiple-output to the terrestrial return channel improves both the spectral and energy efficiencies of the system, but it puts forward detection challenges. In this paper, a joint user activity and signal detection scheme based on the block-sparse compressive sensing (BS-CS) method in the terrestrial return channel is proposed, in which the generalized spatial modulation technology is used. By exploiting the structure and sparsity of the multi-user generalized spatial modulation signal, we formulate the detection problem into a block-sparse recovery problem. Then a BS-CS-based detection algorithm, enhanced structured block-sparse compressive sampling matching pursuit (ESB-CoSaMP), is proposed to detect the active users and transmitted data efficiently. Moreover, the information of active antennas at each user is exploited in ESB-CoSaMP to further improve the accuracy. Simulations show that the proposed detection scheme outperforms the conventional CS and BS-CS-based schemes. <s> BIB008 </s> A Survey on Spatial Modulation in Emerging Wireless Systems: Research Progresses and Applications <s> A. Compressed-Sensing (CS) Theory for SM <s> Spatial-multiplexing aided spatial modulation (SMx-SM) is proposed, which intrinsically amalgamates the concept of vertical bell labs space-time (V-BLAST) and SM to attain a high transmission rate, despite its low number of radio frequency (RF) chains at the transmitter. Specifically, in the SMx-SM scheme, the transmit antennas are partitioned into groups and the SM technique is applied individually to each group. Furthermore, low-complexity threshold-aided compressive sensing-based and message passing-based detectors are derived for our SMx-SM system. Our simulation results show that the proposed SMx-SM system exhibits a better performance despite its lower complexity than the conventional generalized spatial modulation system. More importantly, the proposed SMx-SM system is capable of providing considerable performance gains over the V-BLAST system at the same number of RF chains and throughput. Finally, an upper bound is derived for the average bit error probability, which is confirmed by our simulation results. <s> BIB009 </s> A Survey on Spatial Modulation in Emerging Wireless Systems: Research Progresses and Applications <s> A. Compressed-Sensing (CS) Theory for SM <s> A novel multiple-input and multiple-output transmission scheme termed as space–time block coded quadrature spatial modulation (STBC-QSM) is proposed. It amalgamates the concept of quadrature spatial modulation (QSM) and space–time block coding (STBC) to exploit the diversity benefits of STBC relying on sparse radio frequency chains. In the proposed STBC-QSM scheme, the conventional constellation points of the STBC structure are replaced by the QSM symbols; hence, the information bits are conveyed both by the antenna indices as well as by conventional STBC blocks. Furthermore, an efficient Bayesian compressive sensing (BCS) algorithm is developed for our proposed STBC-QSM system. Both our analytical and simulation results demonstrated that the proposed scheme is capable of providing considerable performance gains over the existing schemes. Moreover, the proposed BCS detector is capable of approaching the maximum likelihood detector's performance despite only imposing a complexity near similar to that of the minimum mean square error detector in the high signal-to-noise ratio regions. <s> BIB010
For (G)SM systems, conventional detection methods such as ML and linear detections can be applied. However, the ML detector has prohibitively high complexity that exponentially grows with the number of active antennas whereas linear detectors, e.g., MMSE and ZF suffer from significant performance loss. Recently, by exploiting the sparse features in (G)SM symbols, several researchers focused on the design of low-complexity CS-based detection schemes to achieve satisfactory performance. Therefore, CS theory becomes a powerful tool that makes the signal reconstruction possible even when the number of available measurements is much smaller than the signal dimension (i.e., the number of receive antennas is much less than that of transmit antennas in underdetermined systems), particularly in the case of large-scale MIMO BIB007 . Since a very large number of transmit antennas are used in large-scale MIMO while only a few of them are active during each transmission, the (G)SM symbols can be considered sparse since most elements of the transmitted block are zeros. By formulating the antenna detection of SM as an 1 -norm convex optimization problem, BIB001 applies the normalized CS to detect the active antenna indices, which saves the computational complexity significantly in the large-scale MIMO implementation. Against the limitation that basis pursuit (BP) algorithm is not suitable for detecting sparse signals corrupted by noise, BIB002 makes some adaptations to counter the effect of noise and formulates the detection of (G)SM signals as a convex quadratic programming problem. A sparse Bayesian learning based detection algorithm is then proposed in BIB003 to reconstruct the (G)SM symbol effectively with low complexity, which shows outstanding performance over other CS-based schemes in the highly underdetermined scenarios (i.e., the receiver only has a small number of antennas). By formulating the (G)SM detection as an 0 -norm optimization problem under the constraint of fixed sparsity, Bayesian CS is applied in BIB005 to solve the detection problem, which shows a better performance than the BP based detector. Several efficient CS-based detectors under the orthogonal matching pursuit framework are proposed in BIB006 for large-scale (G)SM systems, which achieve satisfactory performance with considerably reduced complexity. The application of CS theory to the multiuser detection problems of SM systems also received great attention from many researchers. In BIB004 , the detection problem for SM systems over the multiple-access channel is investigated, in which a low-cost detector based on CS theory is proposed by exploiting the structured sparsity of the problem. Exploiting the distributed and group sparsity in large-scale SM uplink systems,  develops a structured CS-based multiuser detection algorithm with satisfactory performance and low deployment cost. The joint detection problem of user activity and (G)SM signal is investigated over the terrestrial return channel BIB008 , in which the block-sparse CS-based method is developed for solving the joint detection problem by exploiting the structured sparsity inherent in multi-user (G)SM systems. In BIB009 , after partitioning transmit antennas into multiple groups to perform independent SM, corresponding detectors based on threshold-aided CS and message passing are proposed to achieve near-optimal performance with low complexity. In BIB010 , an effective Bayesian CS detector is proposed with low deployment cost for STBC based QSM systems.