A Survey on Spatial Modulation in Emerging Wireless Systems: Research Progresses and Applications <s> NT K <s> In this paper, Sphere Decoding (SD) algorithms for Spatial Modulation (SM) are developed to reduce the computational complexity of Maximum--Likelihood (ML--) optimum detectors, which foresee an exhaustive search of the whole search space and have a complexity that linearly increases with the product of number of transmit--antenna, receive--antenna, and size of the modulation scheme. Three SDs specifically designed for SM are proposed and analyzed in terms of Bit Error Probability (BEP) and computational complexity. By judiciously choosing some key parameters, e.g., the radius of the sphere centered around the received signal, it is shown that the proposed algorithms offer the same BEP as ML--optimum detection, with a significant reduction of the computational complexity. Also, it is shown that none of the proposed SDs is always superior to the others, but the best SD to use depends on the system setup, i.e., the number of transmit--antenna, receive--antenna, and the size of the modulation scheme. The computational complexity trade--off offered by the proposed solutions is studied via analysis and simulation, and numerical results are shown to validate our findings. <s> BIB001 </s> A Survey on Spatial Modulation in Emerging Wireless Systems: Research Progresses and Applications <s> NT K <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> BIB002 </s> A Survey on Spatial Modulation in Emerging Wireless Systems: Research Progresses and Applications <s> NT K <s> In this paper, a novel orthogonal frequency division multiplexing (OFDM) scheme, which is called OFDM with index modulation (OFDM-IM), is proposed for frequency-selective fading channels. In this scheme, inspiring from the recently introduced spatial modulation concept for multiple-input multiple-output (MIMO) channels, the information is conveyed not only by M-ary signal constellations as in classical OFDM, but also by the indices of the subcarriers, which are activated according to the incoming bit stream. Different transceiver structures are proposed and a theoretical error performance analysis is provided for the new scheme. It is shown via computer simulations that the proposed scheme achieves significantly better error performance than classical OFDM due to the information bits carried in the spatial domain by the indices of OFDM subcarriers. <s> BIB003 </s> A Survey on Spatial Modulation in Emerging Wireless Systems: Research Progresses and Applications <s> NT K <s> Generalized spatial modulation (GSM), in which only part of the transmit antennas are activated in each time slot, was recently proposed as a trade-off between spatial modulation (SM) and vertical Bell laboratories space-time (V-BLAST). Although the maximum likelihood (ML) detector is able to achieve the optimal performance, its exhaustive search leads to intractable computational complexity. In this letter, an efficient signal detection algorithm, termed ordered block minimum mean-squared error (OB-MMSE), is proposed for achieving near-ML performance with low complexity. On one hand, an ordering algorithm is proposed to sort the possible transmit antenna combinations (TACs). On the other hand, the possible signal vector for each ordered TAC is detected by block-MMSE equalization. Simulation results show that the proposed OB-MMSE detector provides similar performance to ML with near 80% reduction in complexity. <s> BIB004 </s> A Survey on Spatial Modulation in Emerging Wireless Systems: Research Progresses and Applications <s> NT K <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> BIB005 </s> A Survey on Spatial Modulation in Emerging Wireless Systems: Research Progresses and Applications <s> NT K <s> This letter presents a sphere decoding strategy for generalized spatial modulation (GSM) systems. The proposed modifications reduce the exhaustive tree search for lattice points and exploits the structure of GSM, restraining the tree branches to those that result in valid antenna combinations. As a result, every found lattice point results in valid GSM transmitted symbols. The numerical results exhibit significant complexity reduction. <s> BIB006 </s> A Survey on Spatial Modulation in Emerging Wireless Systems: Research Progresses and Applications <s> NT K <s> In this letter, an improved ordered-block minimum-mean-squared-error (OB-MMSE) detector for generalized spatial modulation systems is presented. We first propose to use the concentrated distance metric derived from the conditional maximum likelihood estimator as the ordering metric for the OB-MMSE and then design a computationally-efficient algorithm for computing this metric. The improved ordering performance of the proposed algorithm allows the early-termination of the OB-MMSE detector without noticeable performance loss which can be exploited to further reduce its complexity. Simulation results show that the proposed algorithm can achieve better performance-complexity tradeoff compared to the existing OB-MMSE detector. <s> BIB007 </s> A Survey on Spatial Modulation in Emerging Wireless Systems: Research Progresses and Applications <s> NT K <s> Spatial modulation (SM) combined with spatial multiplexing is a newly developed transmission scheme in multiple-input multiple-output (MIMO) systems. The resultant system, referred to as generalized SM (GSM), can use the maximum-likelihood (ML) detector jointly detecting the antenna-subset (AS) index and symbol vector. As known, the ML detector can achieve optimum performance; however, its computational complexity can be prohibitively high when the dimension of the GSM system is large. In this paper, we propose new methods to solve the problem. The main idea is to split the detection into two stages, one for the AS index and the other for the symbol vector. For the detection of the AS index, we develop two methods, referred to as Gaussian approximation and QR projection. Once the AS index is detected, conventional low-complexity ML detectors can be applied for the detection of the symbol vector. The diversity order for the proposed methods are further analyzed and an enhanced method is also proposed to achieve near-optimum performance. Finally, the proposed methods are extended to conduct soft detection of GSM systems. Simulations show that our methods significantly outperform existing ones while the detection complexity remains similar. <s> BIB008 </s> A Survey on Spatial Modulation in Emerging Wireless Systems: Research Progresses and Applications <s> NT K <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> BIB009 </s> A Survey on Spatial Modulation in Emerging Wireless Systems: Research Progresses and Applications <s> NT K <s> Generalized spatial modulation (GSM) is a recently proposed appealing multi-input multi-output (MIMO) transmission technique, which is capable of striking a tradeoff between the achievable transmission rate and the cost of radio frequency (RF) chains. In this letter, a novel low-complexity near-optimal soft decision (SoD)-aided detector is proposed for GSM, which considerably reduces the search space by employing a block minimum mean-squared error (B-MMSE) algorithm. Our simulation results show that the proposed detector is capable of achieving a better tradeoff between bit-error-rate (BER) performance and computational complexity compared with the existing matched filter (MF)-based SoD algorithms. <s> BIB010 </s> A Survey on Spatial Modulation in Emerging Wireless Systems: Research Progresses and Applications <s> NT K <s> Generalized spatial modulation (GSM) is a relatively new multi-input multi-output transmission technique that enables a flexible trade-off between the achievable transmission rate and the cost of radio frequency chains. However, due to the constraint of transmit antenna combination and the variation of interchannel interference, the efficient low-complexity demodulation of GSM signals is challenging, especially when soft demodulation is needed. In this paper, we propose two low-complexity algorithms based on the deterministic sequential Monte Carlo (SMC) technique for the demodulation of GSM. The type-I SMC demodulator, which uses the conventional successive interference cancellation as the kernel and draws antenna-wise samples from the extended constellation, is proposed for the overdetermined GSM system. The type-II SMC demodulator, which consists of two stages and uses the orthogonal matching pursuit as the kernel in the first stage, is proposed for the underdetermined GSM system. A key component in both algorithms is an efficient online scheme to eliminate the illegal samples during the sampling process. Both proposed algorithms achieve near-optimal performances with complexity linear in terms of the antenna size. Moreover, owing to their soft-input soft-output nature, they can be employed in a turbo receiver for a coded GSM system. <s> BIB011 </s> A Survey on Spatial Modulation in Emerging Wireless Systems: Research Progresses and Applications <s> NT K <s> Due to the interchannel interference and the varying active antennas in generalized spatial modulation (GSM), it is challenging to detect the transmitted data effectively while imposing low computational burden to the receiver. In this paper, we propose a novel algorithm based on the K-best sphere decoding for the soft detection of the GSM signal, which performs the breadth-first tree search in two stages sequentially. By exploiting the null space of the GSM channel, the inactive antenna searching is carried out antennawise in the first stage, in which a recursive algorithm for updating the QL decomposition (a decomposition of a matrix into a product of an orthogonal matrix and a lower triangular matrix) is proposed to calculate the branch metrics and an effective examination scheme is developed to prune those illegal or repetitive child nodes. Based on the available QL decomposition structure that has been updated recursively during the first stage, the second stage of the proposed detector is then readily concatenated to search for the modulated symbols carried on the active antennas in a one-by-one manner. Moreover, owing to the soft-input soft-output nature, the proposed detector can be applied in a turbo decoder for a coded GSM system. Both complexity analysis and simulation results corroborate the superiority of the proposed soft detector for the GSM system. <s> BIB012
bits is applied to the index selector for activating K antennas (i.e., determining the indices of those active antennas) where j k ∈ T {1, . . . , N T } is the index of the k-th active antenna with j 1 < j 2 · · · < j K and J stands for the active antenna combination (AAC), whose bit mapping procedure can be implemented using the look-up table when the number of AACs is small or combination strategy when the number of AACs is large BIB003 -  . It is worth noting that among NT K possible combinations, only N L = 2 p1 AACs are permitted while the other NT K −N L AACs are illegal due to the integer constraint of mapping bits. Without loss of generality, the set of N L legal AACs is denoted as J = {J j } NL j=1 . The second part with p 2 = K log 2 M bits is then applied to the symbol modulator for generating K constellation symbols transmitted by the active antennas, which generates the transmitting block as where s k is drawn from an order-M constellation A = {a ı } M ı=1 and transmitted by the k-th active antenna. Denote After transmission through the MIMO channel, the signal model at the receiver side is expressed as where ρ strands for the transmit power, w ∼ N c (0, I NR ) denotes an additive white Gaussian noise (AWGN) vector with a zero mean and normalized variance, s [s 1 s 2 . . . s K ] T ∈ A K is a K × 1 constellation symbol vector carried by the Simulation results extracted from BIB011 and BIB012 . active antennas, and H J [h j1 h j2 . . . h jK ] consists of the K columns of H corresponding to K active transmit antennas. The receiver of (G)SM has to detect the indices of the active antennas and demodulate the corresponding constellation symbols simultaneously for information recovery. By performing a joint detection over the active antenna indices and constellation symbols, the ML detector for (G)SM can be expressed as We can observe from (9) that the size of the search space is O(N L · M K ), resulting in a considerably high search complexity, especially for large-scale MIMO or high order constellations. Therefore, many researchers have focused on the design of low-complexity detection algorithms for the (G)SM system, e.g., the CS based detections BIB002 - BIB009 , the ordered block minimum mean-squared-error (OB-MMSE) based detections BIB004 , BIB007 , the message passing based detection  , the Gaussian approximation based detections BIB008 , BIB005 , and sphere decoding (SD) based detections BIB006 - BIB001 . However, the above-mentioned detection algorithms either suffer from suboptimal performance with considerable loss or encounter a fluctuating complexity that depends on the channel conditions, making them unsuitable for practical implementations. Moreover, most existing detectors output hard-decisions, which suffer from some performance loss when channel codes are deployed in the coded (G)SM system. In BIB010 , a soft OB-MMSE based detector is proposed to output soft-decisions for the coded (G)SM system, which sorts the possible AAC based on the specific metric and then proceeds to estimate the constellation symbols associated with the MMSE solution for each AAC. To achieve near-optimal performance but with low complexity for coded (G)SM systems, soft detection algorithms based on deterministic sequential Monte Carlo (DSMC) and K-best SD are proposed in BIB011 , BIB012 , respectively. Fig. 3 shows the performance results of some representative detectors in terms of bit error rate (BER) for the uncoded (G)SM system. It can be observed from Fig. 3 that by showing the ML detector as the benchmark, the detectors proposed by BIB011 and BIB012 can achieve near-optimal performance while other detectors still suffer from some performance loss. To examine the performance of soft decoders, Fig. 4 shows the comparison results in terms of BER for the coded (G)SM system, where the turbo receiver and rate-1/2 constraint length-3 convolutional code are employed. It can be observed that the DSMC based detector in BIB011 achieves nearly the same performance as the MAP detector (acts as the performance benchmark for the turbo receiver) under different iteration numbers, which outperforms the soft OB-MMSE detector in BIB010 significantly.