A Survey on Spatial Modulation in Emerging Wireless Systems: Research Progresses and Applications <s> A. Link-Adaptive SM <s> In this letter, an adaptive spatial modulation (ASM) transmission scheme is proposed to achieve better system performance under a fixed data rate. The proposed scheme is based on a developed modulation order selection criterion (MOSC), so as to minimize the conditioned pairwise error probability (PEP) for each channel realization. Furthermore, the special information-conveying mode of spatial modulation (SM) is utilized to reduce the complexity of the proposed algorithm. Simulation results show that the proposed adaptive SM scheme provides considerable system performance improvement compared to original SM system. <s> BIB001 </s> A Survey on Spatial Modulation in Emerging Wireless Systems: Research Progresses and Applications <s> A. Link-Adaptive SM <s> The problem of adaptive space modulation (ASM) design using partial channel state information at the transmitter (CSIT) is investigated. ASM relies on adaptive modulation of information symbols in the spatial domain using multiple antennas based on some sort of CSIT. The CSIT is exploited to adjust the transmission such that the distances between the receive constel- lation vectors are increased to reduce the probability of error. We assume that the spatial correlation matrices are available as the partial CSIT and introduce two different approaches to design ASM. In the first approach, we consider that all the transmit antennas are active at each transmit interval and, using an upper bound on the average probability of error, design the transmit vectors based on the spatial correlation matrices to improve the performance. In the second approach and to avoid interantenna synchronization, we assume that only one transmit antenna is active at each transmit interval, and we modify a space shift keying (SSK) transmission by transmitting different complex values from different transmit antennas. Finally, we derive a power allocation to improve further the performance in nonstationary channels. By simulation, we show the effectiveness of the proposed approaches in improving the performance in terms of the symbol error rate (SER). Index Terms—Adaptive space modulation (ASM), multiple- input-multiple-output (MIMO), partial channel state informa- tion at the transmitter (CSIT), space shift keying (SSK), spatial modulation (SM). <s> BIB002 </s> A Survey on Spatial Modulation in Emerging Wireless Systems: Research Progresses and Applications <s> A. Link-Adaptive SM <s> Adaptive power allocation (PA) algorithms based on optimization of the minimum distance $d_{\min} $ between signal points at the receiver side are investigated in spatial modulation (SM) systems. First, a closed-form solution of the optimal maximum- $d_{\min} $ -aided PA algorithm is derived in the case of two transmit antennas (TAs) . Moreover, for a higher number of TAs, we propose a numerical approach, which appropriately splits the power between the specific TA pair associated with $d_{\min} $ to increase this distance. Furthermore, our PA-aided SM systems may be readily combined with adaptive modulation (AM) to further improve the system's performance. Our numerical results show that the proposed algorithms provide beneficial system performance improvements compared with both the equal-gain PA-based SM and the identical-throughput PA-aided spatial multiplexing systems. <s> BIB003 </s> A Survey on Spatial Modulation in Emerging Wireless Systems: Research Progresses and Applications <s> A. Link-Adaptive SM <s> We have recently introduced adaptive spatial modulation (ASM) for multiple antenna systems, with the aim of improving the energy efficiency through spatial modulation (SM) and improving the average spectral efficiency (ASE) through adaptive modulation (AM). In this paper, we extend ASM to cognitive radio (CR) systems in an effort to improve the secondary system's performance in terms of energy efficiency and ASE. To this end, we propose two ASM schemes, one referred to as fixed power scheme (FPS) and the other as adaptive power scheme (APS). In both schemes, the secondary transmitter (ST) has limited knowledge of the channel state information (CSI) of the interference link. The difference between the two schemes, however, lies in the way the limited CSI is used to adapt the transmit power and/or modulation. As a benchmark, we also consider the scenario where the ST has perfect knowledge of the CSI of the interference link. For all cases, we analyze the performance in terms of ASE, average delay, and bit error rate (BER). We show that the proposed schemes offer tradeoffs in terms of the previously mentioned performance metrics, thus offering different options for applying ASM to CR systems. We also provide several simulation examples through which we corroborate the analytical results. <s> BIB004 </s> A Survey on Spatial Modulation in Emerging Wireless Systems: Research Progresses and Applications <s> A. Link-Adaptive SM <s> Antenna switch enables multiple antennas to share a common RF chain. It also offers an additional spatial dimension, i.e., antenna index, that can be utilized for data transmission via both signal space and spatial dimension. In this paper, we propose a Huffman coding-based adaptive spatial modulation that generalizes both conventional spatial modulation and transmit antenna selection. Through the Huffman coding, i.e., designing variable length prefix codes, the transmit antennas can be activated with different probabilities. When the input signal is Gaussian distributed, the optimal antenna activation probability is derived through optimizing channel capacity. To make the optimization tractable, closed form upper bound and lower bound are derived as the effective approximations of channel capacity. When the input is discrete QAM signal, the optimal antenna activation probability is derived through minimizing symbol error rate. Numerical results show that the proposed adaptive transmission offers considerable performance improvement over the conventional spatial modulation and transmit antenna selection. <s> BIB005 </s> A Survey on Spatial Modulation in Emerging Wireless Systems: Research Progresses and Applications <s> A. Link-Adaptive SM <s> In this letter, an adaptive spatial modulation (SM) scheme, in which the spatial signatures of the transmitted signals are adaptively selected according to the channel responses, is proposed for the uplink of a millimeter-wave communication system. We first use an iterative method to search for the spatial signatures that maximize the minimum Euclidean distance of the SM symbols. Following this, a suboptimal scheme is provided to reduce the computational complexity. Numerical results show that the proposed adaptive SM scheme can effectively reduce the system symbol-error rate. <s> BIB006 </s> A Survey on Spatial Modulation in Emerging Wireless Systems: Research Progresses and Applications <s> A. Link-Adaptive SM <s> Generalized spatial modulation (GSM) activates $n_{t}$ out of $N_{t}~(1 \leq n_{t} available transmit antennas, and information is conveyed through $n_{t}$ modulated symbols as well as the index of the $n_{t}$ activated antennas. GSM strikes an attractive tradeoff between spectrum efficiency and energy efficiency. Linear precoding that exploits channel state information at the transmitter enhances the system error performance. For GSM with $n_{t}=1$ (the traditional SM), the existing precoding methods suffer from high computational complexity. On the other hand, GSM precoding for $n_{t} \geq 2$ is not thoroughly investigated in the open literature. In this paper, we develop a unified precoding design for GSM systems, which universally works for all $n_{t}$ values. Based on the maximum minimum Euclidean distance criterion, we find that the precoding design can be formulated as a large-scale nonconvex quadratically constrained quadratic program problem. Then, we transform this challenging problem into a sequence of unconstrained subproblems by leveraging augmented Lagrangian and dual ascent techniques. These subproblems can be solved in an iterative manner efficiently. Numerical results show that the proposed method can substantially improve the system error performance relative to the GSM without precoding and features extremely fast convergence rate with a very low computational complexity. <s> BIB007
Under the slow fading channel model, link-adaptive SM can be applied to achieve better BER performance and higher channel utilization by adapting the parameter settings (e.g., modulation order, transmit power and number of transmit antennas) or precoding matrices according to the channel condition. Specifically, after channel estimation, the receiver determines the optimal transmission parameters in terms of modulation order, power allocation profile and antenna selection mode, or the optimal precoders, which is then sent back to the transmitter using a limited feedback link BIB001 - BIB003 . In BIB004 , adaptive SM mechanisms, which adapt the modulation type and/or transmit power through the limited reliable feedback channel, are introduced to cognitive radio systems to enhance both the spectral and energy efficiency of the secondary system. An adaptive SM scheme based on the Huffman coding technique is proposed in BIB005 , which activates transmit antennas with distinct probabilities via Huffman mapping with a variable-length code. In addition, BIB002 exploits spatial correlation as the partial CSI at the transmitter to realize the adaptive SM principle, which is shown to achieve performance improvement. An adaptive unified linear precoding scheme based on the maximum criterion of the minimum Euclidean distance for (G)SM systems is proposed in BIB007 , which maintains the RF chains and is shown to improve the system error performance relative to the (G)SM systems without precoding. The adaptive SM principle is also introduced in mmWave communication systems, where the shortest Euclidean distance of the SM symbols is maximized in an iterative manner to improve error performance BIB006 .