Transmit Antenna Combination Research Articles

Low-Complexity GSM Detection Based on Maximum Ratio Combining

Generalized spatial modulation (GSM) technology is an extension of spatial modulation (SM) technology, and one of its main advantages is to further improve band efficiency. However, the multiple active antennas for transmission also brings the demodulation difficulties at the receiver. To solve the problem of high computational complexity of the optimal maximum likelihood (ML) detection, two sub-optimal detection algorithms are proposed through reducing the number of transmit antenna combinations (TACs) detected at the receiver. One is the maximum ratio combining detection algorithm based on repetitive sorting strategy, termed as (MRC-RS), which uses MRC repetitive sorting strategy to select the most likely TACs in detection. The other is the maximum ratio combining detection algorithm, which is based on the iterative idea of the orthogonal matching pursuit, termed the MRC-MP algorithm. The MRC-MP algorithm reduces the number of TACs through finite iterations to reduce the computational complexity. For M-QAM constellation, a hard-limited maximum likelihood (HLML) detection algorithm is introduced to calculate the modulation symbol. For the M-PSK constellation, a low-complexity maximum likelihood (LCML) algorithm is introduced to calculate the modulation symbol. The computational complexity of these two algorithms for calculating the modulation symbol are independent of modulation order. The simulation results show that for GSM systems with a large number of TACs, the proposed two algorithms not only achieve almost the same bit error rate (BER) performance as the ML algorithm, but also can greatly reduce the computational complexity.

Efficient Hardware Implementation of CORDIC-Based Symbol Detector for GSM MIMO Systems: Algorithm and Hardware Architecture

Aiming at providing an efficient hardware architecture for generalized spatial modulation (GSM) multiple-input multiple-output (MIMO) systems, in this paper a COordinate Rotation DIgital Computer (CORDIC) -based symbol detector is proposed. In the proposed detector, several CORDIC-based Givens rotation modules are conducted in parallel for the transmit antenna combinations (TACs) to facilitate QR-decomposition. After that, the proposed detector uses adders, shifters, and backward substitution mechanisms to currently estimate symbols for the corresponding TAC. At last, the estimated symbols and corresponding TAC index with the smallest distance measurement are chosen as the final solution. In particular, to achieve efficient hardware implementation, the architecture of the proposed detector has several features, including multiplication-free ranking mechanism, parallel CORDIC-based architectures, and shorter-bit-length multipliers. In addition, the overall architecture is pipelined to speed up the processing of the hardware. At last, simulation results reveal the proposed detector performs near to the optimal maximum likelihood (ML), but uses lower computational complexity. Additionally, the VLSI implementation results under the TSMC 90-nm CMOS technology show that the proposed hardware architecture requires 266K gates (KGEs), provides detection throughput 2.008 Gbps, works with pre-processing latency of 47 clock cycles, and has the hardware efficiency 7.54 (Mbps/KGEs) while operating at frequency 200.8 MHz. Moreover, implementation comparisons show the proposed architecture provides high throughput rate as well as hardware efficiency, and works with low pre-processing latency.

Low Complexity Quasi-Optimal Detector for Generalized Spatial Modulation

Generalized Spatial Modulation (GSM) is a promising technique for high data-rates systems where the complexity of the optimal joint detector based on the Maximum Likelihood (ML) criterion increases dramatically in terms of the modulation order and the number of activated transmit antennas. In this letter, a novel detection scheme for GSM systems denoted by O <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> SIC-ML is proposed to achieve the optimal performance with a controllable complexity-performance trade-off. The proposed detector is accompanied with ordering techniques for the transmit antenna combination and symbols to further reduce the complexity and improve the performance, respectively. The result reveals that O <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> SIC-ML allows reaching the non-linear ML detector performance with a 99% complexity reduction.

Sub-Terahertz Wireless System Using Dual-Polarized Generalized Spatial Modulation With RF Impairments

In this paper, we address a multiple-input multiple-output (MIMO) communication system based on generalized spatial modulation (GSM) and dual-polarized (DP) antennas in sub-TeraHertz (sub-THz) bands to improve the Spectral Efficiency (SE) while reducing the spatial correlation effect and the space occupancy. Moreover, the joint Maximum Likelihood (ML) detector and a Modified Ordered Block Minimum Mean-Squared Error (MOB-MMSE) detector algorithm are proposed to detect jointly the complex symbols and the virtual bits conveyed by the activated polarization and the transmit antenna combination index. MOB-MMSE can achieve near-ML performance with low complexity. The performance of DP-GSM system over correlated Rayleigh/Rician fading and indoor sub-THz channels is studied. Provided results show that DP-GSM system is robust to the spatial correlation effects under Rician fading channel. In addition, an average bit-error probability (ABEP) upper bounding is derived and analyzed for the DP-GSM system over correlated Rayleigh/Rician fading channels. Since the sub-THz band suffers from many technological limitations and severe RF-impairments such as low transmit output power and important phase noise (PN), the DP-GSM system is studied by considering the sub-THz impairments. Moreover, the Dual Polarized Spatial Multiplexing (DP-SMX) and the Uni-Polarized GSM (UP-GSM) are compared with the DP-GSM system. The results reveal that DP-GSM with low order modulation schemes as QPSK outperforms the UP-GSM. Besides, DP-GSM and DP-SMX provide a good performance up to medium PN, which is interesting for sub-THz bands, but DP-GSM can reduce the transceiver cost by using a lower number of RF chains when the used transmitter architecture is based on RF-switching.

Fixed-Complexity Tree Search Schemes for Detecting Generalized Spatially Modulated Signals: Algorithms and Hardware Architectures

In the generalized spatial modulation (GenSM) multiple input multiple output (MIMO) system, each block of data bits is mapped to a set of spatially multiplexed (SMX) symbols and an index of transmit antenna combination (TAC) of active antennas. The difficulty for the GenSM MIMO receiver is to detect the SMX symbols and TAC index simultaneously. Recently, we applied the conventional sphere decoding algorithm (SDA) successively to achieve the exact maximum likelihood detection (MLD) of GenSM MIMO signals. The SDA scheme suffers from variable computational complexity and leads to hardware detectors with variable throughput rate. Instead, fixed-complexity tree search algorithms, e.g., reduced fixed sphere decoding (rFSD), with nearly MLD performance are employed to facilitate hardware implementation. Here, we propose to apply the rFSD successively and design a hardware architecture for detecting GenSM MIMO signals under the scenario of 5 transmit antennas, 2 transmit radio frequency chains, 4 receive antennas, and 64-QAM SMX symbols. The VLSI implementation results under the TSMC 90nm CMOS technology reveal that our architecture requires 276.7K gates and provides detection throughput 1.613 Gbps, while operating at 322.6 MHz. Compared with other related architectures, our architecture provides higher detection throughput rate and is of better hardware efficiency.

A Joint Data Mapping and Detection for High Performance Generalized Spatial Modulation

This letter proposes a novel joint data mapping generalized spatial modulation (JDM-GSM) scheme to remove the restriction on the number of active transmit-antenna (TA) combinations in conventional GSM systems. By increasing the number of active TA combinations, the constellation size for signal mapping can be reduced. Consequently, the overall bit error rate (BER) performance of the GSM system can be improved. To reduce the complexity of optimal maximum-likelihood (ML) detector, a joint compressed sensing (JCS) detector for JDM-GSM scheme is proposed. Simulation results and theoretical analysis show that the proposed scheme can be adapted to multiple-input multiple-output (MIMO) systems and achieves better BER performance than that of the conventional GSM.

Codebook-based precoding for generalized spatial modulation with diversity

This paper investigates codebook-based precoding for spatial modulation (SM) and generalized spatial modulation (GSM) systems. Codebook-based precoding allows the system to dispense with full channel state information at the transmitter (CSIT). This considerably reduces the feedback overhead. Phase-only codebooks with systematic structure are investigated since they avoid increasing the peak to average power ratio of the transmitted signal. It is shown that the proposed phase-only codebooks yield equivalent performance to published codebooks that involve gain and phase. In addition, a gain-only codebook is designed to supplement the phase-only codebook and reduce the bit error rate (BER) further. We also compare the performance with the Grassmannian codebooks which are proposed for other multiple-in-multiple-out (MIMO) systems. In GSM systems, several antennas are simultaneously active as a transmit antenna combination (TAC). The BER performance of unprecoded GSM systems is typically inferior to SM systems due to correlation among TACs. However, with codebook precoding, this effect is mitigated, and the performance of the GSM system becomes superior to the SM system. We investigate codebook precoding for GSM systems where precoding is performed per-TAC or per-antenna. Moreover, we investigate the GSM system where the TACs are selected adaptively based on the achievable benefit from codebook precoding. Using computer simulation, it is shown that the performance of the proposed codebooks is very promising in both SM and GSM systems. Per-antenna precoding is superior to per-TAC precoding. Adaptive TACs selection further improves performance.

Secure Precoding Aided Spatial Modulation via Transmit Antenna Selection

In this paper, two transmit antenna selection schemes are proposed for precoding-aided spatial modulation (PSM) to enhance the secrecy performance with reduced hardware complexity. The first strategy is determined by the channel state information (CSI) of both the legitimate and illegitimate links, called deterministic antenna selection based PSM (DAS-PSM), which selects partial transmit antennas to implement zero-forcing (ZF) precoding for maximizing the secrecy rate. For practical implementation, the low-complexity DAS-PSM criterion is demonstrated. The second strategy resorts to random antenna selection (RAS) with the aid of fast radio-frequency switching. Different from the DAS-PSM, this so-called RAS based PSM (RAS-PSM) dispenses with the CSI of the wiretap channel, which generates the ZF precoding matrix associated with randomly selected transmit antenna combination during each symbol period, creating additional turbulence that solely affects the eavesdropper. To combat the issue of low secrecy rate in the high signal-to-noise ratio regime due to the finite-alphabet inputs, time-varying artificial noise with extra power can be incorporated into both aforementioned strategies, which is exemplified in the RAS-PSM. Finally, the secrecy rates of both proposed schemes are theoretically analyzed and evaluated via Monte Carlo simulations, demonstrating that both proposed schemes with different requirements are capable of enhancing the secrecy performance compared to the conventional PSM.

Signal Shaping for Generalized Spatial Modulation and Generalized Quadrature Spatial Modulation

This paper investigates generic signal shaping methods for multiple-data-stream generalized spatial modulation (GenSM) and generalized quadrature spatial modulation (GenQSM) based on the maximizing the minimum Euclidean distance (MMED) criterion. Three cases with different channel state information at the transmitter (CSIT) are considered, including no CSIT, statistical CSIT and perfect CSIT. A unified optimization problem is formulated to find the optimal transmit vector set under size, power and sparsity constraints. We propose an optimization-based signal shaping (OBSS) approach by solving the formulated problem directly and a codebook-based signal shaping (CBSS) approach by finding sub-optimal solutions in discrete space. In the OBSS approach, we reformulate the original problem to optimize the signal constellations used for each transmit antenna combination (TAC). Both the size and entry of all signal constellations are optimized. Specifically, we suggest the use of a recursive design for size optimization. The entry optimization is formulated as a non-convex large-scale quadratically constrained quadratic programming (QCQP) problem and can be solved by existing optimization techniques with rather high complexity. To reduce the complexity, we propose the CBSS approach using a codebook generated by quadrature amplitude modulation (QAM) symbols and a low-complexity selection algorithm to choose the optimal transmit vector set. Simulation results show that the OBSS approach exhibits the optimal performance in comparison with existing benchmarks. However, the OBSS approach is impractical for large-size signal shaping and adaptive signal shaping with instantaneous CSIT due to the demand of high computational complexity. As a low-complexity approach, CBSS shows comparable performance and can be easily implemented in large-size systems.

Fast Maximum Likelihood Detection of the Generalized Spatially Modulated Signals Using Successive Sphere Decoding Algorithms

The generalized spatial modulation (GSM) scheme is used in wireless communication to map each block of data bits to a set of spatially multiplexed (SMX) symbols and an index of transmit antenna combination (TAC) of active antennas. The SMX symbols are then transmitted simultaneously through the multiple active antennas. The detection of the GSM signals at the receiver side needs to recover both the SMX symbols and TAC index. To achieve maximum likelihood detection (MLD) of GSM signals with low complexity, two previous algorithms modify the computationally efficient sphere decoding algorithm (SDA) and needs to discriminate the SMX symbols from the null symbols transmitted by inactive antennas. In this letter, we propose a new successive SDA (SSDA) that employs multiple times of SDA though but does not need to process the null symbols during tree traversals. Particularly, when used together with the radius update and reordering of the multiple SDAs, our SSDA achieves great complexity reduction and is the fastest one among the algorithms that achieve exact MLD of GSM signals.

Ordering- and Partitioning-Aided Sphere Decoding for Generalized Spatial Modulation

In this study, low-complexity sphere decoding (SD) algorithms for generalized spatial modulation (GSM) are proposed. To reduce the computational complexity of the SD algorithm for GSM, layer ordering and transmit antenna combination (TAC) partitioning are employed. The layer ordering scheme determines the detection order of layers based on their reliabilities, which are measured by their minimum mean-square errors (MMSEs). In TAC partitioning, which is combined with the early termination technique, the likely TACs are selected by exploiting an MMSE-based weighting metric to reduce the search space. Simulation results demonstrate that the proposed ordering and partitioning aided SD schemes achieve nearly the same performance as the conventional SD scheme; however, they require significantly low complexity, especially in large GSM multiple-input-multiple-output systems and in the low SNR region.

Transmit Antenna Combination Optimization for Generalized Spatial Modulation Systems

Generalized spatial modulation (GSM), where both the transmit antenna combination (TAC) index and the amplitude phase modulation (APM) symbols convey information, is a novel low-complexity and high efficiency multiple-input multiple-output (MIMO) technique. In conventional GSM (C-GSM), the legitimate TACs are selected randomly to transmit the APM symbols. However, the number of the TACs must be a power of two, hence the excess TACs are discarded, resulting in wasting some resource. To address these issues, in this paper, an optimal TAC set-aided enhanced GSM (E-GSM) scheme is proposed, where the optimal TAC set is selected with the aid of the channel state information (CSI) by maximizing the minimum Euclidean distance. Furthermore, a hybrid mapping GSM (HM-GSM) scheme operating without CSI knowledge is investigated, where the TAC selection and bit-to-TAC mapping are both taken into consideration for optimizing the average Hamming distance. Finally, an enhanced high throughput GSM (E-HT-GSM) scheme is developed, which makes full use of all the TACs. This scheme is capable of achieving an extra one bit transmission rate per time slot. Moreover, the rotated phase is employed and optimized for the reused TACs. Our simulation results show that the proposed E-GSM system and HM-GSM system are capable of outperforming the C-GSM system. Furthermore, the E-HT-GSM system is capable of obtaining one extra bit transmission rate per time slot compared with the C-GSM system.

Signal constellations employing multiplicative groups of Gaussian and Eisenstein integers for Enhanced Spatial Modulation

In this paper, we propose two new signal constellation designs employing Gaussian and Eisenstein Integers for Enhanced Spatial Modulation (ESM). ESM is a novel technique which was propounded by Cheng et al. The advantage of ESM over other Spatial Modulation (SM) schemes lies in its ability to enhance spectral efficiency while keeping the energy efficiency intact. This is done by activating either one or two antennas judiciously depending upon the required trade-off. In ESM, information radiated from the antennas depends upon index of the active transmit antenna combination(s) and also on the set of constellation points chosen, which may include points from multiple constellations. In this paper, we propose signal constellations based on multiplicative groups of Gaussian and Eisenstein integers. The set comprising of Gaussian and Eisenstein integers serves as primary and secondary constellation points for Gaussian Enhanced Spatial Modulation (GESM) scheme. The secondary constellation points are deduced from a single geometric interpolation from the primary constellation points. The Monte Carlo simulation results indicate that the proposed nonuniform constellations achieve impressive SNR gains compared to conventional constellation points used in the design of ESM. This new design has been described for MIMO employing 4 × 4 and 8 × 8 antenna configurations with only two active antennas. Furthermore, a closed form expression for the pairwise error probability (PEP) for the GESM scheme has been deduced. The PEP is utilized to determine the upper bound on the average bit error probability (ABEP). Our simulations indicate that the proposed GESM from Gaussian and Eisenstein integers scheme outperforms all the other variants of SM including conventional ESM by at least 2.5 dB at an average bit error ratio (ABER) of 10−5. Close correspondence between the theoretical analysis and the Monte Carlo simulation results are observed.

Efficient Transmission and Detection Based on RNS for Generalized Space Shift Keying

We propose an efficient transmission scheme for the generalized space shift keying (GSSK) based on the residue number system (RNS). The proposed scheme increases the number of active transmit antenna combinations (TACs), resulting in a higher throughput than that of the conventional GSSK systems. The received signals can be detected by a joint maximum likelihood (ML) detection, whose complexity, however, grows exponentially with the number of active TACs. To solve this problem, we propose a new detection method based on the RNS, whose complexity is much lower than that of the joint ML detection with negligible performance loss.

Soft Demodulation Algorithms for Generalized Spatial Modulation Using Deterministic Sequential Monte Carlo

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.

Improved QRD-M Detection Algorithm for Generalized Spatial Modulation Scheme

Generalized spatial modulation (GSM) is a spectral and energy efficient multiple-input multiple-output (MIMO) transmission scheme. It will lead to imperfect detection performance with relatively high computational complexity by directly applying the original QR-decomposition with M algorithm (QRD-M) to the GSM scheme. In this paper an improved QRD-M algorithm is proposed for GSM signal detection, which achieves near-optimal performance but with relatively low complexity. Based on the QRD, the improved algorithm firstly transforms the maximum likelihood (ML) detection of the GSM signals into searching an inverted tree structure. Then, in the searching process of the M branches, the branches corresponding to the illegitimate transmit antenna combinations (TACs) and related to invalid number of active antennas are cut in order to improve the validity of the resultant branches at each level by taking advantage of characteristics of GSM signals. Simulation results show that the improved QRD-M detection algorithm provides similar performance to maximum likelihood (ML) with the reduced computational complexity compared to the original QRD-M algorithm, and the optimal value of parameter M of the improved QRD-M algorithm for detection of the GSM scheme is equal to modulation order plus one.

Improved generalized spatial modulation via antenna selection

SummaryWhen a high spectral efficiency is needed, the cost of Euclidean distance‐based antenna selection for spatial modulation (EDAS‐SM) in terms of hardware, size, and computational complexity is significantly increased because of the large transmit antenna array required. In comparison, generalized spatial modulation (GSM) can match the spectral efficiency of EDAS‐SM, while using significantly fewer transmit antenna elements. However, the error performance of GSM is naturally limited because of the use of a predetermined and fixed set of transmit antenna combinations. By exploiting knowledge of the channel, the optimal set of transmit antenna combinations can be selected by maximizing the minimum Euclidean distance between transmit vectors. In this paper, an adaptive scheme for selection of the optimal set of transmit antenna combinations is proposed to improve the reliability of GSM. The computational overhead of the said scheme is relatively high; hence, a low‐complexity suboptimal scheme for selection of the set of transmit antenna combinations is further proposed. The improved GSM schemes address the spectral efficiency limitation of EDAS‐SM, while demonstrating superior error performance.

Double space‐time transmit diversity with spatial modulation

A hybrid scheme of the double space-time transmit diversity (DSTTD) and spatial modulation (SM) is proposed. The spectral efficiency of proposed scheme is twice that of DSTTD. Additional bits are transmitted by transmit antenna combinations of SM without widening the bandwidth. An optimised rotated constellation is also proposed according to the antenna combination to reduce inter-channel interference.

Low-Complexity Signal Detection for Generalized Spatial Modulation

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.