Precoding-aided Spatial Modulation Research Articles

Novel Receive Antenna Selection Scheme for Precoding-Aided Spatial Modulation with Lattice Reduction.

In this paper, a new receive antenna subset (RAS) selection scheme is proposed for precoding-aided spatial modulation (PSM). First, a lattice reduction (LR)-based precoder is employed instead of a conventional zero-forcing (ZF) precoder. It is analytically shown that a full diversity gain can be achieved by the LR-based ZF precoder without RAS selection. Then, an optimal LR-based RAS selection criterion is derived for the over-determined LR-based PSM systems, and a suboptimal selection algorithm is additionally presented. It is also shown that optimal and suboptimal RAS selection algorithms based on LR improve the BER performance of the LR-based PSM system. Further, the overall diversity order of the over-determined LR-based PSM systems with optimal LR-based RAS selection is analyzed. Finally, diversity analysis and simulation results show that the LR-ZF-based PSM system with optimal LR-based RAS selection outperforms the conventional ZF-based PSM system with conventional optimal RAS selection.

Performance analysis of precoding‐aided differential spatial modulation systems with transmit antenna selection

In this paper, the performance of precoding-aided differential spatial modulation (PDSM) systems with optimal transmit antenna subset (TAS) selection is examined analytically. The average bit error rate (ABER) performance of the optimal TAS selection-based PDSM systems using a zero-forcing (ZF) precoder is evaluated using theoretical upper bound and Monte Carlo simulations. Simulation results validate the analysis and demonstrate a performance penalty < 2.6 dB compared with precoding-aided spatial modulation (PSM) with optimal TAS selection. The performance analysis reveals a transmit diversity gain of for the ZF-based PDSM (ZF-PDSM) systems that employ TAS selection with transmit antennas, selected transmit antennas, and receive antennas. It is also shown that reducing the number of activated transmit antennas via optimal TAS selection in the ZF-PDSM systems degrades ABER performance. In addition, the impacts of channel estimation errors on the performance of the ZF-PDSM system with TAS selection are evaluated, and the performance of this system is compared with that of ZF-based PSM with TAS selection.

Constructive Interference Precoding for Generalized Precoding-Aided Quadrature Spatial Modulation With Phase-Shift-Keying Signaling

In this letter, we formulate computationally efficient precoder and detector design problems for symbol-level generalized precoding-aided spatial modulation (GPQSM) systems with phase-shift-keying signaling. We first present a novel low-complexity decoupled detector. Subsequently, we formulate two new precoders using constructive interference (CI) techniques to enhance the performance of the proposed decoupled detector. We then demonstrate that both precoder design problems share a unified form, which enables them to be solved efficiently using the existing iterative closed-form algorithm. Finally, we show that our proposed CI precoders under efficient implementation strike the best balance between performance and complexity relative to other benchmark algorithms through numerical simulations.

Decoupled Transmit and Receive Antenna Selection for Precoding-Aided Spatial Modulation

This paper proposes an optimal joint transmit and receive antenna subsets (TRASs) selection scheme for linear precoding-aided spatial modulation (PSM) systems. The optimal joint TRASs selection is performed by exhaustively searching, so that it is difficult to analyze an achievable diversity gain and it has a huge complexity. To tackle this problem, we propose a decoupled TRAS selection method which selects receive antenna subset (RAS) and transmit antenna subset (TAS) in a two-step serial manner. By computing a lower bound on the pairwise error probability and conducting extensive simulations, it is shown that the zero-forcing (ZF)-based PSM system with $N_{T} $ transmit antennas, $N_{S} $ selected transmit antennas, $N_{R} $ receive antennas, and $N_{D} $ selected receive antennas achieves diversity order of $(N_{T} -N_{D} +1)(N_{R} -N_{D} +1)$ even with TAS selection. Furthermore, decreasing the number of active transmit antennas by TAS selection after RAS selection is analytically shown to always degrade the bit error rate performance. The analysis results are validated by simulations. These analytical and simulation results can be regarded as natural extensions of earlier works on receive antenna selection and transmit antenna selection for the PSM systems. In addition, we study and compare two efficient algorithms for TRAS selection. First, incremental and decremental algorithms are employed for separable RAS and TAS successive selection, respectively, which have an excellent performance. It is analytically shown that the computational complexity of the first proposed decoupled suboptimal TRAS selection scheme is enormously reduced compared to the joint optimal and decoupled optimal algorithms. Second, an incremental TAS selection approach replaces the decremental strategy in the first TRAS selection algorithm to further reduce the complexity.

Constructive Interference-Based Symbol-Level Precoding for Generalized Precoding-Aided Spatial Modulation With PSK Signaling

In this letter, we investigate a constructive interference (CI)-based symbol-level precoder design for systems employing generalized precoding-aided spatial modulation (GPSM) with phase-shift-keying signaling. Unlike existing GPSM precoders, which treat interference as a harmful factor that should be suppressed, the proposed CI-based precoders exploit the interference as a resource to enhance detection performance. We formulate the design problem and then derive efficient precoding algorithms with a new parametrization featuring generalized inverses. Simulation results indicated that the proposed CI-based precoders can drastically outperform a conventional zero-forcing GPSM precoder, especially when the system is operated in strong self-interference configurations.

Artificial Noise-Aided Secure Generalized Spatial Modulation for Multiuser Transmission

This letter focuses on the secure downlink multi-user generalized spatial modulation (MU-GSM) system based on the artificial noise (AN). Block diagonalization (BD) is firstly used to eliminate inter-user interference. In addition, the AN which has no impact on legitimate users is adopted to prevent eavesdropping for the first time in MU-GSM communication. Particularly, the proposed MU-GSM system can achieve satisfying security performance even without AN, which is different from the single-user scenario. Finally, the simulation results show that with AN protection and BD, the physical layer security can be significantly enhanced when compared with the random noise scheme and the multi-user precoding-aided spatial modulation.

Precoding-Aided Spatial Modulation Assisted Joint Two-Tier Downlink Reception

In this paper, we consider a two-tier downlink scenario, where femtocell users are interested in receiving both macrocell and femtocell information simultaneously at a single frequency (joint two-tier downlink reception). Unlike in conventional handsets, which use orthogonal schemes for accommodating two-tier downlink reception, we propose two non-orthogonal schemes based on precoding-aided spatial modulation (PSM) for handling cross-tier downlink interference. In both the proposed schemes, the femtocell information is conveyed as an active antenna index at the user (spatial symbol), while the macrocell information is conveyed as a phase shift keyed (PSK) symbol on the activated antenna. Appropriate precoders are designed at femtocell base station (FBS) and macrocell base station (MBS) to manage the cross-tier interference. We derive average transmit powers at the MBS and all FBSs for both the schemes. We also optimize the transmit powers of both the schemes at a given target signal-to-noise ratio (SNR). Further, we exploit the existing cross-tier interference as a source of artificial interference for enhancing the physical layer security of femtocell users. We derive secrecy rates of the proposed schemes, and corroborate the analytical expressions derived throughout the paper with simulation results.

Precoding-Aided Spatial Modulation With Dual-Polarized Antennas Over Correlated Channels

In this letter, we propose a dual-polarized precoding-aided spatial modulation (DPPSM) scheme, which introduces the polarization dimension into conventional precoding-aided spatial modulation (PSM) to transmit an additional information bit, avoiding the occupation of additional physical space while offering extra transmit diversity. We obtain an upper bound on the average bit error probability (ABEP) of the proposed DPPSM scheme over correlated fading channels. We also derive an approximate upper bound on the ABEP to show the diversity order. Simulation results show that the upper bound is tight for a high signal-to-noise ratio (SNR) range, and the bit error rate (BER) performance of the proposed DPPSM scheme is better than that of the conventional PSM scheme at the same spectral efficiency when equipped with an equal amount of antennas. Furthermore, the proposed DPPSM scheme is more robust to Gaussian channel error when the channel estimation imperfection is considered.

Diversity order of precoding‐aided spatial modulation using receive antenna selection

In this Letter, the authors analyse the diversity order of the precoding-aided spatial modulation (PSM) system with receive antenna subset (RAS) selection. It is shown that when there are N T transmit antennas, N R receive antennas, and N S selected receive antennas, the achievable diversity order is given by N T − N S + 1 N R − N S + 1 , where the product gain of N T − N S + 1 is achieved by the zero-forcing precoding scheme and another of N R − N S + 1 can be attained by the optimal RAS selection algorithm.

An Anti-Eavesdropping Strategy for Precoding-Aided Spatial Modulation With Rough CSI of Eve

In this paper, an anti-eavesdropping strategy is proposed for secure precoding-aided spatial modulation networks, under the assumption that the rough channel state information of eavesdropper can be obtained at the transmitter. Traditionally, artificial noise (AN) can be always projected into the null-space of the legitimate channel, however it may lead to some security loss since this strategy dispenses with a holistic consideration for secure transmissions. To reduce the computational complexity of our optimization problem, we derive a closed-form expression that is a loose bound of the approximate rate over the illegitimate channel. Then a concave maximization problem is formulated for optimizing the covariance matrix of AN. Simulation results show that our proposed low-complexity scheme performs closely to the method which directly maximizes the approximate secrecy rate expression, and harvests significant secrecy rate gains compared with the traditional null-space projection benchmark.

A Grouped Pre-Coding Aided Spatial Modulation for MIMO Systems

Pre-coding aided spatial modulation (PSM) is a recently introduced concept that achieves low complexity and low cost at the receiver. However, it is only suitable for the symmetric or under-determined system due to the utilization of the linear pre-coding. In this paper, a novel PSM-based transmission strategy termed as grouped pre-coding aided spatial modulation (group PSM) is proposed for the over-determined MIMO system where the number of receive antennas is larger than the number of transmit antennas. In our group PSM scheme, the receive antennas are equally divided into several groups. A single receive antenna group is selected during each time slot and the index of the receive antenna group is used for conveying extra information bits. We design a low complexity detection method for the proposed scheme and derive the bit error rate expression. To further improve the performance of group PSM, we propose a power allocation method, where the power allocated for each receive antenna group is optimized based on maximizing the minimum Euclidean distance between received group PSM signal constellations. We also generalize our group PSM scheme in order to improve the multiplexing gain and flexibility, where a particular subset of receive antenna groups is activated so as to convey more information bits. Our simulation results validate the accuracy of the theoretical analysis and demonstrate that both the proposed group PSM and generalized group PSM schemes achieve good performance and significantly increase the scalability of PSM in practice.

Transmit Antenna Selection for Precoding-Aided Spatial Modulation

This paper examines the impacts of transmit antenna subset (TAS) selection on the biterror-rate (BER) performance of linear precoding-aided spatial modulation (PSM) multiple-input multipleoutput (MIMO) systems. It is analytically shown that decreasing the number of active transmit antennas by TAS selection, which can be used to reduce the number of RF units at the transmitter side, always degrades the BER performance. The expression of a received signal-to-noise ratio (SNR) loss is also derived and its analytical results are shown to be well-matched with simulation results. Furthermore, it is analyzed that when there are NT transmit antennas, NS selected transmit antennas, and NR receive antennas, an achievable diversity order of the zero-forcing (ZF)-based PSM MIMO systems either with optimal TAS selection or without TAS selection can be given as N T -N R +1. To select an optimal TAS based on exhaustive search, an optimization criterion to maximize the received SNR of the selected TAS is employed. In addition, a low-complexity TAS selection scheme is presented using a decremental strategy. It is also observed that the decremental TAS selection algorithm can achieve almost the same BER and achievable rate performance as the optimal one while attaining much lower complexity. Finally, simulation results show that under the identical number of active transmit antennas, the ZF-PSM MIMO system with TAS selection outperforms the conventional ZF-PSM without TAS selection.

Comments and Corrections Correction to “Transmit Antenna Selection for Precoding-Aided Spatial Modulation”

In the above article [1] , the authors found some mistakes in real summation (RS) computations. As the computational complexity in terms of real summation (RS) is re-evaluated in the revision process, we didn’t consider 2 RSs additionally required for a complex multiplication. The resulting RS complexity expressions of (25) and (28) , and RS complexity in Table 3 were mistaken. They have no impact on the discussion and conclusions in the paper. The corrected results are given here.

Joint Precoding Spatial and Rotating Symbol Modulation for Physical-Layer Security

In traditional generalized precoding-aided spatial modulation (GPSM), the mappings of the receive antenna combination index and the constellation symbol are performed independently. In this letter, we propose a joint GPSM and rotating symbol modulation for physical-layer security in wireless communications, which rotates conventional amplitude/phase modulation symbols according to the receive antenna combination index that is unknown to the eavesdropper. Both theoretical and numerical results for the bit error rate and secrecy rate indicate that the eavesdropper can neither successfully recover the spatial information bits nor symbol information bits, which validate that the proposed scheme can significantly enhance the physical-layer security of the considered communication system.

Signaling–Spatial Constellation Tradeoff in Precoding-Aided Spatial Modulation

Precoding-aided spatial modulation (PSM) is a multi-antenna communication scheme, which jointly modulates information bits into both the spatial index and the signaling constellation. Specifically, the spatial bits are conveyed by the index of a receive antenna, which is steered at by precoding at the transmitter. In this paper, the indices of the receive antennas are called a spatial constellation in contrast to the signaling constellation. We investigate the symbol error rate (SER) of the PSM scheme to strike a fine tradeoff between the signaling and the spatial constellation, i.e., the signaling-spatial constellation tradeoff, which minimizes the system's SER. First, we formulate the SER of the PSM scheme. Then, an explicit upper bound on the SER is determined based on an approximation using a weighted sum of exponentials. By minimizing the SER upper bound, we show that for phase-shift keying modulation, it achieves a sufficiently good tradeoff when the size of the signaling constellation is 4, i.e., the quadrature phase-shift keying. The numerical results show that the signaling-spatial constellation tradeoff determined by the derived SER upper bound significantly outperforms other PSM schemes with equal spectral efficiency.

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.

Generalized Precoding-Aided Spatial Modulation via Receive Antenna Transition

Receive antenna transition, which implies the transition of the active receive antennas during a symbol period, is investigated in this letter to enhance the error performance of the generalized precoding-aided spatial modulation (GPSM). Specifically, the precoding at the transmitter alters once at the midpoint of a symbol duration such that one group of active receive antennas transfers to another group. The antenna transition pattern is then capable to deliver extra spatial information bits. The proposed GPSM scheme has two main advantages. First, the system reliability is remarkably improved. Second, it requires less receive antennas to achieve the same spectral efficiency compared with the existing precoding-aided spatial modulation (PSM) and GPSM schemes. An analytical upper bound on average bit error probability of the proposed scheme is derived by exploring the Wishart distribution feature of the channel matrix and the Gamma approximation. Numerical results validate our analysis and show that the proposed scheme outperforms the existing PSM and GPSM schemes in terms of system reliability.

Low complexity LED grouping based precoding‐aided spatial modulation for highly correlated large‐scale MIMO‐VLC channels

In this study, the authors propose a new precoding-aided spatial modulation (SM) to improve the transmission performance over significantly high correlated indoor multi-input multi-output visible light communication (MIMO-VLC) channels. Especially, their precoder design relies on the fixed-sized light-emitting diode (LED) grouping and transmit beamforming, which plays an important role in enhancing the system performance. First, they propose an approximate discrete-input continuous-output memoryless channel capacity based precoder design, which offers better performance at the cost of high-computational complexity. As far as large-scale MIMO-VLC schemes are considered, the proposed precoder design presents to be impractical. Therefore, they develop a spatial correlation measure-based fast LED grouping algorithm to construct the precoder for large-scale MIMO-VLC systems. Their simulation results show that the proposed precoding-aided SM scheme can outperform the precoding-aided spatial multiplexing over significantly high correlated large-scale MIMO-VLC channels when the proposed fast LED grouping is performed, whereas the latter scheme can perform better than their proposed scheme for less correlated channels.

Precoding-Aided Spatial Modulation for the Wiretap Channel with Relay Selection and Cooperative Jamming

We propose in this paper a physical-layer security (PLS) scheme for dual-hop cooperative networks in an effort to enhance the communications secrecy. The underlying model comprises a transmitting node (Alice), a legitimate node (Bob), and an eavesdropper (Eve). It is assumed that there is no direct link between Alice and Bob, and the communication between them is done through trusted relays over two phases. In the first phase, precoding-aided spatial modulation (PSM) is employed, owing to its low interception probability, while simultaneously transmitting a jamming signal from Bob. In the second phase, the selected relay detects and transmits the intended signal, whereas the remaining relays transmit the jamming signal received from Bob. We analyze the performance of the proposed scheme in terms of the ergodic secrecy capacity (ESC), the secrecy outage probability (SOP), and the bit error rate (BER) at Bob and Eve. We obtain closed-form expressions for the ESC and SOP and we derive very tight upper-bounds for the BER. We also optimize the performance with respect to the power allocation among the participating relays in the second phase. We provide examples with numerical and simulation results through which we demonstrate the effectiveness of the proposed scheme.

Power Allocation for Pre-Coding-Aided Spatial Modulation

In this letter, power allocation (PA) algorithms based on the minimization of the upper bound of the instantaneous bit error probability (BEP) are investigated in pre-coding-aided spatial modulation (PSM) systems. First, an upper bound of the instantaneous BEP is derived when PA is taken into account for the antennas in the PSM system. Moreover, the optimal solution of the PA matrix is derived with the aid of convex optimization techniques, in order to minimize the BEP obtained. Furthermore, a low-complexity suboptimal PA algorithm is proposed, where only the dominant part of the BEP upper bound is considered in the optimization process. Simulation results demonstrate that the proposed algorithms improve on the conventional PSM scheme. Furthermore, when the number of receive antennas is large, the performance of the low-complexity suboptimal PA algorithm is close to that of the optimal PA algorithm.