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

Abstract

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.