A Low-Complexity Iterative Transmit Precoding Algorithm for Spatial Modulation Systems

In this paper, we propose and investigate a low complexity iterative transmit precoding (TPC) algorithm to enhance the bit error rate (BER) performance for Spatial Modulation (SM) systems over flat-fading multiple-input multiple output (MIMO) channels. In literature, various TPC techniques have been conceived, but suffer from either over-simplification or lack of generality, thus a low-complexity iterative TPC algorithm is proposed, in which the TPC matrix is diagonal in order to retain the low-complexity benefit of conventional SM systems. Specifically, we investigate a TPC design to maximize the minimum Euclidean distance d(min) (max-d(min)) between the SM signal points at the receiver side. Different from conventional TPC algorithms, which adjust only two elements in the TPC matrix, all elements of the TPC matrix are iteratively modified until d(min) could not be increased. Furthermore, an efficient computing method of d(min) is proposed when considering PSK-modulated SM systems. Discussion on complexity analysis and convergence behavior are also provided, which proves the low complexity of the proposed algorithm. Simulation results demonstrate that the proposed TPC algorithm is able to achieve lower BER compared with conventional TPC algorithms.