Diagonal precoder designs for spatial modulation

In this paper, we propose diagonal precoder designs of spatial modulation (SM) by minimizing symbol error rate (SER) upper bound. A general precoder design method applicable for any signal-to-noise ratio (SNR) is first proposed. We then carry out asymptotic analysis of the precoder design in the regimes of high and low SNR. In high SNR regime, our proposed precoder design problem is found to be a non-convex quadratically constrained quadratic program (QCQP) problem that can be solved by semi-definite relaxation (SDR) technique. In low SNR regime, we find the closed form expression of the optimal solution that is equivalent to best antenna selection. Simulation results illustrate that our proposed algorithm can significantly enhance the SER performance and has a better performance than other algorithms.