On the Mutual Information and Precoding for Spatial Modulation with Finite Alphabet

In this letter, we investigate the effect of finite alphabet inputs on the performance of spatial modulation (SM) for multiple-input-single-output (MISO) channels. The closed-form expression of the mutual information is first derived in an information-theoretic framework. With careful analysis of the expression, we develop a precoding scheme to improve the performance of SM. Utilizing the theory of traditional constellation design, the precoding coefficient is obtained by maximizing the minimum Euclidean distance. Numerical results demonstrate substantial difference in the mutual information between SM with finite alphabet inputs and SM with Gaussian inputs, and show that our precoding scheme achieves significant gains.