On the mutual information and constellation design criterion of spatial modulation MIMO systems

The mutual information of spatial modulation (SM) based multiple input and multiple output (MIMO) systems with arbitrary number of transceiver antennas is investigated. An expression of the system mutual information is derived. The expression is not in a closed form and may lead to difficulties when trying to optimize the mutual information. To solve this, based on Jensen Inequality we propose an approximation for mutual information, which is in a closed form. We show that the approximation is accurate in both low and high SNR regimes. In addition, based on the approximated version of the system mutual information, two constellation design critera are proposed to maximize the system mutual information with finite alphabet. Numerical results show that both of the two criteria perform well.