Performance analysis of multistream Spatial Modulation with maximum-likelihood detection

In this paper, we provide a theoretical analysis of the optimal Maximum-Likelihood (ML) detector for the recently proposed multistream Spatial Modulation (SM) concept for multiple-input-multiple-output (MIMO) systems. A Union Bound that is based on closed-form formulas is derived for the average bit error probability (ABEP) of the ML detection, which shows an excellent fit with respect to Monte Carlo simulations for the high signal-to-noise ratio (SNR) region. Furthermore, numerical results for different rates are provided regarding the comparison of the ABEP of multistream SM with ML detection with its recently proposed counterpart with suboptimal detection and with the ABEPs of other well-known MIMO schemes, such as conventional Spatial Multiplexing, Alamouti, and SM, which show its advantage over them. In addition, for the examined MIMO configuration and rates, the relative transmit energy efficiency gain of multistream SM with ML detection over the aforementioned methods is calculated for a low target ABEP.