ABEP Evaluation of Spatial Modulation Communication Systems: Improved Analytical Framework

Average bit error probability (ABEP) performance evaluation of spatial modulation (SM) over wireless fading channels has attracted huge interest in the literature. In general, the core step to analytically evaluate such ABEP performance is to theoretically derive the associated average pairwise error probabilities (average-PEPs). However, these average-PEPs have been derived so far in exact and closed-form expressions only for two cases: 1) SM systems with real-valued modulation regardless of the fading channel type, 2) SM systems with complex-valued modulation but only for Rayleigh fading channel type. In case of complex-valued modulation with non Rayleigh fading, such average-PEPs were derived either in exact but integral-form expressions or in closed-form but non-simplified and non-tight approximate expressions. Thus, here, we introduce a new analytical framework to fill this literature gap by deriving new exact and closed-form formulas for the SM system's average-PEPs. We first apply the proposed framework on SM system with perfect channel-state-information (CSI) considering Rayleigh and Rician fading environments as two separate scenarios. Then, in order to show the effectiveness of the proposed approach, we reapply it for the imperfect CSI estimation scenario, where more generic exact average-PEPs are derived. Numerical and simulation results are provided, which show that, as compared to the widely adopted conventional literature approximate method, the proposed framework offers much better accuracy over the whole signal-to-noise-ratio (SNR) region.