BER Analysis for Spatial Modulation in Multicast MIMO Systems

In this paper, we investigate the bit error rate (BER) for multicast multiple-input multiple-output (MIMO) systems, employing spatial modulation (SM) and its variants, called multicast SM-type MIMO systems, in Rayleigh fading channels. The system BER, here, is derived by first attaining the BER of the worst receiver of each channel realization set, and then averaging over all possible sets. We first consider the uncorrelated channels. By exploiting the system statistics, a tight BER upper bound is proposed and the diversity is discussed for the systems. We then perform the asymptotic analysis, and show that the BER of the multicast SM-type MIMO system can be alternatively analyzed by analyzing the simple point-to-point SM-type MIMO system with Weibull fading channels. Through this property, a closed-form asymptotic BER upper bound is provided and the impact of the receiver number on BER is analyzed. Subsequently, our investigation is extended to correlated channels where all the receivers share the same correlation statistics. The BER analysis is performed again through the framework similar to the uncorrelated case. In the analysis, the tight upper bound is derived and the effect of correlations is analyzed. Moreover, we provide an explicit expression for the SNR degradation caused by the receive correlation through the analysis. Finally, simulations are exploited to evaluate the BER of the multicast SM-type MIMO systems and validate the analyses.