Simplified maximum likelihood-based detection schemes for M-ary quadrature amplitude modulation spatial modulation

In this study, the authors propose a simplified maximum likelihood (ML)-based detection scheme for N_t×N_r M-ary quadrature amplitude modulation (M-QAM) spatial modulation (SM) that is computationally less complex than the conventional ML detection scheme. Instead of searching for the transmit antenna index and transmitted symbol pair among all possible N_tM pairs as in the ML-based optimal detection, the proposed simplified ML-based detection scheme firstly searches for pairs of transmit antenna index and transmitted symbol in level-one subsets which the transmitted signal most probably belongs to, and secondly searches for pairs of transmit antenna index and transmitted symbol in level-two subsets among those pairs in level-one subsets. We also extend the simplified ML-based optimal detection into multistage detection. Simulation results validate that the bit error rate (BER) performance of the proposed simplified ML-based detection schemes is almost the same as that of conventional ML detection with significant complexity reduction until a BER of 10^-6.