A Low-Complexity ML Detection Algorithm for Spatial Modulation Systems With $M$PSK Constellation

Spatial modulation (SM), which is a novel transmission scheme, is employed for active transmit antenna indexes and modulated signals to convey the information. To recover the transmitted information bits, the maximum likelihood (ML) joint detector is often used. However, its complexity linearly grows with the number of transmit antennas and the size of the signal set. A reduced-complexity ML optimal algorithm for SM systems with M-QAM has been proposed. However, for M-PSK modulation, there are not similar low-complexity ML detection algorithms yet to our knowledge. In this paper, a low-complexity ML detection algorithm for SM systems with M-PSK modulation is proposed. By exploiting the features of M-PSK constellation, we give the ML-estimated values of the transmitted symbols. Therefore, the ML search complexity is independent of the constellation size. Simulation results show that the proposed algorithm has the same performance as the ML-optimum detector and significant reduction in computational complexity compared with existing detectors for SM systems with M-PSK modulation.