Abstract: Spatial Modulation(SM) has been paid much attention recently as a novel multi-antenna transmission scheme which makes the input information bits into two parts to convey information: one part is used to activate the transmit antenna, the other is used for signal modulation. The Maximum Likelihood (ML) optimal detection algorithm for SM systems have to exhaustively search all the possible active transmit antenna index and transmitted signal, so the ML search complexity is very high. To solve this problem, some low-complexity algorithms are proposed. Being different from the ideas of these algorithms, in this paper, we start from the conventional ML optimal formula and introduce the polar coordinates to obtain an equivalent ML formula which is related with the constellation point’s amplitude and phase. According to the distribution property of the constellation point’s phase, we obtain a new sub-optimal detection algorithm by the approximate calculation of the phase. The new algorithm is closer to the optimal performance with low computational complexity than other sub-optimal algorithm. Finally, in this paper, the simulation results are presented to verify the validity of the algorithm.