Power Allocation for Pre-Coding-Aided Spatial Modulation

In this letter, power allocation (PA) algorithms based on the minimization of the upper bound of the instantaneous bit error probability (BEP) are investigated in pre-coding-aided spatial modulation (PSM) systems. First, an upper bound of the instantaneous BEP is derived when PA is taken into account for the antennas in the PSM system. Moreover, the optimal solution of the PA matrix is derived with the aid of convex optimization techniques, in order to minimize the BEP obtained. Furthermore, a low-complexity suboptimal PA algorithm is proposed, where only the dominant part of the BEP upper bound is considered in the optimization process. Simulation results demonstrate that the proposed algorithms improve on the conventional PSM scheme. Furthermore, when the number of receive antennas is large, the performance of the low-complexity suboptimal PA algorithm is close to that of the optimal PA algorithm.