Unified power allocation for receive spatial modulation based on approximate optimization

In this paper, a novel unified power allocation (PA) framework is proposed for receive (pre-coding aided) spatial modulation (RSM). We find that the PA matrix design can be formulated as a non-convex quadratically constrained quadratic program (QCQP) problem, whose solution is generally intractable. To tackle this problem, we propose a pair of solvers having different trade-offs in terms of bit-error-rate and complexity. Specifically, we first propose a successive convex approximation (SCA) method, to convert the non-convex QCQP problem under consideration into a series of linear convex subproblems, where the latter can be easily solved by the classic polynomial-time-based optimization method, i.e., the interior point method. To further reduce the computational complexity, we propose an augmented Lagrangian multiplier (ALM) method, which transforms the challenging non-convex constrained PA optimization problem into its unconstrained counterpart, which can be efficiently solved by an iterative manner. Our simulation results show that both the proposed SCA and ALM methods are capable of substantially improving the system error performance compared with the conventional RSM system without PA as well as conventional PA-aided RSM schemes