Low-Complexity Precoding for Spatial Modulation

In this paper, we investigate linear precoding for spatial modulation (SM) over multiple-input-multiple-output (MIMO) fading channels. With channel state information available at the transmitter, our focus is to maximize the minimum Euclidean distance among all candidates of SM symbols. We prove that the precoder design is a large-scale non-convex quadratically constrained quadratic program (QCQP) problem. However, the conventional methods, such as semi-definite relaxation and iterative concave-convex process, cannot tackle this challenging problem effectively or efficiently. To address this issue, we leverage augmented Lagrangian and dual ascent techniques, and transform the original large-scale non-convex QCQP problem into a sequence of subproblems. These subproblems can be solved in an iterative manner efficiently. Numerical results show that the proposed method can significantly improve the system error performance relative to the SM without precoding, and features extremely fast convergence rate with very low computational complexity.