Dual-Ascent Inspired Transmit Precoding for Evolving Multiple-Access Spatial Modulation

In this article, we investigate the dual-ascent inspired transmit precoding (TPC) for multiple-access spatial modulation (MASM) in multiple-input multiple-output (MIMO) systems. Note that several novel TPC techniques have been developed in earlier works, to provide a solution for either the maximal-minimum Euclidean distance, or the quadratically constrained quadratic program problems. However, numerical results expose that the system performances degrade distinctly when applying these TPC techniques into MASM-MIMO. The main reason behind is that these TPC techniques are sensitive to the system dimensions and the quadratic constraints. In this context, we first recast the above challenging problems as an unconstrained problem by imposing a penalty over the quadratic constraints. Based on the primal-dual optimality theory, we next propose a Broyden-Fletcher-Goldfarb-Shanno (BFGS) aided dual-ascent approach for finding a global optimum solution to the unconstrained problem. Further, we introduce non-stationary time-varying TPC parameters to characterize an evolving MASM-MIMO in which the signals are multiplexed over a small coherence time, and thereby resulting in dual-ascent aided non-stationary TPC approach. Numerical results manifest that the proposed algorithms possess an inherent robustness to the increasing system dimension and quadratic constraint. Besides, simulation results show the benefits of our algorithms under different kinds of performance metrics.