MMSE sparse beamforming for power-constrained large two-way relay AF networks.

We propose a novel approach for multi-user multi-antenna relay beamforming matrices design for large two-way amplify-and-forward relay networks. In this scenario, multi-antenna users exchange their information streams through a multi-antenna amplify-and-forward relay node in a bi-directional manner. The two key features of our proposed approach are joint iterative user and relay beamforming design based on the mean-square error criterion and the sparse nature of the user and relay beamforming matrices. To solve this non-linear and non-convex problem for the sparse beamforming matrices, we first decouple the primal problem into three convex subproblems. Then, we propose an iterative algorithm which computes the sparse beamforming matrices one at a time by minimizing the mean-square error of each convex subproblem until convergence. Simulation results demonstrate the effectiveness of our proposed sparse beamforming design algorithm and illustrate the fast convergence behavior of our proposed iterative algorithm.