Joint Optimization of Source and Relay for MIMO Two-Way Relay Networks Using MSE Duality

In this letter, the joint optimization of a source-relay pair is proposed for multiple-input multiple-output (MIMO) two-way relay networks. In these networks, since the joint beam-former design problem based on the minimum mean square error (MMSE) is known to be non-convex, it cannot be solved analytically. In order to solve the problem, a novel iterative algorithm is proposed that uses duality relationships. First, the MSE duality for MIMO two-way relay networks is presented; then, this duality is applied to the proposed optimization method, which provides closed-form solutions for all subproblems. Because the proposed algorithm does not involve convex optimization software packages, it efficiently reduces the computational complexity. The numerical results demonstrate that the proposed method improves the MSE performance compared with the conventional method.