Joint source/relay precoding designs in MIMO two-way AF relay systems with MMSE-SIC receiver

This paper considers the joint source and relay linear precoding designs in three-node two-way amplify-and-forward (AF) multiple-input-multiple-output (MIMO) relay systems with the minimum-mean-squared-error (MMSE) successive-interference-cancelation (SIC) receiver. The designs are based on the criterion of minimizing the sum block error rate (sum-BLER). The primal optimization problem is nonconvex and remains unsolved. Aming to find an efficient way to solve the problem, we first resort to the primal decomposition approach where the optimization problem is decoupled into two subproblems called master optimization problem and subproblem optimization problem. Then the source precoding matrices can be derived as a function of the relay precoding matrix by solving the subproblem optimization problem when assuming both of the source precoders have unitary structure. Finally, we propose a structure of the relay precoding matrix with which the master optimization problem can be transferred to a water-filling power allocation problem. Based on the Karuch-Kuhn-Tucker (KKT) conditions, a closed-form solution can be further derived. Numerical results are shown to evaluate the effectiveness of our proposed precoding designs.