Precoding Design of MIMO AF Two-Way Multiple-Relay Systems

The precoding joint optimization is proposed for multiple-input multiple-output (MIMO) two-way multiple-relay systems with amplify-and-forward (AF) strategy in correlated fading channels. The terminal transceivers and relay precoding matrices are designed based on the minimum mean square error (MMSE) criterion. This combined design of precoding matrices and equalizers under power constraints belongs to neither concave nor convex so that the nonlinear matrix-form conjugate gradient (MCG) algorithm is developed to acquire the local optimal solutions. Simulation results demonstrate that the proposed precoding joint architecture possesses a superior bit-error-rate (BER) performance and a faster convergence rate.