Robust Transceiver for AF MIMO Relaying with Direct Link: A Globally Optimal Solution

We study the robust transceiver design for amplify-and-forward (AF) multiple-input-multiple-output (MIMO) relay systems with a direct link and imperfect channel state information (CSI). Under this circumstance, we aim at obtaining the globally optimal transceiver that minimizes the mean-squared error (MSE) of symbol detection. Specifically, given a source beamformer, we first derive closed-form expressions for the optimal relay precoder and destination receiver. Then, to tackle the intricate non-convex problem with respect to source beamformer, we develop an efficient approach involving one-dimensional search and semidefinite programming (SDP). We prove rigourously that the proposed method yields a globally optimal solution. Simulation results verify the pronounced performance provided by the proposed design.