Robust Transceiver Design for Downlink Multiuser MIMO AF Relay Systems

In this paper, we investigate the robust transceiver design for a downlink multiuser multiple-input multiple-output (MIMO) amplify-and-forward (AF) relay system with imperfect channel state information (CSI). We consider that the actual channel is within the neighborhood of a nominal channel and formulate two optimization problems following the philosophy of worst-case robustness, i.e., minimizing the summean-square-error (SMSE) and minimizing the total transmit power for any channel realization in the uncertainty region. In order to efficiently find the solutions, we transform the original problems into suitable forms using the sign-definiteness lemma and then propose an alternating iterative algorithm with guaranteed convergence. To further reduce the computational complexity, the cutting-set method is developed, which alternates between transceiver design and channel determination steps. Moreover, some interesting extensions of the proposed methods are discussed, including various types of uncertainty models and transmit power constraints, nonlinear transceiver structure, and uncertain noise covariance. Simulation results are presented to demonstrate the effectiveness of the proposed robust designs.