Statistically Robust Transceiver Design for Multi-RIS Assisted Multi-User MIMO Systems

In this letter, we investigate the robust transceiver design for a downlink multi-user multiple-input multiple-output (MIMO) system assisted by multiple reconfigurable intelligent surfaces (RISs), where the base station (BS) and multiple users are all equipped with multiple antennas. Different from most previous RIS related works focusing on worst-case performance optimization, which may lead to overly conservative transceiver designs, we assume stochastic channel estimation errors for the considered system, and aim to minimize the average sum mean square error (MSE) of the considered system by jointly optimizing the transmit precoders, the receive equalizers, and the RIS reflecting coefficients. To address the non-convexity of the formulated problem induced by strongly coupled optimization variables, we develop a low-complexity alternating optimization (AO) algorithm to find a locally optimal solution, where the unique optimal solution to each subproblem can be derived in closed-form. Numerical simulations demonstrate the robustness and excellent average sum MSE performance of the proposed AO algorithm compared to the adopted benchmark scheme.