Toward Ergodic Sum Rate Maximization of Multiple-RIS-Assisted MIMO Multiple Access Channels Over Generic Rician Fading

Reconfigurable intelligent surface (RIS) has recently been widely investigated in wireless communication systems due to its low deployment cost and high-performance gain. In this work, we study the multiple-RIS-assisted uplink multiple-user multiple-input multiple-output (MU-MIMO) communication systems, where each user's signal is sent to the base station via both the direct and the reflected links. To obtain informative insight into the considered system with the statistical channel information, we first derive the closed-form expression for the ergodic sum rate of the MU-MIMO systems by applying the operator-valued free probability theory. Then, the covariance matrices of the transmit signals and the phase shifts of the RIS elements are jointly optimized to maximize the derived asymptotic ergodic sum rate via alternating optimization (AO). Specifically, the AO procedure is composed of a water-filling algorithm and a gradient descent algorithm over the Riemannian manifold and the two algorithms iterate until convergence. The numerical results show the accuracy of the asymptotic expression compared to the Monte Carlo simulation and the superiority of the proposed AO algorithm compared to the benchmark. Furthermore, the rank deficiency of the MIMO channel can be significantly improved by the deployment of multiple RISs and the proposed AO algorithm.