Sum-Rate Maximization of RIS-Aided Multi-User MIMO Systems With Statistical CSI

This paper investigates a reconfigurable intelligent surface (RIS)-aided multi-user multiple-input multiple-output (MIMO) system by considering only the statistical channel state information (CSI) at the base station (BS). We aim to maximize its sum-rate via the joint optimization of precoding matrix at the BS and phase shifts vector at the RIS. However, the multi-user MIMO transmissions and the spatial correlations make the optimization cumbersome. For tractability, an asymptotic sum-rate is derived under a large number of the reflecting elements. By adopting the asymptotic sum-rate as the objective function, optimal designs of the transmit precoding matrix and the phase shifts vector can be decoupled and solved individually. More specifically, a high-quality suboptimal solution of the transmit precoding matrix and phase shifts vectors can be obtained by utilizing the water-filling algorithm and the projected gradient ascent (PGA) algorithm, respectively. Comparing to the case of the instantaneous CSI assumed at the BS, the proposed algorithm based on the statistical CSI can achieve comparable performance but with much lower channel estimation overhead, information feedback overhead, and computational complexity, which is more affordable and appealing for practical applications. Moreover, the impact of spatial correlation on the asymptotic sum-rate is examined by using majorization theory.