MIMO MAC Empowered by Reconfigurable Intelligent Surfaces: Capacity Region and Large System Analysis

Smart wireless environments enabled by multiple distributed Reconfigurable Intelligent Surfaces (RISs) have recently attracted significant research interest as a wireless connectivity paradigm for sixth Generation (6G) networks. In this paper, using random matrix theory methods, we calculate the mean of the sum Mutual Information (MI) for the correlated Multiple-Input Multiple-Output (MIMO) Multiple Access Channel (MAC) in the presence of multiple RISs, in the large-antenna number limit. We thus obtain the capacity region boundaries, after optimizing over the tunable RISs' phase configurations. Furthermore, we obtain a closed-form expression for the variance of the sum-MI metric, which together with the mean provides a tight Gaussian approximation for the outage probability. The derived results become relevant in the presence of fast-fading, when channel estimation is extremely challenging. Our numerical investigations showcased that, when the angle-spread in the neighborhood of each RIS is small, which is expected for higher carrier frequencies, the communication link strongly improves from optimizing the ergodic MI of the multiple RISs.We also found that, increasing the number of transmitting users in such MIMO-MAC-RIS systems results to rapidly diminishing sum-MI gains, hence, providing limits on the number of users that can be efficiently served by a given RIS.