WMMSE-Based Rate Maximization for RIS-Assisted MU-MIMO Systems

Reconfigurable intelligent surface (RIS) technology, given its ability to favorably modify wireless communication environments, will play a pivotal role in the evolution of future communication systems. This paper proposes rate maximization techniques for both single-user and multiuser MIMO systems, based on the well-known weighted minimum mean square error (WMMSE) criterion. Using a suitable weight matrix, the WMMSE algorithm tackles an equivalent weighted mean square error (WMSE) minimization problem to achieve the sum-rate maximization. By considering a more practical RIS system model that employs a tensor-based representation enforced by the electromagnetic behavior exhibited by the RIS panel, we detail both the sum-rate maximizing and WMSE minimizing strategies for RIS phase shift optimization by deriving the closed-form gradient of the WMSE and the sum-rate with respect to the RIS phase shift vector. Our simulations reveal that the proposed rate maximization technique, rooted in the WMMSE algorithm, exhibits superior performance when compared to other benchmarks.