Alternating Minimization Algorithm for Multiuser RIS-assisted MIMO Systems

A reconfigurable intelligent surface (RIS) is a real-time controllable reflect-array that consists of a large number of discrete elements which introduce a phase-shift to the incoming signals. These passive surfaces are helpful to partially control the radio environment by properly configuring the phase-shift matrix and, thus, the direction of the reflected signals. This paper proposes the joint design of the user precoders and the RIS phase-shift matrix in the uplink of a multiuser (MU) multiple-input multiple-output (MIMO) system. The RIS phase-shift matrix and the user precoders are designed to minimize the mean square error (MSE) of the estimated user symbols via an alternating minimization projected gradient (PG) algorithm. Numerical results show that the proposed solution leads to substantial achievable sum-rate gains with respect to baseline strategies that do not account for the inter-user interference in the precoder design and the proper RIS phase-shift matrix configuration.