Scalable Beamforming Design for Multi-RIS-Aided MU-MIMO Systems with Imperfect CSIT

Abstract

This paper presents a scalable beamforming design for maximizing the spectral efficiency (SE) of multi-reconfigurable intelligent surface (RIS)-aided communications through joint optimization of the precoder and RIS phase shifts in multi-user multiple-input multiple-output (MU-MIMO) systems under imperfect channel state information at the transmitter (CSIT). To address key challenges of the joint optimization problem, we first decompose it into two subproblems by deriving a proper lower bound. We then leverage a generalized power iteration (GPI) approach to identify a superior local optimal precoding solution. We further extend this approach to the RIS design using regularization; we set a RIS regularization function to efficiently handle the unit-modulus constraints, and also find the superior local optimal solution for RIS phase shifts under the GPI-based optimization framework. Subsequently, we propose an alternating optimization method. Our proposed algorithm offers scalable multi-RIS beamforming in terms of computational complexity that scales linearly with the number of RISs, while achieving superior performance. We further reduce the complexity with respect to the number of RIS elements by using diagonal approximation of the channel error covariance and avoiding direct matrix inversion. Simulations validate the proposed algorithm in terms of both the sum SE performance and the scalability.