Optimizing the Achievable Sum-Rate in OFDM-Based Multi-User MIMO Systems Assisted by Multiple Beyond-Diagonal RISs

Massive multiple-input, multiple-output (MIMO) systems operating in the millimeter wave (mmWave) and terahertz (THz) frequency bands offer high data rates and spatial multiplexing, yet they face significant propagation challenges. Reconfigurable intelligent surfaces (RISs) and their different architectures have emerged as a promising solution to these challenges, having the potential to enhance system performance. This paper addresses the joint sum-rate maximization problem in multi-user, multi-stream, multi-carrier MIMO systems aided by multiple parallel RIS panels. To minimize the inter-user interference, we adopt a problem formulation that adds a regularization term. To solve the resulting problem, we then propose a regularized cyclic block proximal gradient (MU-RCBPG) algorithm, which can jointly optimize precoders and RIS phase shifts without increasing the complexity compared to traditional single-valued decomposition (SVD)-based methods. The resulting algorithm has a flexible design that allows it to support configurations with beyond-diagonal RIS (BD-RIS), conventional diagonal RIS (D-RIS), and active D-RIS. Numerical results demonstrate that the MU-RCBPG algorithm outperforms existing RIS-aided schemes in various scenarios.