Physically-Consistent Modeling and Optimization of Non-local RIS-Assisted Multi-User MIMO Communication Systems

Mutual Coupling (MC) emerges as an inherent feature in Reconfigurable Intelligent Surfaces (RISs), particularly, when they are fabricated with sub-wavelength inter-element spacing. Hence, any physically-consistent model of the RIS operation needs to accurately describe MC-induced effects. In addition, the design of the ElectroMagnetic (EM) transmit/receive radiation patterns constitutes another critical factor for efficient RIS operation. The latter two factors lead naturally to the emergence of non-local RIS structures, whose operation can be effectively described via non-diagonal phase shift matrices. In this paper, we focus on jointly optimizing MC and the radiation patterns in multi-user MIMO communication systems assisted by non-local RISs, which are modeled via the scattering parameters. We particularly present a novel problem formulation for the joint optimization of MC, radiation patterns, and the active and passive beamforming in a physically-consistent manner, considering either reflective or transmissive RIS setups. Differently from the current approaches that design the former two parameters on the fly, we present an offline optimization method which is solved for both considered RIS functionalities. Our extensive simulation results, using both parametric and geometric channel models, showcase the validity of the proposed optimization framework over benchmark schemes, indicating that improved performance is achievable without the need for optimizing MC and the radiation patterns of the RIS on the fly, which can be rather cumbersome.