Electromagnetically-Consistent Modeling and Optimization of Mutual Coupling in RIS-Assisted Multi-User MIMO Communication Systems

TL;DR

The paper tackles mutual coupling (MC) in RIS-assisted multi-user MIMO systems by adopting a physically-consistent end-to-end model built on $S$-parameters, capturing non-local RIS behavior through non-diagonal phase shift matrices. It introduces an offline optimization of the MC parameters over channel ensembles and couples this with online optimization of active and passive beamforming, using a two-block alternating approach (inner: $\rho$, $\mathbf{F}$, $\boldsymbol{\Upsilon}$; outer: $\boldsymbol{\Sigma}_{\alpha\alpha}, \boldsymbol{\Sigma}_{\alpha\beta}$) and a projection-based update with a closed-form per-element solution. The key contributions are the joint offline MC design within a physically-consistent RIS model, the decomposition into two subproblems, and a practical projected gradient/descent with a closed-form projection that yields observable sum-rate gains over baseline models. The results demonstrate that MC optimization can meaningfully improve performance and that offline optimization suffices to realize substantial gains without requiring real-time MC reconfiguration, offering a scalable path for RIS deployments. The work advances RIS design by showing how engineered MC, via $S$-parameters, can be exploited to enhance system capacity in multi-user MIMO settings.

Abstract

Mutual Coupling (MC) is an unavoidable feature in Reconfigurable Intelligent Surfaces (RISs) with sub-wavelength inter-element spacing. Its inherent presence naturally leads to non-local RIS structures, which can be efficiently described via non-diagonal phase shift matrices. In this paper, we focus on optimizing MC in RIS-assisted multi-user MIMO wireless communication systems. We particularly formulate a novel problem to jointly optimize active and passive beamforming as well as MC in a physically consistent manner. To characterize MC, we deploy scattering parameters and propose a novel approach to optimize them through an offline optimization method, rather than optimizing MC on the fly. Our numerical results showcase that the system performance increases with the proposed MC optimization, and this improvement is achievable without the need for optimizing MC on-the-fly, which can be rather cumbersome.

Figures (3)

• Figure 1: Transmit/receive space- and port-side RIS patterns.
• Figure 2: Sum-rate performance versus the transmit power $P$ in dBm for various system parameters.
• Figure 3: Sum-rate performance versus the number of RIS elements $M$ considering $Q=10$ channel samples, $K=5$, $P=50$ dBm, and $N=32$.