Beyond Diagonal Reconfigurable Intelligent Surfaces with Mutual Coupling: Modeling and Optimization

TL;DR

This work addresses the practical challenge of mutual coupling in beyond diagonal RIS (BD-RIS) aided communications by deriving a BD-RIS model that jointly uses scattering and impedance parameter analyses. It introduces a general optimization algorithm for BD-RIS, applicable to single-, group-, and fully-connected architectures, to maximize the channel gain in a SISO setup. The core contributions include a tractable BD-RIS channel expression that isolates mutual coupling effects, a Neumann-series–based iterative optimization of the BD-RIS impedance with convergence guarantees, and performance evaluations showing that BD-RIS gains scale with mutual coupling and architectural connectivity. The findings highlight the potential of BD-RIS to substantially boost rate/coverage when mutual coupling is properly accounted in the design, informing practical RIS deployments with dense, non-diagonal interconnections.

Abstract

This work studies the modeling and optimization of beyond diagonal reconfigurable intelligent surface (BD-RIS) aided wireless communication systems in the presence of mutual coupling among the RIS elements. Specifically, we first derive the mutual coupling aware BD-RIS aided communication model using scattering and impedance parameter analysis. Based on the obtained communication model, we propose a general BD-RIS optimization algorithm applicable to different architectures of BD-RIS to maximize the channel gain. Numerical results validate the effectiveness of the proposed design and demonstrate that the larger the mutual coupling the larger the gain offered by BD-RIS over conventional diagonal RIS.

Figures (3)

• Figure 1: Schematic circuit topologies for a 4-element BD-RIS with (a) single-connected, (b) group-connected, and (c) fully-connected architectures.
• Figure 2: Channel gain versus the number of iterations ($M = 16$).
• Figure 3: Channel gain versus the number of BD-RIS elements.