Beyond-Diagonal RIS Architecture Design and Optimization under Physics-Consistent Models

TL;DR

This work addresses BD-RIS design under physics-consistent, multiport network models that capture mutual coupling and impedance mismatching. It derives a compact channel form $\mathbf{H}=\bar{\mathbf{H}}_{RT}+\bar{\mathbf{H}}_{RI}\bar{\boldsymbol{\Theta}}\bar{\mathbf{H}}_{IT}$ and shows that band-connected RIS achieves the same channel-shaping capabilities as fully-connected RIS for MIMO, while requiring far fewer admittances. The authors develop a globally optimal SDR-based algorithm for single-stream MIMO and an ADMM-based method for multiuser MIMO, with SISO closed-form solutions, and validate the framework via simulations demonstrating that mutual coupling can boost performance and that unilateral approximation is accurate over practical ranges. These results unify and extend conventional BD-RIS analyses to physics-consistent models, providing architecture guidance and scalable optimization tools for realistic RIS deployments. The work thus offers practical insights for RIS hardware design and algorithmic optimization in EM-aware wireless systems.

Abstract

Reconfigurable intelligent surface (RIS) is a promising technology for future wireless communication systems. Conventional RIS is constrained to a diagonal scattering matrix, which limits its flexibility. Recently, beyond-diagonal RIS (BD-RIS) has been proposed as a more general RIS architecture class that allows inter-element connections and shows great potential for performance improvement. Despite extensive progress on BD-RIS, most existing studies rely on simplified channel models that ignore practical electromagnetic (EM) effects such as mutual coupling and impedance mismatching. To address this gap, this paper investigates the architecture design and optimization of BD-RIS under the general physics-consistent model derived with multiport network theory in recent literature. Building on a compact reformulation of this model, we show that band-connected RIS achieves the same channel-shaping capability as fully-connected RIS, which extends existing results obtained for conventional channel models. We then develop optimization methods under the general physics-consistent model; specifically, we derive closed-form solutions for single-input single-output (SISO) systems, propose a globally optimal semidefinite relaxation (SDR)-based algorithm for single-stream multi-input multi-output (MIMO) systems, and design an efficient alternating direction method of multipliers (ADMM)-based algorithm for multiuser MIMO systems. Using the proposed algorithms, we conduct comprehensive simulations to evaluate the impact of various EM effects and approximations, including mutual coupling among RIS antennas and the commonly adopted unilateral approximation, on system performance.

Figures (5)

• Figure 1: Multiport model of a RIS-aided MIMO system.
• Figure 2: Receive power and sum-rate versus the number of RIS elements for different channel models and inter-element spacing $d$.
• Figure 3: Relative performance of the solutions obtained from approximate channel models with respect to the solution obtained from the general physics-consistent model, which is computed as $\frac{F(\mathbf{H}(\bar{\boldsymbol{\Theta}}_{\text{app}}),\mathbf{W}_{\text{app}})}{F(\mathbf{H}(\bar{\boldsymbol{\Theta}}^*),\mathbf{W}^*)}\times 100\%$, where $F(\mathbf{H}(\bar{\boldsymbol{\Theta}}),\mathbf{W})$ is the receive power (i.e., $F(\mathbf{H}(\bar{\boldsymbol{\Theta}}),\mathbf{W})=\|\mathbf{H}(\bar{\boldsymbol{\Theta}})\|_2^2$) for the SISO and single-stream MIMO systems, and is the sum-rate (i.e., $F(\mathbf{H}(\bar{\boldsymbol{\Theta}}),\mathbf{W})=\sum_{k=1}^{N_R}\log(1+\frac{|\mathbf{h}_k(\bar{\boldsymbol{\Theta}})^H\mathbf{w}_k|^2}{\sum_{j\neq k}|\mathbf{h}_k(\bar{\boldsymbol{\Theta}})^H\mathbf{w}_j|^2+\sigma^2})$) for the multiuser MISO system, $(\bar{\boldsymbol{\Theta}}_{\text{app}},\mathbf{W}_{\text{app}})$ is the solution obtained using the approximate model $\mathbf{H}_{\text{app},2}$ or $\mathbf{H}_{\text{app},3}$, and $(\bar{\boldsymbol{\Theta}}^*,\mathbf{W}^*)$ is the solution obtained using $\mathbf{H}$.
• Figure 4: Relative performance of the solutions obtained from approximate channel models versus the number of transmit antennas and receive antennas/users, where $N_T=N_R$. The number of RIS elements is fixed as $N_I=64$.
• Figure 5: Relative performance of the solution obtained from approximate channel model $\mathbf{H}_{\text{app,2}}$ versus the distance (normalized by wavelength) between transmitter and RIS. The number of RIS elements is fixed as $N_I=64$. The number of transmit and receive antennas for the MIMO system is $N_T=N_R=4$. The numbers of transmit antennas and users for the multiuser MISO system are set as the same.

Theorems & Definitions (8)

• Lemma 1
• proof
• Proposition 1: A Compact Form of \ref{['general']}
• proof
• Proposition 2
• proof
• Remark 1: A Low-Dimensional SDR
• Lemma 2: graph