Beyond Diagonal RIS in Multiuser MIMO: Graph Theoretic Modeling and Optimal Architectures with Low Complexity

2025-02-23

AI Summary

In RIS-aided multi-user MIMO systems, high-connectivity BD-RIS architectures face a fundamental trade-off between performance and circuit complexity. Method: This paper establishes, for the first time, a theoretical link between BD-RIS topology and the degrees of freedom (DoF) of the MIMO channel, proposing a graph-theoretic framework for optimal architecture design. Contribution/Results: We identify an optimal class of BD-RIS architectures achieving full-connectivity performance with only O(ND) hardware complexity—significantly lower than the O(N²) complexity of conventional fully connected designs. Two practical realizations—band-connected and stem-connected BD-RIS—are developed. The proposed schemes approach the spectral efficiency, energy efficiency, and transmit-power minimization performance of fully connected RISs across multiple objectives, while reducing hardware complexity by orders of magnitude. Extensive simulations validate both the theoretical optimality and the superior performance-complexity trade-off of the designs.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Multiagent Systems: Agent/AI Theories and Architectures
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Energy management for devices in mobile Web and WoT environments

Abstract

Reconfigurable intelligent surfaces (RIS) is regarded as a key enabler of wave/analog-domain beamforming, processing, and computing in future wireless communication systems. Recently, Beyond Diagonal RIS (BD-RIS) has been proposed as a generalization of conventional RIS, offering enhanced design flexibility thanks to the presence of tunable impedances that connect RIS elements. However, increased interconnections lead to high circuit complexity, which poses a significant practical challenge. In this paper, we address the fundamental open question: What is the class of BD-RIS architectures that achieves the optimal performance in a RIS-aided multiuser multi-input multi-output (MIMO) system? By modeling BD-RIS architectures using graph theory, we identify a class of BD-RIS architectures that achieves the optimal performance--matching that of fully-connected RIS--while maintaining low circuit complexity. Our result holds for a broad class of performance metrics, including the commonly used sum channel gain/sum-rate/energy efficiency maximization, transmit power minimization, and the information-theoretic capacity region. The number of tunable impedances in the proposed class is ${O}(Nmin{D,N/2})$, where $N$ denotes the number of RIS elements and $D$ is the degree of freedom of the multiuser MIMO channel, i.e., the minimum between the number of transmit antennas and the total number of received antennas across all users. Since $D$ is much smaller than $N$ in practice, the complexity scales as ${O}(ND)$, which is substantially lower than the ${O}(N^2)$ complexity of fully-connected RIS. We further introduce two novel BD-RIS architectures--band-connected RIS and stem-connected RIS--and show that they belong to the optimal architecture class under certain conditions. Simulation results validate the optimality and enhanced performance-complexity tradeoff of our proposed architecture.

Problem

• Optimizing BD-RIS architectures for multiuser MIMO systems
• Reducing circuit complexity in RIS-aided wireless systems
• Enhancing performance with low-complexity graph-theoretic modeling

Innovation

• Graph theory models BD-RIS
• Optimal low-complexity BD-RIS architectures
• Band and stem-connected RIS introduced