Global Optimal Closed-Form Solutions for Intelligent Surfaces With Mutual Coupling: Is Mutual Coupling Detrimental or Beneficial?

2024-11-07

IEEE Transactions on Wireless Communications

AI Summary

This work addresses beyond-diagonal reconfigurable intelligent surfaces (BD-RIS) with mutual coupling, for which no rigorous global optimization framework accounting for coupling effects existed. Method: We establish the first mutual-coupling-aware global optimization theory, proposing a closed-form solution via matrix eigenanalysis and complex-domain optimization to maximize channel gain under fully connected and tree-connected architectures. Contribution/Results: We theoretically reveal that mutual coupling can enhance average channel gain in Rayleigh fading—refuting the common misconception that coupling is inherently detrimental—and derive a closed-form expression and scaling law for the maximum achievable gain with coupling. Both architectures are proven to share an identical theoretical gain upper bound. Mutual-coupling-agnostic optimization incurs up to 5 dB performance loss. Our results provide the first rigorous theoretical foundation for BD-RIS modeling, design, and deployment.

Technology Category

• Search and Optimization: Non-convex Optimization
• Intelligent Robots: Learning & Optimization for ROB
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Search and Retrieval-Augmented AI: Retrieval-Augmented Generation (RAG) and multi-modal RAG
• Security and Privacy: Large-scale security measurements
• Systems and Infrastructure for Web, Mobile and WoT: Energy management for devices in mobile Web and WoT environments

Abstract

Reconfigurable Intelligent Surface (RIS) is a breakthrough technology enabling the dynamic control of the propagation environment in wireless communications through programmable surfaces. To improve the flexibility of conventional diagonal RIS (D-RIS), beyond diagonal RIS (BD-RIS) has emerged as a family of more general RIS architectures. However, D-RIS and BD-RIS have been commonly explored neglecting mutual coupling effects, while the global optimization of RIS with mutual coupling, its performance limits, and scaling laws remain unexplored. This study addresses these gaps by deriving global optimal closed-form solutions for BD-RIS with mutual coupling to maximize the channel gain, specifically fully- and tree-connected RISs. Besides, we provide the expression of the maximum channel gain achievable in the presence of mutual coupling and its scaling law in closed form. By using the derived scaling laws, we analytically prove that mutual coupling increases the channel gain on average under Rayleigh fading channels. Our theoretical analysis, confirmed by numerical simulations, shows that both fully- and tree-connected RISs with mutual coupling achieve the same channel gain upper bound when optimized with the proposed global optimal solutions. Furthermore, we observe that a mutual coupling-unaware optimization of RIS can cause a channel gain degradation of up to 5 dB.

Problem

• Derives global optimal closed-form solutions for BD-RIS with mutual coupling
• Analyzes mutual coupling effects on channel gain and scaling laws
• Compares performance of mutual coupling-aware and unaware RIS optimization

Innovation

• Derived global optimal closed-form solutions for BD-RIS
• Proved mutual coupling increases channel gain under Rayleigh fading
• Achieved channel gain upper bound with mutual coupling optimization