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

TL;DR

This paper derives the first global optimal closed-form solutions for optimizing reconfigurable intelligent surfaces with mutual coupling, revealing that mutual coupling can enhance channel gain and that ignoring it may degrade performance.

Contribution

It introduces the first global optimal closed-form solutions for BD-RIS with mutual coupling, including maximum channel gain expressions and scaling laws, advancing understanding of mutual coupling effects.

Findings

Mutual coupling can increase average channel gain under Rayleigh fading.

Optimized RIS with mutual coupling achieves the same upper bound as ideal cases.

Ignoring mutual coupling can cause up to 5 dB performance degradation.

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.