On the Path-Loss of Reconfigurable Intelligent Surfaces: An Approach Based on Green's Theorem Applied to Vector Fields

TL;DR

This paper presents a physics-based analytical model for the path-loss of wireless links involving reconfigurable intelligent surfaces, using Green's theorem to account for surface properties and wave polarization in different deployment regimes.

Contribution

It introduces a novel Green's theorem-based approach to characterize path-loss in RIS-assisted wireless links, applicable to various surface configurations and regimes.

Findings

Closed-form expressions for far-field and near-field regimes.

Impact of design parameters on path-loss.

Analytical model incorporating polarization and surface size.

Abstract

In this paper, we introduce a physics-based analytical characterization of the free-space path-loss of a wireless link in the presence of a reconfigurable intelligent surface. The proposed approach is based on the vector generalization of Green's theorem. The obtained path-loss model can be applied to two-dimensional homogenized metasurfaces, which are made of sub-wavelength scattering elements and that operate either in reflection or transmission mode. The path-loss is formulated in terms of a computable integral that depends on the transmission distances, the polarization of the radio waves, the size of the surface, and the desired surface transformation. Closed-form expressions are obtained in two asymptotic regimes that are representative of far-field and near-field deployments. Based on the proposed approach, the impact of several design parameters and operating regimes is unveiled.