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A Universal Framework for Multiport Network Analysis of Reconfigurable Intelligent Surfaces

Matteo Nerini, Shanpu Shen, Hongyu Li, Marco Di Renzo, Bruno Clerckx

TL;DR

This work introduces a universal, EM-consistent framework for analyzing RIS-aided communications using impedance ($Z$), admittance ($Y$), and scattering ($S$) parameters. It derives three general channel models that account for impedance mismatching and mutual coupling, and proves their equivalence; under unilateral and perfect-matching approximations, these reduce to widely used channel models while revealing additional structural insights. The paper then discusses RIS architectures (conventional and BD-RIS) and provides optimization strategies tailored to each parameter set, supported by numerical results that confirm model equivalence and highlight performance gains from mutual coupling and BD-RIS configurations. The framework enables rigorous model selection and parameter mappings across representations, facilitating more accurate RIS design, optimization, and experimental validation in practical wireless systems.

Abstract

Reconfigurable intelligent surface (RIS) is an emerging paradigm able to control the propagation environment in wireless systems. Most of the research on RIS has been dedicated to system optimization and, with the advent of beyond diagonal RIS (BD-RIS), to RIS architecture design. However, developing general and unified electromagnetic (EM)-consistent models for RIS-aided systems remains an open problem. In this study, we propose a universal framework for the multiport network analysis of RIS-aided systems. With our framework, we model RIS-aided systems and RIS architectures through impedance, admittance, and scattering parameter analysis. Based on these analyses, three equivalent models are derived accounting for the effects of impedance mismatching and mutual coupling. The three models are then simplified by assuming large transmission distances, perfect matching, and no mutual coupling to understand the role of the RIS in the communication model. The derived simplified models are consistent with the typical model used in related literature, although we show that an additional approximation is commonly considered in the literature. We discuss the benefits of each analysis in characterizing and optimizing the RIS and how to select the most suitable parameters according to the needs. Numerical results provide additional evidence of the equivalence of the three analyses.

A Universal Framework for Multiport Network Analysis of Reconfigurable Intelligent Surfaces

TL;DR

This work introduces a universal, EM-consistent framework for analyzing RIS-aided communications using impedance (), admittance (), and scattering () parameters. It derives three general channel models that account for impedance mismatching and mutual coupling, and proves their equivalence; under unilateral and perfect-matching approximations, these reduce to widely used channel models while revealing additional structural insights. The paper then discusses RIS architectures (conventional and BD-RIS) and provides optimization strategies tailored to each parameter set, supported by numerical results that confirm model equivalence and highlight performance gains from mutual coupling and BD-RIS configurations. The framework enables rigorous model selection and parameter mappings across representations, facilitating more accurate RIS design, optimization, and experimental validation in practical wireless systems.

Abstract

Reconfigurable intelligent surface (RIS) is an emerging paradigm able to control the propagation environment in wireless systems. Most of the research on RIS has been dedicated to system optimization and, with the advent of beyond diagonal RIS (BD-RIS), to RIS architecture design. However, developing general and unified electromagnetic (EM)-consistent models for RIS-aided systems remains an open problem. In this study, we propose a universal framework for the multiport network analysis of RIS-aided systems. With our framework, we model RIS-aided systems and RIS architectures through impedance, admittance, and scattering parameter analysis. Based on these analyses, three equivalent models are derived accounting for the effects of impedance mismatching and mutual coupling. The three models are then simplified by assuming large transmission distances, perfect matching, and no mutual coupling to understand the role of the RIS in the communication model. The derived simplified models are consistent with the typical model used in related literature, although we show that an additional approximation is commonly considered in the literature. We discuss the benefits of each analysis in characterizing and optimizing the RIS and how to select the most suitable parameters according to the needs. Numerical results provide additional evidence of the equivalence of the three analyses.
Paper Structure (34 sections, 2 theorems, 104 equations, 4 figures, 3 tables)

This paper contains 34 sections, 2 theorems, 104 equations, 4 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Multiport Network Analysis
  3. Modeling Based on the Impedance Parameters
  4. Modeling Based on the Admittance Parameters
  5. Modeling Based on the Scattering Parameters
  6. General RIS-Aided Communication Model
  7. Universal Framework
  8. Impedance Parameters Analysis
  9. Admittance Parameters Analysis
  10. Scattering Parameters Analysis
  11. Equivalence Between General Models
  12. RIS-Aided Communication Model Using the Unilateral Approximation
  13. Universal Framework
  14. Impedance Parameters Analysis
  15. Admittance Parameters Analysis
  16. ...and 19 more sections

Key Result

Proposition 1

The general channel model based on the $Z$-parameters eq:Hgen-z is equivalent to the general channel model based on the $Y$-parameters eq:Hgen-y.

Figures (4)

  • Figure 1: Multiport model of an RIS-aided communication system.
  • Figure 2: Average received signal power obtained with the model $h$ and the widely used model $h^\prime$.
  • Figure 3: Relative difference between the average received signal power obtained with the model $h$ and the widely used model $h^\prime$.
  • Figure 4: Average received signal power maximized using $Z$-, $Y$-, and $S$-parameters.

Theorems & Definitions (4)

  • Proposition 1
  • proof
  • Proposition 2
  • proof