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A Mode-Matching Approach to the Design of RIS-Aided Communications

Ahmed Najjar, Hajar El Hassani, Marco Di Renzo, Kezhi Wang, Merouane Debbah

TL;DR

This work tackles efficient RIS-aided anomalous reflection by modeling the RIS as a spatially periodic surface-impedance boundary and solving for the reflected field with a mode-matching approach based on Floquet harmonics. By expanding the surface impedance as $Z_s(y) = \sum_p z_p e^{-j 2 \pi p y / D}$ and solving the resulting linear system, the authors quantify how power is redistributed among propagating and evanescent Floquet modes through the reflection matrix $\boldsymbol{\Gamma}$ and coefficients $B_n$. They compare three impedance profiles—cotangent, GO-like, and globally optimal—and show that enforcing global power conservation (as in the optimal profile) concentrates energy into the desired harmonic with minimal sidelobes, at the cost of higher implementation complexity. The EM-consistent framework provides a principled basis for RIS design and highlights the trade-offs between simplicity and beamforming efficiency in practical wireless systems.

Abstract

Reconfigurable intelligent surface (RIS) is an emerging technology for application to wireless communications. In this paper, we consider the problem of anomalous reflection and model the RIS as a periodic surface impedance boundary. We utilize the mode matching method and Floquets expansion representation to compute the field reflected from a spatially periodic RIS, and evaluate the performance versus implementation complexity tradeoffs of RIS aided communications based on the global design criterion. This allows us to maximize the power reflected towards the intended direction of propagation, while minimizing the power reradiated towards undesired directions of propagation. In addition, we discuss the advantages of the proposed electromagnetically consistent approach to the design of RIS aided wireless systems.

A Mode-Matching Approach to the Design of RIS-Aided Communications

TL;DR

This work tackles efficient RIS-aided anomalous reflection by modeling the RIS as a spatially periodic surface-impedance boundary and solving for the reflected field with a mode-matching approach based on Floquet harmonics. By expanding the surface impedance as and solving the resulting linear system, the authors quantify how power is redistributed among propagating and evanescent Floquet modes through the reflection matrix and coefficients . They compare three impedance profiles—cotangent, GO-like, and globally optimal—and show that enforcing global power conservation (as in the optimal profile) concentrates energy into the desired harmonic with minimal sidelobes, at the cost of higher implementation complexity. The EM-consistent framework provides a principled basis for RIS design and highlights the trade-offs between simplicity and beamforming efficiency in practical wireless systems.

Abstract

Reconfigurable intelligent surface (RIS) is an emerging technology for application to wireless communications. In this paper, we consider the problem of anomalous reflection and model the RIS as a periodic surface impedance boundary. We utilize the mode matching method and Floquets expansion representation to compute the field reflected from a spatially periodic RIS, and evaluate the performance versus implementation complexity tradeoffs of RIS aided communications based on the global design criterion. This allows us to maximize the power reflected towards the intended direction of propagation, while minimizing the power reradiated towards undesired directions of propagation. In addition, we discuss the advantages of the proposed electromagnetically consistent approach to the design of RIS aided wireless systems.
Paper Structure (5 sections, 23 equations, 3 figures, 1 table)

This paper contains 5 sections, 23 equations, 3 figures, 1 table.

Table of Contents

  1. Introduction
  2. System Model
  3. Mode-Matching Based Electromagnetic Model
  4. Numerical Results
  5. Conclusion

Figures (3)

  • Figure 1: Geometrical configuration of the RIS. The surface lies in the $xy$-plane, is periodic along $y$, and is modeled as a surface-impedance boundary illuminated by a transverse electric (TE)-polarized plane wave.
  • Figure 2: Comparison of the Floquet coefficients magnitude for the three impedance profiles.
  • Figure 3: Comparison of the normalized far-field radiation patterns for the three impedance profiles.