Design of Reconfigurable Intelligent Surfaces by Using S-Parameter Multiport Network Theory -- Optimization and Full-Wave Validation

TL;DR

This paper presents a comprehensive, electromagnetically consistent RIS model based on multiport network theory in the S-parameter domain, explicitly accounting for mutual coupling and structural scattering that conventional RIS models neglect. It introduces new optimization schemes (S-UNI and S-OPT, with a structural-scattering aware extension S-OPT(ω)) that leverage Neumann-series approximations to efficiently tune RIS loads via the scattering matrix, achieving faster convergence than Z-based approaches. A key contribution is the explicit incorporation and suppression of structural (specular) scattering through a weighted objective and Pareto analysis, enabling RIS designs that maximize non-specular power while reducing unwanted reflections. The authors validate the theory and algorithms with full-wave MoM simulations (FEKO) across dipole- and patch-based RIS implementations, demonstrating close agreement between multiport-model predictions and full-wave results and confirming the importance of including mutual coupling and structural scattering in RIS optimization for realistic deployments.

Abstract

Multiport network theory has been proved to be a suitable abstraction model for analyzing and optimizing reconfigurable intelligent surfaces (RISs) in an electromagnetically consistent manner, especially for studying the impact of the electromagnetic mutual coupling among radiating elements that are spaced less than half of the wavelength apart and for considering the interrelation between the amplitude and phase of the reflection coefficients. Both representations in terms of Z-parameter (impedance) and S-parameter (scattering) matrices are widely utilized. In this paper, we embrace multiport network theory for analyzing and optimizing the reradiation properties of RIS-aided channels, and provide four new contributions. (i) We offer a thorough comparison between the Z-parameter and S-parameter representations. This comparison allows us to unveil that typical scattering models utilized for RIS-aided channels ignore the structural scattering from an RIS, which is well documented in antenna theory. We show that the structural scattering results in an unwanted specular reflection. (ii) We develop an iterative algorithm for optimizing, in the presence of electromagnetic mutual coupling, the tunable loads of an RIS based on the S-parameters representation. We prove that small perturbations of the step size of the algorithm result in larger variations of the S-parameter matrix compared with the Z-parameter matrix, resulting in a faster convergence rate. (iii) We generalize the proposed algorithm to suppress the specular reflection due to the structural scattering, while maximizing the received power towards the direction of interest, and analyze the effectiveness and tradeoffs of the proposed approach. (iv) We validate the theoretical findings and algorithms with numerical simulations and a commercial full-wave electromagnetic simulator based on the method of moments.

Figures (14)

• Figure 1: Considered $N$-port network representation.
• Figure 2: Considered scenario. The RIS elements can be either free standing thin wire dipoles (as illustrated in the figure) or rectangular patches on a grounded substrate (detailed next and illustrated in Fig. \ref{['fig:7x7Ris']}). The scenario in the presence of blocking objects is presented in Fig. \ref{['fig:shield_no_shield_Setup']} and is elaborated next.
• Figure 3: Considered scenario in the presence of blocking objects (shields) near the transmitter and receiver (position $P_3$).
• Figure 4: Scattered field after RIS optimization based on the "No Shield" ($Z_{RT}$ is nullified) and "With Shield" methods.
• Figure 5: Full-wave simulations (the receiver is in $P_4$). Setup: (a) $d_y = \lambda/2$; (b) $d_y = \lambda/4$; (c) $d_y = \lambda/8$; (d) $d_y = \lambda/16$.