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Active Reconfigurable Intelligent Surface Assisted MIMO: Electromagnetic-Compliant Modeling with Mutual Coupling

Yang Cao, Wenchi Cheng, Jingqing Wang, Wei Zhang

TL;DR

This work develops an electromagnetic (EM) compliant, mutual-coupling (MC) aware model for active reconfigurable intelligent surface (RIS) aided MIMO systems by integrating S-parameter based active RIS modeling with multiport network theory. The authors derive a detailed EM-consistent channel representation that captures impedance mismatches and MC among transmitter, RIS elements, and receiver, and propose a joint beamforming and RIS reflection optimization using a Sherman–Morrison/Neumann-series based alternating optimization (SMaN AO) algorithm. Through a sequence of transformations to a tractable mean-squared-error (MSE) form and decomposed subproblems, the method simultaneously updates the transmit beamformer and the RIS amplitude and phase configurations, accounting for RIS amplification power $P_{\max}^A$ and reflection bounds $\Gamma_{\max}$. Numerical results demonstrate that MC effects materially impact achievable rates and that neglecting MC can cause significant performance gaps; the EM-compliant model with MC yields substantial gains over MC-unaware and passive RIS variants, highlighting its practical importance for EM-consistent RIS design and optimization in 6G systems.

Abstract

Reconfigurable Intelligent Surfaces (RIS) represent a transformative technology for sixth-generation (6G) wireless communications, but it suffers from a significant limitation, namely the double-fading attenuation. Active RIS has emerged as a promising solution, effectively mitigating the attenuation issues associated with conventional RIS-assisted systems. However, the current academic work on active RIS focuses on the system-level optimization of active RIS, often overlooking the development of models that are compatible with its electromagnetic (EM) and physical properties. The challenge of constructing realistic, EM-compliant models for active RIS-assisted communication, as well as understanding their implications on system-level optimization, remains an open research area. To tackle these problems, in this paper we develop a novel EM-compliant model with mutual coupling (MC) for active RIS-assisted wireless systems by integrating the developed scattering-parameter ($S$-parameter) based active RIS framework with multiport network theory, which facilitates system-level analysis and optimization. To evaluate the performance of the EM-compliant active RIS model, we design the joint optimization scheme based on the transmit beamforming at the transmitter and the reflection coefficient at the active RIS to maximize the achievable rate of EM-compliant active RIS-assisted MIMO system. To tackle the inherent non-convexity of this problem, we employ the Sherman-Morrison inversion and Neumann series (SMaN)-based alternating optimization (AO) algorithm. Simulation results verified that EM property (i.e., MC effect) is an indispensable factor in the optimization process of MIMO systems. Neglecting this effect introduces a substantial performance gap, highlighting its significance in the more pronounced the MC effect is, the greater the gap in achievable rates.

Active Reconfigurable Intelligent Surface Assisted MIMO: Electromagnetic-Compliant Modeling with Mutual Coupling

TL;DR

This work develops an electromagnetic (EM) compliant, mutual-coupling (MC) aware model for active reconfigurable intelligent surface (RIS) aided MIMO systems by integrating S-parameter based active RIS modeling with multiport network theory. The authors derive a detailed EM-consistent channel representation that captures impedance mismatches and MC among transmitter, RIS elements, and receiver, and propose a joint beamforming and RIS reflection optimization using a Sherman–Morrison/Neumann-series based alternating optimization (SMaN AO) algorithm. Through a sequence of transformations to a tractable mean-squared-error (MSE) form and decomposed subproblems, the method simultaneously updates the transmit beamformer and the RIS amplitude and phase configurations, accounting for RIS amplification power and reflection bounds . Numerical results demonstrate that MC effects materially impact achievable rates and that neglecting MC can cause significant performance gaps; the EM-compliant model with MC yields substantial gains over MC-unaware and passive RIS variants, highlighting its practical importance for EM-consistent RIS design and optimization in 6G systems.

Abstract

Reconfigurable Intelligent Surfaces (RIS) represent a transformative technology for sixth-generation (6G) wireless communications, but it suffers from a significant limitation, namely the double-fading attenuation. Active RIS has emerged as a promising solution, effectively mitigating the attenuation issues associated with conventional RIS-assisted systems. However, the current academic work on active RIS focuses on the system-level optimization of active RIS, often overlooking the development of models that are compatible with its electromagnetic (EM) and physical properties. The challenge of constructing realistic, EM-compliant models for active RIS-assisted communication, as well as understanding their implications on system-level optimization, remains an open research area. To tackle these problems, in this paper we develop a novel EM-compliant model with mutual coupling (MC) for active RIS-assisted wireless systems by integrating the developed scattering-parameter (-parameter) based active RIS framework with multiport network theory, which facilitates system-level analysis and optimization. To evaluate the performance of the EM-compliant active RIS model, we design the joint optimization scheme based on the transmit beamforming at the transmitter and the reflection coefficient at the active RIS to maximize the achievable rate of EM-compliant active RIS-assisted MIMO system. To tackle the inherent non-convexity of this problem, we employ the Sherman-Morrison inversion and Neumann series (SMaN)-based alternating optimization (AO) algorithm. Simulation results verified that EM property (i.e., MC effect) is an indispensable factor in the optimization process of MIMO systems. Neglecting this effect introduces a substantial performance gap, highlighting its significance in the more pronounced the MC effect is, the greater the gap in achievable rates.

Paper Structure

This paper contains 17 sections, 2 theorems, 66 equations, 10 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. EM-Compliant Model and Multiport Network Analysis
  3. $S$-Parameter Based Modeling of Active RIS
  4. EM-Compliant Model Based on Multiport Network Theory
  5. Differences From Conventional Model
  6. System Model And Problem Formulation
  7. System Model
  8. Problem Formulation And Transformation
  9. Proposed Alternating Optimization
  10. Update $\boldsymbol{\rm {W}}$
  11. Update $\boldsymbol{\rm {\Gamma}}_A$
  12. Optimize the amplitude matrix $\boldsymbol{\rm \Lambda}_{R\space A}$
  13. Optimize the phase matrix $\boldsymbol{\rm \Theta}$
  14. Simulation Results and Analysis
  15. Conclusions
  16. ...and 2 more sections

Key Result

Theorem 1

Based on multiport network theory, we formulate $\boldsymbol{\rm b}_R$ as a function of $\boldsymbol{\rm a}_S$ and $\boldsymbol{\rm a}_N$ to derive the EM-compliant model for active RIS-assisted MIMO communication as follows: where we introduce the definitions as follows: with $\chi_1, \chi_2\in\left\{T,R\right\}$ and $\boldsymbol{\rm I}$ being the identity matrix of the dimension corresponding

Figures (10)

  • Figure 1: Illustration of the active RIS architecture and the equivalent network of active RIS element.
  • Figure 2: Illustration of the EM-compliant model based on multiport network theory.
  • Figure 3: Plane diagram of simulated active RIS-assisted wireless communication system.
  • Figure 4: Convergence with fixed active RIS size.
  • Figure 5: (a) Convergence behavior of Sherman-Morrison inversion based BCD subalgorithm. (b) Convergence behavior of Neumann series approximation based subalgorithm.
  • ...and 5 more figures

Theorems & Definitions (3)

  • Theorem 1
  • Remark 1
  • Theorem 2