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Physically Consistent Modeling of Stacked Intelligent Metasurfaces Implemented with Beyond Diagonal RIS

Matteo Nerini, Bruno Clerckx

TL;DR

This paper derives a physically consistent channel model for SIM-aided systems using multiport network theory, capturing mutual coupling across transmitter, SIM layers, and receiver. It provides a general channel form $ oldsymbol{H}=oldsymbol{S}_{21}(oldsymbol{I}+oldsymbol{S}_{11})^{-1}$ and a simplified product model $ oldsymbol{H}=ar{oldsymbol{H}}^{R}ar{oldsymbol{ heta}}^{(L)}ar{oldsymbol{H}}^{(L)} ablaar{oldsymbol{ heta}}^{(1)}ar{oldsymbol{H}}^{(1)}$, under unilateral approximation and perfect matching. The study compares D-RIS and BD-RIS architectures, showing that a 1-layer BD-RIS can achieve the BD upper bound and outperform D-RIS, with BD-RIS offering better scalability and lower complexity in some configurations. These results guide design choices for SIM hardware and lay groundwork for more general SIM optimization and prototyping efforts.

Abstract

Stacked intelligent metasurface (SIM) has emerged as a technology enabling wave domain beamforming through multiple stacked reconfigurable intelligent surfaces (RISs). SIM has been implemented so far with diagonal RIS (D-RIS), while SIM implemented with beyond diagonal RIS (BD-RIS) remains unexplored. Furthermore, a model of SIM accounting for mutual coupling is not yet available. To fill these gaps, we derive a physically consistent channel model for SIM-aided systems and clarify the assumptions needed to obtain the simplified model used in related works. Using this model, we show that 1-layer SIM implemented with BD-RIS achieves the performance upper bound with limited complexity.

Physically Consistent Modeling of Stacked Intelligent Metasurfaces Implemented with Beyond Diagonal RIS

TL;DR

This paper derives a physically consistent channel model for SIM-aided systems using multiport network theory, capturing mutual coupling across transmitter, SIM layers, and receiver. It provides a general channel form and a simplified product model , under unilateral approximation and perfect matching. The study compares D-RIS and BD-RIS architectures, showing that a 1-layer BD-RIS can achieve the BD upper bound and outperform D-RIS, with BD-RIS offering better scalability and lower complexity in some configurations. These results guide design choices for SIM hardware and lay groundwork for more general SIM optimization and prototyping efforts.

Abstract

Stacked intelligent metasurface (SIM) has emerged as a technology enabling wave domain beamforming through multiple stacked reconfigurable intelligent surfaces (RISs). SIM has been implemented so far with diagonal RIS (D-RIS), while SIM implemented with beyond diagonal RIS (BD-RIS) remains unexplored. Furthermore, a model of SIM accounting for mutual coupling is not yet available. To fill these gaps, we derive a physically consistent channel model for SIM-aided systems and clarify the assumptions needed to obtain the simplified model used in related works. Using this model, we show that 1-layer SIM implemented with BD-RIS achieves the performance upper bound with limited complexity.
Paper Structure (7 sections, 1 theorem, 50 equations, 3 figures)

This paper contains 7 sections, 1 theorem, 50 equations, 3 figures.

Table of Contents

  1. Introduction
  2. SIM-Aided System Model Based on Multiport Network Theory
  3. General SIM-Aided Channel Model
  4. Simplified SIM-Aided Channel Model
  5. Implementing SIM with D-RIS and BD-RIS
  6. Numerical Results
  7. Conclusion

Key Result

Proposition 1

Consider the cascade system represented in Fig. fig:cascade, consisting of an $N_P$-port network, with scattering matrix $\mathbf{P}\in\mathbb{C}^{N_P\times N_P}$ given by where $\mathbf{P}_{11}\in\mathbb{C}^{N_1\times N_1}$ and $\mathbf{P}_{22}\in\mathbb{C}^{N_2\times N_2}$, with $N_P=N_1+N_2$, and an $N_Q$-port network, with scattering matrix $\mathbf{Q}\in\mathbb{C}^{N_Q\times N_Q}$ given by

Figures (3)

  • Figure 1: SIM-aided communication system diagram.
  • Figure 2: Cascade of two multiport networks.
  • Figure 3: Normalized channel gain $G=\vert h\vert^2/(\Vert\bar{\mathbf{h}}^{R}\Vert^2\Vert\bar{\mathbf{h}}^{(1)}\Vert^2)$ and circuit complexity of SIM implemented with D-RIS and BD-RIS.

Theorems & Definitions (2)

  • Proposition 1
  • proof