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Physics-Compliant Modeling and Scaling Laws of Multi-RIS Aided MIMO Systems

Matteo Nerini, Gabriele Gradoni, Bruno Clerckx

TL;DR

This work introduces a physics-compliant channel model for multi-RIS aided MIMO systems using multiport network theory, capturing impedance mismatch, mutual coupling, and RIS structural scattering. It shows clear differences from the widely used model that neglects structural scattering, derives LoS and multipath scaling laws, and develops alternating-optimization algorithms for both RIS architectures (reflective and transmissive) and BD-RIS variants. The results demonstrate substantial performance gaps between the two models that grow with the number of RISs $L$ and with multipath richness, underscoring the need to adopt physics-based models in RIS research and system design. Practically, the findings impact RIS reconfiguration, placement, channel estimation, and beam routing, and motivate experimental validation of multi-RIS systems.

Abstract

Reconfigurable intelligent surface (RIS) enables the control of wireless channels to improve coverage. To further extend coverage, multi-RIS aided systems have been explored, where multiple RISs steer the signal via a multi-hop path. However, deriving a physics-compliant channel model for multi-RIS aided systems is still an open problem. In this study, we fill this gap by modeling multi-RIS aided systems through multiport network theory, and deriving a channel model accounting for impedance mismatch, mutual coupling, and structural scattering. The derived physics-compliant model differs from the model widely used in literature, which omits the RIS structural scattering. To quantify this difference, we derive the channel gain scaling laws of the two models under line-of-sight (LoS) and multipath channels. Theoretical insights, validated by numerical results, show an important discrepancy between the physics-compliant and the widely used models, increasing with the number of RISs and multipath richness. In a multi-hop system aided by four 128-element RISs with multipath channels, optimizing the RISs using the widely used model and applying their solutions to the physics-compliant model achieves only 7% of the maximum channel gain. This highlights how severely mismatched channel models can be, calling for more accurate models in communication theory.

Physics-Compliant Modeling and Scaling Laws of Multi-RIS Aided MIMO Systems

TL;DR

This work introduces a physics-compliant channel model for multi-RIS aided MIMO systems using multiport network theory, capturing impedance mismatch, mutual coupling, and RIS structural scattering. It shows clear differences from the widely used model that neglects structural scattering, derives LoS and multipath scaling laws, and develops alternating-optimization algorithms for both RIS architectures (reflective and transmissive) and BD-RIS variants. The results demonstrate substantial performance gaps between the two models that grow with the number of RISs and with multipath richness, underscoring the need to adopt physics-based models in RIS research and system design. Practically, the findings impact RIS reconfiguration, placement, channel estimation, and beam routing, and motivate experimental validation of multi-RIS systems.

Abstract

Reconfigurable intelligent surface (RIS) enables the control of wireless channels to improve coverage. To further extend coverage, multi-RIS aided systems have been explored, where multiple RISs steer the signal via a multi-hop path. However, deriving a physics-compliant channel model for multi-RIS aided systems is still an open problem. In this study, we fill this gap by modeling multi-RIS aided systems through multiport network theory, and deriving a channel model accounting for impedance mismatch, mutual coupling, and structural scattering. The derived physics-compliant model differs from the model widely used in literature, which omits the RIS structural scattering. To quantify this difference, we derive the channel gain scaling laws of the two models under line-of-sight (LoS) and multipath channels. Theoretical insights, validated by numerical results, show an important discrepancy between the physics-compliant and the widely used models, increasing with the number of RISs and multipath richness. In a multi-hop system aided by four 128-element RISs with multipath channels, optimizing the RISs using the widely used model and applying their solutions to the physics-compliant model achieves only 7% of the maximum channel gain. This highlights how severely mismatched channel models can be, calling for more accurate models in communication theory.

Paper Structure

This paper contains 15 sections, 1 theorem, 79 equations, 10 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Multiport Network Theory
  3. Multi-RIS Aided Channel Model
  4. Channel Model with Perfect Matching and No Mutual Coupling
  5. Channel Model in the Presence of Reflective, Hybrid, and Multi-Sector RISs
  6. Channel Gain Scaling Laws with Line-of-Sight Channels
  7. Physics-Compliant Channel Model
  8. Widely Used Channel Model
  9. Channel Gain Maximization with Multipath Channels
  10. Physics-Compliant Channel Model
  11. Widely Used Channel Model
  12. Numerical Results
  13. Line-of-Sight Channels
  14. Multipath Channels
  15. Conclusion

Key Result

Proposition 1

Consider a square block matrix $\mathbf{M}\in\mathbb{C}^{LN\times LN}$ having square matrices $\mathbf{D}_\ell\in\mathbb{C}^{N\times N}$ in the diagonal, for $\ell=1,\ldots,L$, and square matrices $\mathbf{S}_{\ell,\ell-1}\in\mathbb{C}^{N\times N}$ in the subdiagonal, for $\ell=2,\ldots,L$, with all If all $\mathbf{D}_\ell$ are invertible, the inverse of $\mathbf{M}$, denoted as $\mathbf{N}=\mathb

Figures (10)

  • Figure 1: Multi-RIS aided MIMO system modeled through multiport network theory.
  • Figure 2: Multi-RIS aided MIMO system.
  • Figure 3: Average channel gain with unit path gain, i.e., $\Lambda=1$, of the physics-compliant model $\mathbf{H}$ and the widely used model $\mathbf{H}^\prime$, under LoS channels.
  • Figure 4: Relative difference $\eta$ between the average channel gain of the physics-compliant model $\mathbf{H}$ and the widely used model $\mathbf{H}^\prime$, under LoS channels.
  • Figure 5: Normalized gain $\rho$ of the physics-compliant model $\mathbf{H}$ obtained by optimizing the RISs based on the widely used model $\mathbf{H}^\prime$, under LoS channels.
  • ...and 5 more figures

Theorems & Definitions (2)

  • Proposition 1
  • proof