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

Matteo Nerini, Gabriele Gradoni, Bruno Clerckx

TL;DR

This study modeling multi-RIS aided systems through multiport network theory, and deriving the scaling law of the physics-compliant channel gain shows a significant discrepancy between the physics-compliant and the widely used models.

Abstract

Reconfigurable intelligent surface (RIS) is a revolutionary technology enabling the control of wireless channels and improving coverage in wireless networks. To further extend coverage, multi-RIS aided systems have been explored, where multiple RISs steer the signal toward the receiver 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 the scaling law of the physics-compliant channel gain. The derived physics-compliant channel model differs from the widely used model, where the structural scattering of the RISs is neglected. Theoretical insights, validated by numerical results, show a significant discrepancy between the physics-compliant and the widely used models. This discrepancy increases with the number of RISs and decreases with the number of RIS elements, reaching 200% in a system with eight RISs with 128 elements each.

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

TL;DR

This study modeling multi-RIS aided systems through multiport network theory, and deriving the scaling law of the physics-compliant channel gain shows a significant discrepancy between the physics-compliant and the widely used models.

Abstract

Reconfigurable intelligent surface (RIS) is a revolutionary technology enabling the control of wireless channels and improving coverage in wireless networks. To further extend coverage, multi-RIS aided systems have been explored, where multiple RISs steer the signal toward the receiver 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 the scaling law of the physics-compliant channel gain. The derived physics-compliant channel model differs from the widely used model, where the structural scattering of the RISs is neglected. Theoretical insights, validated by numerical results, show a significant discrepancy between the physics-compliant and the widely used models. This discrepancy increases with the number of RISs and decreases with the number of RIS elements, reaching 200% in a system with eight RISs with 128 elements each.

Paper Structure

This paper contains 8 sections, 1 theorem, 30 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Multiport Network Theory
  3. Multi-RIS Aided Channel Model
  4. Channel Gain Scaling Laws
  5. Physics-Compliant Channel Model
  6. Widely Used Channel Model
  7. Numerical Results
  8. 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 (3)

  • Figure 1: Multi-RIS aided system modeled through multiport network theory.
  • Figure 2: Multi-RIS aided system.
  • Figure 3: Relative difference between the average channel gain with the physics-compliant model $\text{E}[\vert h\vert^2]$ and the widely used model $\text{E}[\vert h^\prime\vert^2]$.

Theorems & Definitions (2)

  • Proposition 1
  • proof