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Localized and Distributed Beyond Diagonal Reconfigurable Intelligent Surfaces with Lossy Interconnections: Modeling and Optimization

Matteo Nerini, Golsa Ghiaasi, Bruno Clerckx

TL;DR

This work broadens RIS research by introducing distributed BD-RIS and modeling its interconnections with transmission-line theory to capture phase variation and losses. It derives scaling laws showing that lossless distributed BD-RIS can yield orders-of-magnitude gains over conventional RIS and localized BD-RIS, driven by interconnections enabling signal propagation inside the BD-RIS. To bridge theory and practice, the paper develops three simplified lossy BD-RIS models and an optimization framework that alternates between RIS impedance settings and transmit/receive beamforming, demonstrating substantial performance gains even when losses are present. The findings suggest distributed BD-RIS as a powerful tool for extended coverage and higher data rates in future wireless networks, with practical deployment insights and directions for further research.

Abstract

Reconfigurable intelligent surface (RIS) is a key technology to control the communication environment in future wireless networks. Recently, beyond diagonal RIS (BD-RIS) emerged as a generalization of RIS achieving larger coverage through additional tunable impedance components interconnecting the RIS elements. However, conventional RIS and BD-RIS can effectively serve only users in their proximity, resulting in limited coverage. To overcome this limitation, in this paper, we investigate distributed RIS, whose elements are distributed over a wide region, in opposition to localized RIS commonly considered in the literature. The scaling laws of distributed BD-RIS reveal that it offers significant gains over distributed conventional RIS and localized BD-RIS, enabled by its interconnections allowing signal propagation within the BD-RIS. To assess the practical performance of distributed BD-RIS, we model and optimize BD-RIS with lossy interconnections through transmission line theory. Our model accounts for phase changes and losses over the BD-RIS interconnections arising when the interconnection lengths are not much smaller than the wavelength. Numerical results show that the performance of localized BD-RIS is only slightly impacted by losses, given the short interconnection lengths. Besides, distributed BD-RIS can achieve orders of magnitude of gains over conventional RIS, even in the presence of low losses.

Localized and Distributed Beyond Diagonal Reconfigurable Intelligent Surfaces with Lossy Interconnections: Modeling and Optimization

TL;DR

This work broadens RIS research by introducing distributed BD-RIS and modeling its interconnections with transmission-line theory to capture phase variation and losses. It derives scaling laws showing that lossless distributed BD-RIS can yield orders-of-magnitude gains over conventional RIS and localized BD-RIS, driven by interconnections enabling signal propagation inside the BD-RIS. To bridge theory and practice, the paper develops three simplified lossy BD-RIS models and an optimization framework that alternates between RIS impedance settings and transmit/receive beamforming, demonstrating substantial performance gains even when losses are present. The findings suggest distributed BD-RIS as a powerful tool for extended coverage and higher data rates in future wireless networks, with practical deployment insights and directions for further research.

Abstract

Reconfigurable intelligent surface (RIS) is a key technology to control the communication environment in future wireless networks. Recently, beyond diagonal RIS (BD-RIS) emerged as a generalization of RIS achieving larger coverage through additional tunable impedance components interconnecting the RIS elements. However, conventional RIS and BD-RIS can effectively serve only users in their proximity, resulting in limited coverage. To overcome this limitation, in this paper, we investigate distributed RIS, whose elements are distributed over a wide region, in opposition to localized RIS commonly considered in the literature. The scaling laws of distributed BD-RIS reveal that it offers significant gains over distributed conventional RIS and localized BD-RIS, enabled by its interconnections allowing signal propagation within the BD-RIS. To assess the practical performance of distributed BD-RIS, we model and optimize BD-RIS with lossy interconnections through transmission line theory. Our model accounts for phase changes and losses over the BD-RIS interconnections arising when the interconnection lengths are not much smaller than the wavelength. Numerical results show that the performance of localized BD-RIS is only slightly impacted by losses, given the short interconnection lengths. Besides, distributed BD-RIS can achieve orders of magnitude of gains over conventional RIS, even in the presence of low losses.
Paper Structure (23 sections, 2 theorems, 69 equations, 10 figures)

This paper contains 23 sections, 2 theorems, 69 equations, 10 figures.

Table of Contents

  1. Introduction
  2. Localized and Distributed BD-RIS-Aided System Model
  3. Scaling Laws
  4. Gain of Fully- over Single-Connected Localized RIS
  5. Gain of Fully- over Single-Connected Distributed RIS
  6. Gain of Distributed over Localized Single-Connected RIS
  7. Gain of Distributed over Localized Fully-Connected RIS
  8. General Lossy BD-RIS Model
  9. Modeling the Admittance Matrix: Off-Diagonal Entries
  10. Modeling the Admittance Matrix: Diagonal Entries
  11. Simplified Lossy BD-RIS Models
  12. Model with Interconnection Lengths Multiple of $\lambda/2$
  13. Model with Lossless Interconnections
  14. Model with Interconnection Lengths Multiple of $\lambda/2$ and Lossless Interconnections
  15. Lossy BD-RIS Optimization
  16. ...and 8 more sections

Key Result

Proposition 1

Given $N$ different positive real number collected in a vector $\boldsymbol{\xi}\in\mathbb{R}_{+}^{N\times1}$, the generalized mean with exponent $p\in\mathbb{R}_{*}$ of the elements of $\boldsymbol{\xi}$$M_p(\boldsymbol{\xi})$ satisfy

Figures (10)

  • Figure 1: (a) Localized and (b) distributed RIS-aided communication system.
  • Figure 2: (a) $\mathcal{G}^{\text{Dis}}$, (b) $\mathcal{G}^{\text{SC}}$, and (c) $\mathcal{G}^{\text{FC}}$ for different values of path-loss exponent and number of RIS elements.
  • Figure 3: (a) $\mathcal{G}^{\text{Dis}}$, (b) $\mathcal{G}^{\text{SC}}$, and (c) $\mathcal{G}^{\text{FC}}$ for different locations of the receiver.
  • Figure 4: (a) Port $m$ connected to ground through $Z_m$ and (b) ports $m$ and $n$ interconnected through $Z_{n,m}$ and a transmission line of length $\ell_{n,m}$.
  • Figure 5: Equivalent circuit to be studied to compute (a) the off-diagonal entry $[\mathbf{Y}]_{n,m}$ and (b) the diagonal entry $[\mathbf{Y}]_{m,m}$.
  • ...and 5 more figures

Theorems & Definitions (4)

  • Proposition 1
  • proof
  • Proposition 2
  • proof