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Exploring Spatial Flexibility and Phase Design in Fluid Reconfigurable Intelligent Surfaces: A Physical Layer Security Perspective

J. D. Vega-Sánchez, V. H. Garzón Pacheco, N. V. Orozco Garzón, D. A. Riofrío Almeida, D. P. Moya Osorio

TL;DR

The paper addresses secrecy outages in fluid reconfigurable intelligent surfaces (FRIS) and compares their performance to traditional planar and compact RIS. It introduces a closed-form, ML-based end-to-end channel characterization, and a Q-learning framework to adaptively position FRIS elements, complemented by a distributed method for phase and beamforming optimization. Key findings show significant SOP gains from FRIS over conventional RIS without phase optimization, and persistent advantages over compact RIS due to reduced spatial correlation; however, these gains shrink when conventional RIS employs fully optimized BF and PS. The work highlights the value of spatial flexibility for secrecy under restricted PS optimization, and emphasizes the role of spatial diversity in mitigating eavesdropping threats in FRIS-enabled deployments.

Abstract

This work examines the secrecy outage probability (SOP) in Fluid Reconfigurable Intelligent Surfaces (FRIS) and contrasts their performance against two alternative RIS architectures: a traditional planar RIS and a compact RIS layout. To characterize the end-to-end FRIS channel, a maximum likelihood estimation (MLE) approach is introduced, while a Q-learning algorithm is employed to adaptively select the spatial positions of FRIS elements. Numerical evaluations show that optimizing element placement in FRIS significantly improves SOP compared to conventional RIS without phase adaptation. However, these improvements become less evident once the conventional RIS implements optimized beamforming (BF) and phase-shift (PS) controlling. In addition, FRIS maintains a clear advantage over compact RIS designs with optimized BF and PS, mainly due to its lower spatial correlation. Results further indicate that reducing the inter-element distance negatively impacts SOP, highlighting the importance of spatial diversity.

Exploring Spatial Flexibility and Phase Design in Fluid Reconfigurable Intelligent Surfaces: A Physical Layer Security Perspective

TL;DR

The paper addresses secrecy outages in fluid reconfigurable intelligent surfaces (FRIS) and compares their performance to traditional planar and compact RIS. It introduces a closed-form, ML-based end-to-end channel characterization, and a Q-learning framework to adaptively position FRIS elements, complemented by a distributed method for phase and beamforming optimization. Key findings show significant SOP gains from FRIS over conventional RIS without phase optimization, and persistent advantages over compact RIS due to reduced spatial correlation; however, these gains shrink when conventional RIS employs fully optimized BF and PS. The work highlights the value of spatial flexibility for secrecy under restricted PS optimization, and emphasizes the role of spatial diversity in mitigating eavesdropping threats in FRIS-enabled deployments.

Abstract

This work examines the secrecy outage probability (SOP) in Fluid Reconfigurable Intelligent Surfaces (FRIS) and contrasts their performance against two alternative RIS architectures: a traditional planar RIS and a compact RIS layout. To characterize the end-to-end FRIS channel, a maximum likelihood estimation (MLE) approach is introduced, while a Q-learning algorithm is employed to adaptively select the spatial positions of FRIS elements. Numerical evaluations show that optimizing element placement in FRIS significantly improves SOP compared to conventional RIS without phase adaptation. However, these improvements become less evident once the conventional RIS implements optimized beamforming (BF) and phase-shift (PS) controlling. In addition, FRIS maintains a clear advantage over compact RIS designs with optimized BF and PS, mainly due to its lower spatial correlation. Results further indicate that reducing the inter-element distance negatively impacts SOP, highlighting the importance of spatial diversity.

Paper Structure

This paper contains 13 sections, 2 theorems, 16 equations, 3 figures, 2 algorithms.

Table of Contents

  1. Introduction
  2. System and Channel Models
  3. Problem Formulation and Algorithm Design
  4. Problem Formulation
  5. Optimization Algorithm Design
  6. Q-Learning for Position Selection
  7. Distributed Phase Shift and Beamforming Optimization
  8. Performance Analysis
  9. Approximate SNR Distributions
  10. Secrecy Outage Probability
  11. Numerical results and discussions
  12. Conclusions
  13. Proof of Proposition \ref{['Propos1']}

Key Result

Proposition 1

Once the parameter vector $\bm{\varphi}_i$ is estimated with MLE, the PDF of $H_\mathrm{E}$ and the CDF of $H_\mathrm{B}$ of the received SNR can be approximated using a Gamma distribution via $\gamma_{i,(\mathcal{P}^\star)}=\overline\gamma_i|H_i|^2$. So, the corresponding expressions are given by

Figures (3)

  • Figure 1: System model for FRIS-enabled communication.
  • Figure 2: Spatial configuration and OP achieved for FRIS-aided Multiple-Input Single-Output (MISO). In all figures, the dashed lines represent analytical solutions, while markers correspond to MC simulations. Also, for a fair comparison, the RIS is configured with the same number of elements $M$ as the FRIS in all cases.
  • Figure 3: SOP vs. $\overline{\gamma}_\mathrm{B}$ for $L=4$, $M=100$, and different inter-element spacings between fluid elements. Markers denote MC simulations whereas the solid lines represent analytical solutions.

Theorems & Definitions (4)

  • Proposition 1
  • proof
  • Proposition 2
  • proof