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RIS-Assisted Secure Transmission Exploiting Statistical CSI of Eavesdropper

Cen Liu, Chang Tian, Peixi Liu

TL;DR

This work tackles secure downlink transmission using reconfigurable intelligent surfaces when only the eavesdropper's statistical CSI is available. It derives a deterministic lower bound on the ergodic secrecy rate (ESR), denoted $\bar{R}_{\rm S}^{\rm lb}$, and reformulates the stochastic ESR maximization into a deterministic LESR maximization problem. To solve this non-convex problem, the authors propose the penalty dual convex approximation (PDCA) algorithm based on penalty dual decomposition (PDD), with a inner BSCA loop for joint beamforming and RIS phase shifts and an outer loop for Lagrange multiplier and penalty updates, guaranteeing convergence to a KKT point with reduced complexity. Numerical results show that PDCA outperforms the conventional alternating optimization (AO) approach and that the LESR bound is a tight proxy for ESR under statistical CSI, underscoring the security gains achievable with RIS under practical CSI assumptions. The approach provides a practical framework for secure RIS-assisted communications where instantaneous Eve CSI is unavailable.

Abstract

We investigate the reconfigurable intelligent surface (RIS) assisted downlink secure transmission where only the statistical channel of eavesdropper is available. To handle the stochastic ergodic secrecy rate (ESR) maximization problem, a deterministic lower bound of ESR (LESR) is derived. We aim to maximize the LESR by jointly designing the transmit beamforming at the access point (AP) and reflect beamforming by the phase shifts at the RIS. To solve the non-convex LESR maximization problem, we develop a novel penalty dual convex approximation (PDCA) algorithm based on the penalty dual decomposition (PDD) optimization framework, where the exacting constraints are penalized and dualized into the objective function as augmented Lagrangian components. The proposed PDCA algorithm performs double-loop iterations, i.e., the inner loop resorts to the block successive convex approximation (BSCA) to update the optimization variables; while the outer loop adjusts the Lagrange multipliers and penalty parameter of the augmented Lagrangian cost function. The convergence to a Karush-Kuhn-Tucker (KKT) solution is theoretically guaranteed with low computational complexity. Simulation results show that the proposed PDCA scheme is better than the commonly adopted alternating optimization (AO) scheme with the knowledge of statistical channel of eavesdropper.

RIS-Assisted Secure Transmission Exploiting Statistical CSI of Eavesdropper

TL;DR

This work tackles secure downlink transmission using reconfigurable intelligent surfaces when only the eavesdropper's statistical CSI is available. It derives a deterministic lower bound on the ergodic secrecy rate (ESR), denoted , and reformulates the stochastic ESR maximization into a deterministic LESR maximization problem. To solve this non-convex problem, the authors propose the penalty dual convex approximation (PDCA) algorithm based on penalty dual decomposition (PDD), with a inner BSCA loop for joint beamforming and RIS phase shifts and an outer loop for Lagrange multiplier and penalty updates, guaranteeing convergence to a KKT point with reduced complexity. Numerical results show that PDCA outperforms the conventional alternating optimization (AO) approach and that the LESR bound is a tight proxy for ESR under statistical CSI, underscoring the security gains achievable with RIS under practical CSI assumptions. The approach provides a practical framework for secure RIS-assisted communications where instantaneous Eve CSI is unavailable.

Abstract

We investigate the reconfigurable intelligent surface (RIS) assisted downlink secure transmission where only the statistical channel of eavesdropper is available. To handle the stochastic ergodic secrecy rate (ESR) maximization problem, a deterministic lower bound of ESR (LESR) is derived. We aim to maximize the LESR by jointly designing the transmit beamforming at the access point (AP) and reflect beamforming by the phase shifts at the RIS. To solve the non-convex LESR maximization problem, we develop a novel penalty dual convex approximation (PDCA) algorithm based on the penalty dual decomposition (PDD) optimization framework, where the exacting constraints are penalized and dualized into the objective function as augmented Lagrangian components. The proposed PDCA algorithm performs double-loop iterations, i.e., the inner loop resorts to the block successive convex approximation (BSCA) to update the optimization variables; while the outer loop adjusts the Lagrange multipliers and penalty parameter of the augmented Lagrangian cost function. The convergence to a Karush-Kuhn-Tucker (KKT) solution is theoretically guaranteed with low computational complexity. Simulation results show that the proposed PDCA scheme is better than the commonly adopted alternating optimization (AO) scheme with the knowledge of statistical channel of eavesdropper.

Paper Structure

This paper contains 12 sections, 19 equations, 5 figures, 1 table, 2 algorithms.

Table of Contents

  1. Introduction
  2. System Model
  3. Problem Formulation
  4. Ergodic Secrecy Rate Maximization
  5. Problem Reformulation
  6. The Proposed Penalty Dual Convex Approximation Algorithm
  7. Augmented Lagrangian Problem
  8. Proposed BSCA Algorithm for Solving AL Problem
  9. Proposed PDCA Algorithm and Computational Complexity
  10. Simulation Results
  11. Conclusion
  12. Proof of Proposition 1

Figures (5)

  • Figure 1: RIS-assisted single-user MISO wireless system in the presence of a single-antenna eavesdropper.
  • Figure 2: Simulation setup.
  • Figure 3: ESR and LESR versus $P_{\rm max}$ and $N$.
  • Figure 4: ESR and LESR versus the $Y$-Coordinates of Eve, user and RIS when $P_{\rm max} = 5$dBm and $N=160$.
  • Figure 5: ESR and SR versus $P_{\rm max}$ when $N=32$