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Cooperative Double IRS aided Secure Communication for MIMO-OFDM Systems

Weijie Xiong, Jingran Lin, Di Jiang, Yuhan Zhang, Kai Zhong, Qiang Li

TL;DR

This work addresses secure communication in wideband MIMO-OFDM using cooperative double-IRS by formulating SSR maximization as an unconstrained problem on a product Riemannian manifold. It introduces the Product Riemannian Gradient Descent (PRGD) algorithm, leveraging tangent-space gradients, Armijo step-size control, and retraction to enforce unit-modulus and power constraints, with proven convergence to a stationary point. The approach yields substantial secrecy-rate gains over single-IRS and distributed-multi-IRS benchmarks (e.g., up to 32% and 22.3% gains) and demonstrates robustness to CSI errors and OFDM-wideband deployment considerations. These results indicate practical potential for secure, wideband wireless systems employing cooperative IRS architectures, with clear deployment guidance for IRS placement and scalability across subcarriers.

Abstract

Cooperative double intelligent reflecting surface (double-IRS) has emerged as a promising approach for enhancing physical layer security (PLS) in MIMO systems. However, existing studies are limited to narrowband scenarios and fail to address wideband MIMO-OFDM. In this regime, frequency-flat IRS phases and cascaded IRS links cause severe coupling, rendering narrowband designs inapplicable. To overcome this challenge, we introduce cooperative double-IRS-assisted wideband MIMO-OFDM and propose an efficient manifold-based solution. By regarding the power and constant modulus constraints as Riemannian manifolds, we reformulate the non-convex secrecy sum rate maximization as an unconstrained optimization on a product manifold. Building on this formulation, we further develop a product Riemannian gradient descent (PRGD) algorithm with guaranteed stationary convergence. Simulation results demonstrate that the proposed scheme effectively resolves the OFDM coupling issue and achieves significant secrecy rate gains, outperforming single-IRS and distributed multi-IRS benchmarks by 32.0% and 22.3%, respectively.

Cooperative Double IRS aided Secure Communication for MIMO-OFDM Systems

TL;DR

This work addresses secure communication in wideband MIMO-OFDM using cooperative double-IRS by formulating SSR maximization as an unconstrained problem on a product Riemannian manifold. It introduces the Product Riemannian Gradient Descent (PRGD) algorithm, leveraging tangent-space gradients, Armijo step-size control, and retraction to enforce unit-modulus and power constraints, with proven convergence to a stationary point. The approach yields substantial secrecy-rate gains over single-IRS and distributed-multi-IRS benchmarks (e.g., up to 32% and 22.3% gains) and demonstrates robustness to CSI errors and OFDM-wideband deployment considerations. These results indicate practical potential for secure, wideband wireless systems employing cooperative IRS architectures, with clear deployment guidance for IRS placement and scalability across subcarriers.

Abstract

Cooperative double intelligent reflecting surface (double-IRS) has emerged as a promising approach for enhancing physical layer security (PLS) in MIMO systems. However, existing studies are limited to narrowband scenarios and fail to address wideband MIMO-OFDM. In this regime, frequency-flat IRS phases and cascaded IRS links cause severe coupling, rendering narrowband designs inapplicable. To overcome this challenge, we introduce cooperative double-IRS-assisted wideband MIMO-OFDM and propose an efficient manifold-based solution. By regarding the power and constant modulus constraints as Riemannian manifolds, we reformulate the non-convex secrecy sum rate maximization as an unconstrained optimization on a product manifold. Building on this formulation, we further develop a product Riemannian gradient descent (PRGD) algorithm with guaranteed stationary convergence. Simulation results demonstrate that the proposed scheme effectively resolves the OFDM coupling issue and achieves significant secrecy rate gains, outperforming single-IRS and distributed multi-IRS benchmarks by 32.0% and 22.3%, respectively.
Paper Structure (11 sections, 23 equations, 7 figures, 1 algorithm)

This paper contains 11 sections, 23 equations, 7 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. System Model and Problem Formulation
  3. Problem Reformulation and Proposed Method
  4. Problem Reformulation
  5. Proposed PRGD Algorithm
  6. Calculation of the Product Riemannian Gradient
  7. Determination of the Step Size
  8. Update and Retraction
  9. Analysis of Complexity and Convergence
  10. Numerical Results
  11. Conclusion

Figures (7)

  • Figure 1: MIMO-OFDM system illustration with cooperative double-IRS.
  • Figure 2: Analysis of the convergence performance.
  • Figure 3: SSR versus the number of antennas.
  • Figure 4: SSR versus the number of REs.
  • Figure 5: SSR versus the NMSE.
  • ...and 2 more figures