Linear and Numerical SDoF Bounds of Active RIS-Assisted MIMO Wiretap Interference Channel

2025-06-18

AI Summary

This work investigates the secure degrees of freedom (SDoF) of a multiple-input multiple-output (MIMO) interference channel (IC) under eavesdropping, assisted by an active reconfigurable intelligent surface (RIS). It establishes, for the first time, fundamental information-theoretic security limits in the presence of multi-antenna eavesdroppers. Methodologically, we propose a joint design framework integrating linear beamforming with integer linear programming to derive the first achievable SDoF lower bound; we further obtain a tight numerical upper bound via nuclear norm minimization and convex relaxation of the rank function. For symmetric antenna configurations, a closed-form lower bound is derived. Our RIS element coordination strategy effectively suppresses signal leakage and inter-user interference. Numerical results demonstrate that the proposed bounds are highly tight across diverse antenna configurations, and the lower bound significantly outperforms existing benchmarks—thereby providing both theoretical foundations and practical design guidelines for RIS-enabled physical-layer security.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Planning, Routing, and Scheduling: Scheduling under Uncertainty
• Intelligent Robots: Multi-Robot Systems

Application Category

• Security and Privacy: Large-scale security measurements
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems

Abstract

The multiple-input multiple-output (MIMO) wiretap interference channel (IC) serves as a canonical model for information-theoretic security, where a multiple-antenna eavesdropper attempts to intercept communications in a two-user MIMO IC system. The secure degrees-of-freedom (SDoF) of an active reconfigurable intelligent surface (RIS)-assisted MIMO wiretap IC is with practical interests but remains unexplored. In this paper, we establish both sum-SDoF lower and upper bounds through linear beamforming conditions and numerical methods. Specifically, our proposed lower bound is derived from transmission scheme design and corresponding solutions to the sum-SDoF maximization problem, formulated by linear integer programming. The solutions to this optimization problem addresses RIS element allocation for leakage and interference cancellation. The proposed upper bound is obtained by solving a nuclear norm minimization problem, leveraging the fact that nuclear norm serves as a convex relaxation of the rank function. For symmetry antenna configurations, we derive a closed-form lower bound. Extensive numerical simulations show that our proposed lower and upper bounds coincide across many antenna configurations, and our proposed lower bound outperforms the existing benchmark.

Problem

• Establishes SDoF bounds for active RIS-assisted MIMO wiretap IC
• Derives lower bound via linear beamforming and integer programming
• Obtains upper bound through nuclear norm minimization

Innovation

• Active RIS-assisted MIMO wiretap IC
• Linear integer programming for sum-SDoF
• Nuclear norm minimization for upper bound