Secure Beamforming in Multi-User Multi-IRS Millimeter Wave Systems

2025-09-29

AI Summary

This work addresses the secrecy rate maximization problem under user fairness constraints in multi-intelligent reflecting surface (IRS)-aided millimeter-wave multiuser communication systems. To tackle the highly non-convex joint optimization of base station beamforming and continuous IRS phase shifts, we propose a low-complexity algorithm based on the block coordinate descent framework, integrating successive convex approximation, penalty methods, and an efficient discrete-phase mapping scheme—guaranteeing convergence to a Karush–Kuhn–Tucker (KKT) point of the original problem. Unlike conventional semidefinite programming (SDP)-based approaches, the proposed method overcomes computational bottlenecks in large-scale IRS scenarios, maintaining high convergence speed and substantial performance gains even as the number of IRS elements and IRS units increases. Simulation results demonstrate that the proposed scheme significantly outperforms benchmark schemes—including maximum-ratio transmission and IRS-free systems—in terms of worst-user secrecy rate and Jain’s fairness index.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Machine Learning: Optimization
• Multiagent Systems: Mechanism Design

Application Category

• Security and Privacy: Large-scale security measurements
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments

Abstract

We study the secrecy rate maximization problem in a millimeter wave (mmWave) network, consisting of a base station (BS), multiple intelligent reflecting surfaces (IRSs) (or reconfigurable intelligent surfaces (RISs)), multiple users, and a single eavesdropper. To ensure a fair secrecy rate among all the users, we adopt a max-min fairness criterion which results in a mixed integer problem. We first relax discrete IRSs phase shifts to the continuous ones. To cope with the non-convexity of the relaxed optimization problem, we leverage the penalty method and block coordinate descent approach to divide it into two sub-problems, which are solved by successive convex approximation (SCA). Then, we propose a low-complexity mapping algorithm where feasible IRSs phase shifts are obtained. Mathematical evaluation shows the convergence of sub-problems to a Karush-Kuhn-Tucker (KKT) point of the original ones. Furthermore, the convergence guarantee of the overall proposed algorithm and computational complexity are investigated. Finally, simulation results show our proposed algorithm outweighs the conventional solutions based on the semi-definite programming (SDP) in terms of convergence and secrecy rate, especially in a larger number of IRSs and phase shifts where SDP suffers from rank-one approximation. Maximum ratio transmission (MRT) and IRS-free systems are also considered as other benchmarks.

Problem

• Maximizing secrecy rates in multi-user multi-IRS millimeter wave networks
• Solving non-convex optimization with penalty methods and block coordinate descent
• Developing low-complexity algorithms for feasible IRS phase shift mapping

Innovation

• Relaxing discrete IRS phase shifts to continuous variables
• Using penalty method and block coordinate descent for optimization
• Applying successive convex approximation to solve sub-problems