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

Anahid Rafieifar, Hosein Ahmadinejad, S. Mohammad Razavizadeh, Jiguang He

TL;DR

This work tackles the problem of maximizing the minimum secrecy rate in a multi-user mmWave downlink aided by multiple RISs in the presence of a single eavesdropper. It introduces a continuous relaxation of discrete IRS phase shifts combined with a penalty method and a block-coordinate-descent framework, where active and passive beamforming are alternately optimized via successive convex approximation and a low-complexity mapping to feasible IRS phases. The authors provide convergence proofs to KKT points for the subproblems and overall algorithm, analyze computational complexity, and demonstrate through simulations that the proposed method outperforms conventional SDP-based solutions, especially as the number of RISs and phase shifts increases, with MRT and IRS-free benchmarks as references. The proposed approach offers a scalable, practically implementable strategy for secure beamforming in complex RIS-aided mmWave networks, enabling better secrecy rates under realistic discrete-phase constraints and large IRS 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.

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

TL;DR

This work tackles the problem of maximizing the minimum secrecy rate in a multi-user mmWave downlink aided by multiple RISs in the presence of a single eavesdropper. It introduces a continuous relaxation of discrete IRS phase shifts combined with a penalty method and a block-coordinate-descent framework, where active and passive beamforming are alternately optimized via successive convex approximation and a low-complexity mapping to feasible IRS phases. The authors provide convergence proofs to KKT points for the subproblems and overall algorithm, analyze computational complexity, and demonstrate through simulations that the proposed method outperforms conventional SDP-based solutions, especially as the number of RISs and phase shifts increases, with MRT and IRS-free benchmarks as references. The proposed approach offers a scalable, practically implementable strategy for secure beamforming in complex RIS-aided mmWave networks, enabling better secrecy rates under realistic discrete-phase constraints and large IRS 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.

Paper Structure

This paper contains 25 sections, 2 theorems, 51 equations, 7 figures, 1 table, 3 algorithms.

Table of Contents

  1. Introduction
  2. Related Works
  3. Contributions
  4. Organization
  5. System, Channel, and Signal Model
  6. System Model
  7. Channel Model
  8. Signal Model
  9. Problem Formulation
  10. Proposed Algorithm
  11. Active Beamforming Optimization
  12. Passive Beamforming Optimization
  13. Overall Proposed Algorithm Based on BCD for Solving $\mathcal{P}'$
  14. Mapping Algorithm to Acquire Feasible IRSs Phase Shifts
  15. Performance Analysis
  16. ...and 10 more sections

Key Result

Theorem 1

Consider a maximization problem with objective function $f_0(\mathbf{x})$ which is concave, bounded and differentiable, as well as convex and differentiable constraints $f_i(\mathbf{x}) \ge 0, \forall i\in\{1,...,N\}$, the SCA method based on first-order Taylor expansion of $f_i(\mathbf{x}),~\foral

Figures (7)

  • Figure 1: The secure communication system consisting of multiple users and IRSs, a single BS, and one eavesdropper.
  • Figure 2: Our simulation setup consisting of a single BS, multiple IRSs, two users in presence of an eavesdropper.
  • Figure 3: Convergence rate of the Algorithm 3.
  • Figure 4: Minimum secrecy rate versus the transmit power for two cases: $L=2$ and $L=4$, where $M=4$ and $N=16$.
  • Figure 5: Minimum secrecy rate versus the number of BS antennas for two cases: $L=2$ and $L=4$.
  • ...and 2 more figures

Theorems & Definitions (4)

  • Theorem 1
  • proof
  • Theorem 2
  • proof