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Resource Allocation for Secure IRS-assisted Multiuser MISO Systems
Dongfang Xu, Xianghao Yu, Yan Sun, Derrick Wing Kwan Ng, Robert Schober
TL;DR
Secure IRS-assisted multiuser MISO communication requires jointly allocating IRS phases, information beamforming, and artificial noise to protect against eavesdroppers. The paper develops an alternating optimization framework for this non-convex design and reports substantially higher system sum secrecy rates than two baseline schemes.
Problem
Efficient resource allocation for maximizing sum secrecy rate in multiuser IRS-assisted systems with artificial noise and unit-modulus IRS constraints remains open.
Method
The paper jointly optimizes IRS phase shifts, BS beamforming, and artificial-noise covariance using alternating optimization, successive convex approximation, semidefinite relaxation, and manifold optimization.
Results
The proposed scheme substantially improves system sum secrecy rate over two baselines that respectively use random IRS phases or omit artificial noise.
Takeaways & Limitations
Joint IRS, beamforming, and artificial-noise design can enhance secure communication performance in IRS-assisted multiuser MISO systems.
Abstract
from arXiv · showhide
In this paper, we study resource allocation design for secure communication in intelligent reflecting surface (IRS)-assisted multiuser multiple-input single-output (MISO) communication systems. To enhance physical layer security, artificial noise (AN) is transmitted from the base station (BS) to deliberately impair the channel of an eavesdropper. In particular, we jointly optimize the phase shift matrix at the IRS and the beamforming vectors and AN covariance matrix at the BS for maximization of the system sum secrecy rate. To handle the resulting non-convex optimization problem, we develop an efficient suboptimal algorithm based on alternating optimization, successive convex approximation, semidefinite relaxation, and manifold optimization. Our simulation results reveal that the proposed scheme substantially improves the system sum secrecy rate compared to two baseline schemes.
I. INTRODUCTION
The paper identifies an open problem in secure IRS-assisted multiuser systems: jointly designing IRS phases, beamforming, and artificial noise under unit-modulus constraints to maximize sum secrecy rate.
- I. INTRODUCTION: IRSs provide programmable, reconfigurable, and power-efficient propagation control for beyond-5G communication systems.Their passive reflecting elements can improve coverage while requiring little operational power.
- I. INTRODUCTION: Prior secure IRS-assisted studies focused on single-user secrecy or relaxed IRS constraints, leaving multiuser sum-secrecy optimization with artificial noise unresolved.Approximating the unit-modulus constraint may simplify optimization but lead to performance loss.
- I. INTRODUCTION: The paper jointly optimizes the IRS phase shift matrix, downlink beamforming vectors, and BS artificial-noise covariance matrix to maximize system sum secrecy rate.Artificial noise is used to impair the eavesdropper while the other variables are optimized jointly.
A. Notations
This section establishes notation for matrices, vectors, complex spaces, matrix operations, distributions, and gradients used throughout the paper.
- A. Notations: Boldface capitals and lowercase letters denote matrices and vectors, while R, C, and H identify real, complex, and Hermitian matrix spaces.The notation also defines identity matrices, transposes, conjugate transposes, rank, trace, and diagonal matrices.
- A. Notations: The notation defines Hadamard products, real-part extraction, statistical expectation, complex Gaussian distributions, and the positive-part operator.It also introduces symbols for gradients and distributional definitions.
B. IRS-assisted Multiuser Wireless Communication System
The system consists of a multi-antenna BS, single-antenna users and eavesdropper, and a programmable IRS that mediates communication when direct links are blocked.
- B. IRS-assisted Multiuser Wireless Communication System: The considered system contains a BS, an eavesdropper, an IRS, and multiple desired users; Figure 1 illustrates one eavesdropper and K = 3 users.The direct BS-to-user and BS-to-eavesdropper links are blocked by a building.
- B. IRS-assisted Multiuser Wireless Communication System: The BS has N_T > 1 antennas, users and eavesdropper have one antenna, and the IRS has M programmable phase shifters.A controller programs and reconfigures the passive IRS.
- B. IRS-assisted Multiuser Wireless Communication System: The model assumes perfect whole-system channel state information is available at the BS for resource allocation.The direct links are unavailable because of unfavorable propagation conditions such as building blockage.
- B. IRS-assisted Multiuser Wireless Communication System: The transmitted signal combines K information-bearing signals with artificial noise generated as a zero-mean complex Gaussian vector with covariance matrix Z ⪰ 0.Each user signal uses beamforming vector w_k, while artificial noise is transmitted to impair the eavesdropper.
- B. IRS-assisted Multiuser Wireless Communication System: Users and the eavesdropper receive signals through IRS-reflected channels involving their respective IRS channel vectors and the IRS phase-shift matrix.The reflected links use channel vectors g_k and l for users and eavesdropper, respectively.
III. OPTIMIZATION PROBLEM FORMULATION
The paper formulates resource allocation as maximizing system sum secrecy rate over the users’ beamforming vectors, artificial-noise covariance, and IRS phase-shift matrix.
- III. OPTIMIZATION PROBLEM FORMULATION: The reported results are a theoretical performance benchmark because practical systems may not provide perfect channel state information at the BS.The paper explicitly notes that perfect CSI may be unavailable in practice.
A. Achievable Rate and Secrecy Rate
The paper models user achievable rates and eavesdropper capabilities to define secrecy rates for secure multiuser communication.
- A. Achievable Rate and Secrecy Rate: User k’s achievable rate is defined as R_k = log2(1 + Γ_k).
- A. Achievable Rate and Secrecy Rate: The eavesdropper is assumed capable of canceling all multiuser interference before decoding user k’s message.
- A. Achievable Rate and Secrecy Rate: The achievable secrecy rate between the BS and user k is defined from the legitimate-user and eavesdropper rates.
B. Optimization Problem Formulation
The optimization jointly selects BS beamforming, artificial-noise covariance, and IRS phase shifts to maximize system sum secrecy rate under transmit-power and IRS constraints.
- B. Optimization Problem Formulation: The objective maximizes system sum secrecy rate by optimizing w_k, Z, and Φ.
- B. Optimization Problem Formulation: Constraint C1 limits the BS transmit power to P_max, while the positive-part operator does not affect the optimum.
- B. Optimization Problem Formulation: Because coupled variables and the IRS unit-modulus constraint make the problem globally difficult, the authors develop an alternating-optimization suboptimal algorithm.
IV. SOLUTION OF THE PROBLEM
The solution alternates between BS resource variables and IRS phases, using SCA and SDR for beamforming and AN and manifold optimization for the IRS.
- IV. SOLUTION OF THE PROBLEM: If user k’s secrecy rate is non-positive, the algorithm turns off that user and reallocates its power to other users.
- IV. SOLUTION OF THE PROBLEM: The reformulation enforces unit-modulus IRS elements, positive semidefinite AN and beamforming matrices, and rank constraints linking W_k to w_k w_k^H.
- IV. SOLUTION OF THE PROBLEM: Alternating optimization iteratively updates {W, Z} with u fixed, then updates u with W and Z fixed.
- IV. SOLUTION OF THE PROBLEM: For fixed IRS phases, the method applies successive convex approximation and semidefinite relaxation; for fixed BS variables, it applies manifold optimization.
A. SCA and SDR
The SCA-SDR procedure constructs convex approximations, relaxes rank constraints, and iteratively tightens an upper bound until convergence to a locally optimal solution.
- A. SCA and SDR: SCA constructs global underestimators of G1 and G2 at feasible points, producing an upper-bound optimization problem.
- A. SCA and SDR: SDR removes the rank-one constraint so the remaining relaxed problem can be solved efficiently with convex optimization software.
- A. SCA and SDR: Algorithm 1 repeatedly solves the approximated problem, updates W and Z, and stops when convergence is reached.
- A. SCA and SDR: If P_max > 0, an optimal beamforming matrix satisfying Rank(W_k) ≤ 1 can always be obtained.
- A. SCA and SDR: The algorithm’s objective is non-increasing across iterations and is guaranteed to converge to a locally optimal solution.
B. Oblique Manifold Optimization
The unit-modulus IRS constraint defines an oblique manifold, so the paper applies Riemannian optimization to update the IRS phases while preserving feasibility. An alternating scheme combines this manifold update with beamforming and AN optimization and is guaranteed to converge to a suboptimal solution.
- B. Oblique Manifold Optimization: Direct manifold optimization handles the non-convex unit-modulus constraint and guarantees convergence to a suboptimal solution.Unlike semidefinite relaxation approaches, the method exploits the oblique-manifold structure directly.
- B. Oblique Manifold Optimization: The oblique manifold automatically satisfies constraint C2 during optimization of the IRS phase vector.The paper characterizes C2 as the unit-modulus condition on the vector entries.
- B. Oblique Manifold Optimization: Riemannian gradients are projected onto the tangent space, while vector transport transfers search directions between tangent spaces during conjugate-gradient updates.Retraction then maps the updated tangent-space vector back onto the oblique manifold.
- B. Oblique Manifold Optimization: Algorithm 2 iteratively selects a step size, retracts the search direction, updates the Riemannian gradient, and computes conjugate search directions.The algorithm uses Polak–Ribiere updates within the oblique-manifold optimization procedure.
- B. Oblique Manifold Optimization: The alternating algorithm solves the beamforming and AN subproblem with Algorithm 1, updates the IRS phases with Algorithm 2, and stops when the objective change falls below tolerance.The final solution consists of the resulting W, Z, and u iterates.
V. SIMULATION RESULTS
Simulations show that the proposed resource-allocation scheme outperforms two baselines, while secrecy rate depends on network geometry and increases with users. Increasing IRS phase shifters provides greater gains than increasing BS antennas in the reported cases.
- Maximum transmit power: The proposed scheme outperforms both baseline schemes in average system sum secrecy rate across the simulated maximum-transmit-power settings.Jointly optimizing the IRS phase shifts, beamforming vectors, and AN covariance improves propagation toward users while impairing the eavesdropper; the baselines use random IRS phases or omit AN.
- Maximum transmit power: IRS location must be chosen carefully because network geometry significantly affects the system sum secrecy rate.
- Number of users: Average system sum secrecy rates increase monotonically with the number of legitimate users because all schemes exploit multiuser diversity.
- Number of users: Adding IRS phase shifters yields a larger performance gain than adding BS antennas in the two additional parameter cases.Case 2 uses NT = 6 and M = 10, whereas Case 1 uses NT = 10 and M = 6; extra phase shifters provide power and beamforming gains.
VI. CONCLUSION
The optimization analysis establishes convexity and strong duality for a beamforming subproblem, then uses KKT conditions to show that an optimal beamforming matrix is rank one under the stated positive-power and secrecy conditions.
- Beamforming optimization: If the relevant dual condition is nonpositive, the algorithm stops transmitting information to user k and reallocates the corresponding power to other users.
- Beamforming optimization: The beamforming subproblem is jointly convex, satisfies Slater’s condition, and therefore has strong duality.
- Rank-one optimality: The rank-one proof constructs a unit-norm eigenvector associated with the maximum eigenvalue of matrix Δ.