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Intelligent Reflecting Surface Assisted Secrecy Communication: Is Artificial Noise Helpful or Not?
Xinrong Guan, Qingqing Wu, Rui Zhang
TL;DR
The paper investigates whether AN is still useful when IRS reflect beamforming assists secure transmission against multiple eavesdroppers. It formulates a joint beamforming problem and solves it sub-optimally by alternating optimization, finding that AN remains beneficial and can outperform IRS without AN as eavesdroppers increase.
Problem
Whether AN remains helpful in IRS-assisted secrecy communication is open because prior IRS beamforming studies did not include transmit jamming.
Method
The paper jointly optimizes transmit beamforming with AN and IRS reflect beamforming using an alternating optimization algorithm for the non-convex coupled problem.
Results
AN improves secrecy rate with IRS, especially at high transmit power or with more eavesdroppers; IRS without AN can underperform AN without IRS as eavesdroppers increase.
Takeaways & Limitations
IRS reflect beamforming does not eliminate the usefulness of AN, particularly when available transmit spatial degrees of freedom are insufficient against many eavesdroppers.
Abstract
from arXiv · showhide
In this letter, we investigate whether the use of artificial noise (AN) is helpful to enhance the secrecy rate of an intelligent reflecting surface (IRS) assisted wireless communication system. Specifically, an IRS is deployed nearby a single-antenna receiver to assist in the transmission from a multi-antenna transmitter, in the presence of multiple single-antenna eavesdroppers. Aiming to maximize the achievable secrecy rate, a design problem for jointly optimizing transmit beamforming with AN or jamming and IRS reflect beamforming is formulated, which is however difficult to solve due to its non-convexity and coupled variables. We thus propose an efficient algorithm based on alternating optimization to solve the problem sub-optimally. Simulation results show that incorporating AN in transmit beamforming is beneficial under the new setup with IRS reflect beamforming. In particular, it is unveiled that the IRS-aided design without AN even performs worse than the AN-aided design without IRS as the number of eavesdroppers near the IRS increases.
I. INTRODUCTION
The paper asks whether artificial noise remains useful when IRS reflect beamforming adds spatial degrees of freedom to secrecy communication. It jointly considers transmit beamforming with AN and IRS reflect beamforming, finding AN especially helpful as transmit power or eavesdropper count increases.
- IRS motivation: IRS adaptively controls reflected signal strength and direction through passive element-wise amplitude or phase adjustments.Its low-power operation comes from reflecting signals without amplification.
- Security motivation: Artificial noise is particularly useful when eavesdroppers outnumber transmit antennas, because transmit beamforming lacks enough spatial degrees of freedom to null all eavesdropper channels.AN supplements beamforming by degrading eavesdropper reception.
- Open question: Prior IRS secrecy studies jointly designed active transmit and passive reflect beamforming but did not consider transmit jamming with AN.The usefulness of AN in the IRS-assisted setup therefore remained open.
- Paper objective: The paper maximizes secrecy rate through joint transmit beamforming with AN and IRS reflect beamforming to determine when AN remains necessary.It examines the impact of IRS-provided degrees of freedom and the conditions under which AN is most helpful.
- Headline findings: Simulations show AN improves secrecy rate with IRS, especially at high transmit power or with more eavesdroppers.With more reflecting elements, AN’s gain stays roughly constant when eavesdroppers are far from the IRS but decreases when they are nearby.
A. System Model
The system has a multi-antenna transmitter, single-antenna legitimate receiver and eavesdroppers, and an IRS near the legitimate receiver. Alice sends information and optional AN under a power budget, while the IRS applies controllable phase shifts.
- Network configuration: Alice communicates confidentially with single-antenna Bob through an IRS deployed nearby, while facing K single-antenna eavesdroppers.The transmitter and IRS have M antennas and N reflecting elements, respectively.
- IRS model: The IRS reflection matrix uses element phase shifts θ_n ∈ [0, 2π) to control the combined incident signal.Each of the N reflecting elements applies its own phase shift.
- Channel assumptions: The model assumes quasi-static flat fading and perfect channel state information at Alice and the IRS for joint beamforming and jamming design.The assumption characterizes the performance limit of the considered system.
- Transmit model: Alice transmits an independent information signal and an independent jamming or AN signal using beamforming vectors f1 and f2.The transmitted signal is represented as x = f1s + f2a.
- Power and reception: The information and AN beamformers jointly obey Alice’s maximum transmit-power constraint.The received signal at Bob or Eve combines the direct and IRS-assisted components with additive noise.
B. Problem Formulation
The paper formulates secrecy-rate maximization over Alice’s information and jamming beamformers and the IRS reflect beamformer under a total power constraint. Non-concavity and variable coupling motivate an alternating optimization solution.
- Optimization objective: The objective is to maximize achievable secrecy rate by jointly designing Alice’s transmit beamforming and jamming and Rose’s reflect beamforming.The design is subject to Alice’s total transmit-power constraint.
- Rate model: Bob’s and Eve’s achievable rates are defined as log(1 + γ_b) and log(1 + γ_ek), measured in bits/second/Hertz.The logarithm is base 2.
- Non-convexity: The problem is difficult because its objective is non-concave and its optimization variables are coupled.Fixing either the transmit variables or IRS variable makes the resulting problem more tractable.
- Solution strategy: An alternating optimization algorithm iteratively optimizes the transmit variables and IRS reflect beamformer with the other fixed until convergence.The method solves the original problem sub-optimally.
A. Optimizing f1 and f2 for Given v
For fixed IRS reflect beamforming, the transmit and AN design is lifted into matrix variables, relaxed through SDR, and solved by alternating optimization with auxiliary variables.
- Effective channels: The effective Alice-to-Bob and Alice-to-Eve channels combine the direct and IRS-reflected channels.These effective channels are used to reformulate the transmit-design problem.
- Semidefinite relaxation: The rank-one beamforming matrices F1 = f1f1^H and F2 = f2f2^H are relaxed using semidefinite relaxation because rank constraints are non-convex.The relaxation produces a convexified formulation, though rank-one recovery is not guaranteed.
- Objective reformulation: A supporting lemma transforms logarithmic rate terms using auxiliary variables whose tight bound occurs at t = 1/x.This enables a tractable reformulation of the secrecy-rate objective.
- Convex subproblems: The reformulated problem is convex with respect to either the matrix variables or auxiliary variables when the other block is fixed.Alternating optimization can therefore update the two blocks iteratively.
- Algorithm: The algorithm alternately updates transmit matrices and auxiliary variables until the objective converges, then recovers f1 and f2.Rank-one matrices yield direct beamformers; otherwise Gaussian randomization provides an approximate recovery.
B. Optimizing v for Given f1 and f2
For fixed transmit beamforming, the IRS reflect beamforming subproblem is transformed into tractable convex subproblems and solved iteratively, followed by recovery of the reflection coefficients.
- Convex reformulation: For given f1 and f2, the IRS optimization is reduced using Lemma 1 and semidefinite relaxation under unit-modulus reflection constraints.The relaxed matrix ˜V is constrained to be positive semidefinite with unit diagonal entries.
- Alternating solution: The resulting problem is convex in either ˜V or (zb, zek) when the other variables are fixed.This motivates alternating optimization between the reflection matrix and auxiliary variables.
- Alternating solution: The relaxed IRS problem is approximately solved by alternately optimizing ˜V and (zb, zek), with the latter having a closed-form optimum for fixed ˜V.The optimal ˜V is then obtained through a procedure similar to (P1.5).
- Coefficient recovery: An eigenvalue decomposition with Gaussian randomization extracts ˜v from ˜V before producing the IRS reflection coefficients.The recovered coefficients satisfy the unit-modulus constraints through the phase-based construction in (16).
C. Overall Algorithm
The overall iterative procedure uses a small threshold and a maximum iteration count to determine when the alternating optimization terminates.
- C. Overall Algorithm: Algorithm 2 terminates when the fractional decrease in the objective is below ϵ or the iteration count reaches L.These parameters control convergence stopping and the maximum computational effort.
IV. SIMULATION RESULTS
Simulations compare secrecy-rate designs across transmit power, eavesdropper count, IRS size, and two eavesdropper placements. AN generally improves secrecy, with especially strong benefits when many eavesdroppers are near the IRS.
- Simulation setup: The simulations compare AN/IRS, AN/No-IRS, No-AN/IRS, and No-AN/No-IRS designs under two eavesdropper placements.Setup (a) places local eavesdroppers near Bob and the IRS, while Setup (b) places remote eavesdroppers on the opposite side of Alice.
- Transmit power: As maximum transmit power increases, AN-aided designs outperform corresponding designs without AN with and without the IRS.The comparison holds in both eavesdropper placements.
- Transmit power: Increasing transmit power alone becomes inefficient at high power because (1 + γb)/(1 + max_k γek) converges to a constant.The convergence motivates incorporating AN for secrecy-rate improvement.
- Number of eavesdroppers: When K = 1, AN and No-AN secrecy rates are almost identical because transmit beamforming has sufficient spatial DoF to suppress eavesdropper signals.As K increases, insufficient nulling DoF make allocating power to jamming more beneficial.
- Number of eavesdroppers: For Setup (a), AN/No-IRS outperforms No-AN/IRS when K ≥6, showing that AN can be more effective than IRS without AN near the IRS.With Bob and eavesdroppers close to the IRS, IRS-provided DoF may be insufficient to prevent information leakage.
- IRS size: With more IRS reflecting elements, AN needs fewer elements to reach the same secrecy rate as No-AN, while its gain decreases in Setup (a) and remains nearly constant in Setup (b).In Setup (a), larger IRS DoF can degrade eavesdropper reception; in Setup (b), remote eavesdroppers are outside the IRS coverage.
- Eavesdropper placement: Setup (b) always achieves higher IRS-aided secrecy rates than Setup (a), regardless of whether AN is used.Local eavesdroppers in Setup (a) share the IRS-covered region with Bob, making their reception harder to degrade.
V. CONCLUSION
The study finds that artificial noise remains necessary in IRS-assisted secrecy communication, especially as the number of eavesdroppers increases. An alternating-optimization algorithm addresses the joint transmit/reflect beamforming design.
- The authors formulate a secrecy-rate maximization problem jointly designing transmit beamforming, artificial noise, and IRS reflect beamforming.
- An alternating-optimization algorithm is developed to solve the non-convex joint design problem efficiently.
- Simulations verify that artificial noise remains necessary even when an IRS is deployed.
- Transmit and reflect beamforming alone generally cannot handle increasing eavesdropper numbers because of insufficient spatial degrees of freedom.
- Artificial noise improves the secrecy rate in challenging scenarios with many eavesdroppers.