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Intelligent Reflecting Surfaces Assisted Secure Transmission Without Eavesdropper's CSI
Hui-Ming Wang, Jiale Bai, Limeng Dong
TL;DR
Earlier IRS-assisted secrecy schemes assume Eve’s CSI is known, while this paper studies transmission without it. The authors jointly optimize beamforming and jamming, and report that security remains achievable with higher Bob QoS thresholds and more IRS elements, with OM outperforming MM.
Problem
Earlier IRS secrecy schemes - assume Eve’s CSI is perfectly known, although Eve is usually hidden and passive.
Source: §I · p. 1Method
The scheme minimizes confidential-signal power to meet Bob’s QoS, uses residual power for artificial noise, and applies OM and MM algorithms to the non-convex design.
Source: §I · p. 1Results
Security can still be guaranteed without Eve’s CSI by increasing Bob’s QoS threshold and IRS element count; OM achieves a higher secrecy rate than MM.
Source: §I · p. 1, §IV · p. 4Takeaways & Limitations
The simulations report that the joint beamforming-and-jamming scheme improves security in an IRS-assisted MISO system without Eve’s CSI.
Source: §V · p. 4
Abstract
from arXiv · showhide
In this letter, improving the security of an intelligent reflecting surface (IRS) assisted multiple-input single-output (MISO) communication system is studied. Different from the ideal assumption in existing literatures that full eavesdropper's (Eve's) channel state information (CSI) is available, we consider a more practical scenario without Eve's CSI. To enhance the security of this system given a total transmit power at transmitter (Alice), we propose a joint beamforming and jamming approach, in which a minimum transmit power is firstly optimized at Alice so as to meet the quality of service (QoS) at legitimate user (Bob), and then artificial noise (AN) is emitted to jam the eavesdropper by using the residual power at Alice. Two efficient algorithms exploiting oblique manifold (OM) and minorizationmaximization (MM) algorithms, respectively, are developed for solving the resulting non-convex optimization problem. Simulation results have been provided to validate the performance and convergence of the proposed algorithms.
I. INTRODUCTION
The paper addresses the practical gap that earlier IRS secrecy schemes - assume Eve’s CSI is known. It proposes joint beamforming and jamming without Eve’s CSI and reports security gains under higher Bob QoS thresholds and more IRS elements.
I. INTRODUCTION
- An IRS is a planar surface of low-cost passive elements whose independently adjusted phases collaboratively provide passive beamforming.The paper identifies IRS as a candidate technology for future wireless networks.Source: §I · p. 1
- Earlier IRS secrecy studies - assume Eve’s CSI is perfectly known, although Eve is usually hidden and passive.The paper identifies this assumption as impractical because Eve does not actively exchange CSI with Alice.Source: §I · p. 1
- The proposed scheme minimizes confidential-signal power to meet Bob’s QoS, then uses all residual power for artificial noise to jam Eve.The scheme is framed for a total transmit-power budget at Alice.Source: §I · p. 1
- The paper develops an oblique manifold algorithm and also investigates a minorization-maximization algorithm for the non-convex optimization problem.Both are proposed approaches to solving the optimization problem.Source: §I · p. 1
- Security can still be guaranteed without Eve’s CSI by increasing Bob’s QoS threshold and the number of IRS reflecting elements; OM performs better than MM.These are the paper’s stated comparisons with the full-CSI case and between the proposed algorithms.Source: §I · p. 1
II. SYSTEM MODEL
The system model considers Alice transmitting to Bob in the presence of Eve, with an IRS assisting the communication. Alice has multiple antennas, while Bob and Eve each have one antenna; the IRS has L reflecting elements.
II. SYSTEM MODEL
- The modeled system includes Alice, Bob, Eve, and an IRS; Alice has Nt antennas, Bob and Eve each have one antenna, and the IRS has L reflecting elements.The channel model is quasi-static and flat-fading.Source: §II · p. 1
- The IRS phase shifts are represented by the diagonal matrix Q, whose entries are unit-magnitude phase coefficients.The system figure depicts the IRS-assisted MISO communication system.Source: §II · p. 1, Figure 1 · p. 2
- Alice’s total transmit power is split between signal power PT and artificial-noise power PJ.The stated budget is PA = PT + PJ.Source: §II · p. 2
III. JOINT BEAMFORMING AND JAMMING SCHEME
Without Eve’s CSI, the scheme uses artificial noise orthogonal to Bob’s equivalent channel and allocates only the power needed to meet Bob’s QoS to the confidential signal. The resulting design optimizes Alice’s beamformer and IRS phase shifts under a non-convex unit-modulus constraint.
III. JOINT BEAMFORMING AND JAMMING SCHEME
- The artificial noise is projected onto the null space of Bob’s equivalent channel, so it is directed at Eve without being aligned with Bob’s channel.The method is motivated by the unknown Eve channels, which prevent directly maximizing secrecy rate.Source: §III · p. 2
- Alice’s confidential signal uses minimum power to meet Bob’s QoS, leaving the largest possible residual budget for artificial noise to jam Eve.The target QoS is denoted γ, and residual AN power is PJ = PA − PT.Source: §III · p. 2
- The design minimizes Alice’s transmit-beamformer power by optimizing the beamformer w and IRS phase matrix Q subject to Bob’s QoS constraint.Because the IRS changes signal phase only, each diagonal coefficient of Q must have unit modulus.Source: §III · p. 2
- For a fixed IRS phase matrix, maximum-ratio transmission is optimal for Alice’s beamformer, reducing the design to a phase-only optimization.The equivalent formulation maximizes the norm of Bob’s equivalent channel, but remains non-convex.Source: §III · p. 2
A. Oblique Manifold Algorithm
The Oblique Manifold (OM) algorithm solves P3 by optimizing phase variables on a unit-modulus manifold. Its iterations use Riemannian conjugate-gradient steps, transport, and retraction, and converge to a critical point.
A. Oblique Manifold Algorithm
- OM handles the unit-modulus constraint by optimizing the phase vector on a Riemannian submanifold of C^L.The algorithm seeks a suboptimal solution of P3.Source: A. Oblique Manifold Algorithm · p. 2
- Each iteration projects the Euclidean gradient onto the tangent space, then uses conjugate-gradient search with transport and retraction.The Polak-Ribiere parameter sets the conjugate search direction; retraction returns the updated point to the manifold.Source: A. Oblique Manifold Algorithm · pp. 2–3
- The OM algorithm is guaranteed to converge to a critical point of P3, where the Riemannian gradient of the objective is zero.The conjugate-gradient parameter α_i is chosen by the Polak-Ribiere rule.Source: A. Oblique Manifold Algorithm · p. 3
B. Minorization-Maximization Algorithm
The MM algorithm solves P3 by iteratively minimizing an upper bound of its objective over feasible phase vectors. The update aligns each phase with the corresponding entry of β, and iteration yields a local optimum.
B. Minorization-Maximization Algorithm
- MM constructs an approximate upper bound of the objective and iteratively minimizes it subject to the constraints.The converged point is a local optimum.Source: B. Minorization-Maximization Algorithm · p. 3
- For a feasible current point q^k, the next iterate is bounded using β = (λ_max(A)I − A)q^k + b.Dropping the constant term gives the P5 approximation.Source: B. Minorization-Maximization Algorithm · p. 3
- The P5 optimum aligns each q_i phase with β_i, giving a closed-form update.The feasible point is updated iteratively until the objective converges, yielding a local optimum for P3.Source: B. Minorization-Maximization Algorithm · p. 3
C. AN Signalling Strategy
After solving P1, the scheme uses Alice's residual transmit power for artificial-noise signaling in Bob's channel null space. Because Eve's CSI is unknown, the AN is isotropically allocated across that space.
C. AN Signalling Strategy
- After solving P1, the residual power P_J = P_A − P_T* is used for AN signaling in the null space of Bob's channel.The rank-1 matrix H_B has a null space of dimension N_t − 1.Source: C. AN Signalling Strategy · p. 3
- With Eve's channel CSI unknown, the scheme uses isotropic AN with equal power across each dimension of null(H_B).The resulting covariance uses the zero-eigenvalue eigenvectors of H_B; substituting it with the beamformer and Q gives the scheme's actual secrecy rate.Source: C. AN Signalling Strategy · p. 3
IV. SIMULATION RESULT
The simulations show that the proposed scheme can guarantee security without Eve’s CSI, with performance shaped by the QoS threshold, IRS size, and power allocation. Both algorithms converge, but MM requires fewer iterations than OM.
IV. SIMULATION RESULT
- Both algorithms converge, but MM requires significantly fewer iterations than OM; larger L increases iteration needs, and OM consequently takes more computational time.The convergence plot is under Nt = 5 and γ = 10 dB.Source: Figure 2 · p. 4, §IV · p. 4
- Without Eve’s CSI, the scheme still guarantees security, although secrecy rate is lower than with full CSI; increasing IRS elements and Bob’s QoS threshold can improve security.The figure reports secrecy rate under Nt = 5, averaged over 1000 randomly generated channels.Source: Figure 3 · p. 4, §IV · p. 4
- IRS raises secrecy rate versus no IRS, and OM exceeds MM because OM needs less minimum transmit power, leaving more residual power for artificial noise.With fixed total power, raising γ can initially improve secrecy rate, but excessive γ leaves too little power for AN and can make P1 infeasible.Source: §IV · p. 4
- The γ = 20 dB and γ = 25 dB curves cross: at small L, 25 dB leaves less power for AN, while sufficient reflection power lets it outperform 20 dB.As L grows, the IRS supplies more reflected power, allowing Alice to allocate more power to AN while increasing the legitimate information rate.Source: §IV · p. 4
V. CONCLUSION
The conclusion presents a joint beamforming-and-jamming scheme for IRS-assisted MISO security without Eve’s CSI, with OM and MM algorithms and simulations validating convergence and improved security.
V. CONCLUSION
- The proposed joint beamforming and jamming scheme targets improved physical-layer security in an IRS-assisted MISO system without Eve’s CSI.The scheme jointly optimizes Alice’s transmit beamforming and the IRS phase shifts.Source: §V · p. 4
- OM and MM algorithms are proposed to jointly optimize Alice’s transmit beamforming and IRS phase shifts.Source: §V · p. 4
- Simulations validate algorithm convergence and show that the joint scheme improves security.Source: §V · p. 4