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Enabling Secure Wireless Communications via Intelligent Reflecting Surfaces
Xianghao Yu, Dongfang Xu, Robert Schober
TL;DR
The paper addresses secure wireless communication with an IRS-assisted system facing an eavesdropper. It jointly optimizes transmitter beamforming and IRS phase shifts using BCD- and MM-based algorithms, and reports improved secrecy and energy efficiency, especially with large-scale IRSs.
Problem
Existing secure-wireless methods can require costly helpers or additional power, motivating cost-effective and energy-efficient IRS-assisted physical-layer security.
Method
The paper jointly optimizes the transmitter beamformer and programmable IRS phase shifts using element-wise BCD and AO-MM algorithms for non-convex secrecy-rate optimization.
Results
Simulations show significant secrecy-rate gains from IRS deployment, while element-wise BCD suits small IRSs and AO-MM suits large IRSs.
Takeaways & Limitations
Large-scale IRS deployment is reported as more beneficial than enlarging the transmitter antenna array for secrecy-rate improvement and energy efficiency.
Abstract
from arXiv · showhide
In this paper, we propose to utilize intelligent reflecting surfaces (IRSs) for enhancing the physical layer security of wireless communications systems. In particular, an IRS-assisted secure wireless system is considered, where a multi-antenna transmitter communicates with a single-antenna receiver in the presence of an eavesdropper. To maximize the secrecy rate, both the beamformer at the transmitter and the IRS phase shifts are jointly optimized. Based on the block coordinate descent (BCD) and minorization maximization (MM) techniques, two efficient algorithms are developed to solve the resulting non-convex optimization problem for small- and large-scale IRSs, respectively. Simulation results show that IRSs can significantly improve physical layer security if the proposed algorithms are employed. Furthermore, we reveal that deploying large-scale IRSs is more efficient than enlarging the antenna array size of the transmitter for both boosting the secrecy rate and enhancing the energy efficiency.
I. INTRODUCTION
Existing secure-wireless approaches can incur high helper costs or extra power consumption. This paper studies IRS-assisted security by jointly optimizing transmit beamforming and IRS phase shifts under a non-convex formulation.
- Motivation: Existing cooperative relaying, artificial-noise beamforming, and cooperative-jamming approaches can impose excessive cost or additional power consumption.These limitations motivate a cost-effective and energy-efficient paradigm for secure wireless systems.
- Motivation: IRSs can be coated onto existing infrastructure, reducing implementation cost and complexity while consuming no power as passive devices.The supplied passage is truncated after describing the IRS power advantage.
- System and contribution: The considered system uses a multi-antenna transmitter, single-antenna legitimate receiver, single-antenna eavesdropper, and programmable IRS phase shifters.The model assumes quasi-static flat-fading channels and perfect CSI at the transmitter and IRS.
- System and contribution: The paper maximizes secrecy rate by jointly optimizing the transmitter beamformer and IRS phase shifts, yielding a non-convex optimization problem.The formulation constrains the IRS phase-shift entries to unit modulus and limits transmit power by P.
- System and contribution: Two BCD- and MM-based algorithms are proposed, with one suited to small-scale IRSs and the other advantageous for large-scale IRSs.The paper claims locally optimal solutions for both the beamformer and phase shifts.
III. DESIGN OF SECURE IRS-ASSISTED WIRELESS SYSTEMS
BCD solves the non-convex problem by optimizing different variable blocks iteratively while holding the remaining blocks fixed, providing an efficient but generally sub-optimal approach.
- BCD methodology: BCD alternately optimizes different subsets of variables while fixing the other subsets in each iteration.For this paper, BCD is used as the main methodology for solving P1 efficiently.
A. Transmit Beamformer Design
With the IRS phase shifts fixed, the beamformer is optimized through a generalized eigenvalue formulation, while IRS phase shifts provide an additional degree of freedom for shaping effective channels.
- Transmit Beamformer Design: For a fixed IRS phase-shift matrix, the beamformer design is formulated as a separate optimization problem.The beamformer update is developed within the BCD procedure.
- Transmit Beamformer Design: The optimal beamformer allocates all transmit power and is obtained from a generalized eigenvalue problem.The resulting solution is given in the paper’s Lemma 1.
- Transmit Beamformer Design: The beamformer is designed to reduce alignment with the effective eavesdropping channel while aligning with the effective legitimate-receiver channel.The IRS adds a degree of freedom for shaping these effective channels through its phase shifts.
- Transmit Beamformer Design: The paper notes that no general approach is available for optimally designing the IRS phase-shift matrix.It therefore proposes two approaches for optimizing the phase shifts within BCD.
B. Element-Wise BCD
Element-wise BCD treats each IRS phase shift as a separate block and uses closed-form block updates, guaranteeing monotonic improvement and convergence to a locally optimal solution.
- Element-Wise BCD: Element-wise BCD optimizes each phase shift θk as one block while the other phase shifts and beamformer are fixed.The method is summarized in Algorithm 1.
- Element-Wise BCD: Given the beamformer and remaining phase shifts, the method computes an optimal update for θk.The update is presented in Lemma 2 and uses the paper’s closed-form expression.
- Convergence: The objective function monotonically increases because each BCD block uses a closed-form globally optimal solution.The objective is also upper bounded by the point-to-point MISO channel capacity.
- Convergence: Algorithm 1 converges to a locally optimal solution of P1.Its convergence follows from monotonic objective improvement together with the upper bound.
- Complexity: The M + 1 block structure causes slow convergence when the IRS has many reflecting elements.This scalability issue motivates a different large-scale-IRS algorithm.
C. Alternating Optimization With MM
The paper replaces element-wise phase updates with a two-block alternating optimization scheme and uses MM to update all IRS phase shifts in parallel. The resulting AO-MM algorithm monotonically increases the objective and converges to a local optimum, while trading fewer block updates for potentially more iterations.
- AO-MM formulation: The phase shift matrix Φ is treated as one BCD block, reducing the algorithm to two-block alternating optimization.The two blocks are the transmitter beamformer and the entire IRS phase shift matrix.
- MM phase-shift update: The phase-shift optimization is reformulated under unit-modulus constraints, with all phase shifts updated in parallel during each AO iteration.The phase vector satisfies |v_k| = 1 for k ∈ {1, 2, · · ·, M}.
- MM phase-shift update: MM constructs a lower-bound surrogate that touches the objective at the current iterate and is easier to maximize.The surrogate maximizer supplies the next phase-shift iterate, producing monotonic objective improvement.
- Convergence: The AO-MM algorithm monotonically increases the objective and converges to a local optimum using closed-form updates.Algorithm 2 applies the closed-form beamformer and MM phase-shift solutions.
- Initialization: The proposed initialization uses the dominant left singular vector of R_l and is heuristic because it ignores the denominator of the objective function.The initialization is intended to construct initial IRS phase shifts for the non-convex problem.
- Complexity comparison: The element-wise BCD algorithm has M+1 blocks per iteration, whereas AO-MM has fewer block updates but may require more iterations because its parallel phase updates are sub-optimal.Thus, the algorithms trade block count per iteration against the number of iterations required for convergence.
IV. SIMULATION RESULTS
The numerical evaluation assumes independent Rayleigh-fading channels and averages the results over 1000 channel realizations. It specifies the noise power and the transmitter–IRS and IRS–receiver distances used in the simulations.
- Simulation setup: The simulations assume independent Rayleigh-fading channels with path loss characterized by exponent α and a 10-meter reference distance.The path loss exponent is denoted by α.
- Simulation setup: The noise power at both the legitimate receiver and the eavesdropper is set to σ2_e = −80 dBm.
- Simulation setup: Results in Figs. 4 and 5 are averaged over 1000 channel realizations, using distances r_TR, r_Rl, and r_Re for the transmitter–IRS and IRS–receiver links.r_Rl and r_Re denote the IRS distances to the legitimate receiver and eavesdropper, respectively.
A. Comparison of the Proposed Algorithms
The element-wise BCD algorithm converges faster for small IRSs, whereas AO-MM becomes preferable as the number of reflecting elements increases.
- A. Comparison of the Proposed Algorithms: For M = 5, element-wise BCD converges in fewer iterations despite updating six blocks per iteration versus AO-MM’s two.Its faster convergence follows from globally optimal solutions for all blocks.
- A. Comparison of the Proposed Algorithms: For M = 40, element-wise BCD updates 41 blocks per iteration, while AO-MM updates only two.The larger block count slows element-wise BCD as the IRS grows.
- A. Comparison of the Proposed Algorithms: Element-wise BCD suits small-scale IRS systems, whereas AO-MM is preferable for large-scale IRS systems.The algorithm choice depends on how the number of reflecting elements affects per-iteration updates and iteration count.
B. Average Secrecy Rate Evaluation
The proposed algorithms achieve the same average secrecy rate, and IRS deployment provides a significant secrecy-rate gain over a benchmark without an IRS.
- B. Average Secrecy Rate Evaluation: Both proposed algorithms achieve the same average secrecy rate.The comparison is shown for different algorithms in Fig. 4.
- B. Average Secrecy Rate Evaluation: The IRS-assisted system provides a significant secrecy-rate gain over the benchmark system without an IRS.The benchmark uses optimal transmit beamforming for security provisioning.
- B. Average Secrecy Rate Evaluation: The results indicate that deploying IRSs is a promising approach for improving physical layer security in wireless communications systems.This conclusion follows from the reported secrecy-rate comparison with the non-IRS benchmark.
C. Massive MIMO or Massive IRS?
The evaluation compares scaling transmit antennas with scaling IRS reflecting elements and finds larger secrecy-rate benefits from increasing the IRS size, alongside an energy-efficiency advantage.
- C. Massive MIMO or Massive IRS?: Fig. 5 evaluates average secrecy rate across different numbers of IRS reflecting elements M and transmit antennas Nt.The experiment fixes P = 5 dBm, α = 4, rTR = 200 m, rRl = 150 m, rRe = 100 m, rTl = 300 m, and rTe = 110 m.
- C. Massive MIMO or Massive IRS?: With Nt = 10 fixed, the evaluation increases the number of IRS reflecting elements, while a second curve varies Nt with M = 10.The red curve represents increasing IRS size; the blue curve represents increasing transmit-antenna count.
- C. Massive MIMO or Massive IRS?: Increasing the number of IRS reflecting elements is more beneficial for improving secrecy rate than increasing the number of transmit antenna elements.This is the paper’s direct comparison between large-scale IRS deployment and transmitter-array enlargement.
- C. Massive MIMO or Massive IRS?: Because the IRS is passive, deploying a large-scale IRS is more energy-efficient than installing additional RF chains and power amplifiers.The comparison concerns increasing transmitter antenna elements versus increasing IRS reflecting elements.
V. CONCLUSIONS
The paper proposes IRS deployment to improve physical layer security and develops two algorithms for joint beamformer and IRS phase-shift optimization. Simulations report substantial potential for improving both security and energy efficiency.
- V. CONCLUSIONS: The paper proposes deploying IRSs to improve the physical layer security of wireless communications networks.The conclusion frames IRS deployment as the paper’s central security approach.
- V. CONCLUSIONS: Element-wise BCD and AO-MM jointly optimize the transmitter beamformer and IRS phase shifts.The algorithms are designed for the resulting joint optimization problem.
- V. CONCLUSIONS: Element-wise BCD is preferable for small-scale IRS-assisted systems, while AO-MM is advantageous for systems with large-scale IRSs.The conclusion assigns each algorithm to the IRS scale where it is more suitable.
- V. CONCLUSIONS: Simulation results confirm the potential of IRSs to improve the security and energy efficiency of future communications systems.This is the paper’s reported overall simulation-based conclusion.
APPENDIX
The appendix derives a per-element optimization condition for the reflecting phase θ_k and identifies the maximizing solution through trigonometric simplification and second-derivative checking.
- Because the phase shift matrix Φ is diagonal, P3's objective can be rewritten as a function of the k-th reflecting element.
- Differentiating the objective with respect to θ_k and setting the derivative to zero yields a trigonometric stationarity equation.
- Basic trigonometric manipulation simplifies the stationarity condition to A_k sin θ_k + B_k cos θ_k = d_l,k d_e,k sin(p_e,k − p_l,k).
- When A_k ≥ 0, introducing an auxiliary angle recasts the equation into a form involving A_k^2 + B_k^2.
- The objective is verified to be maximized at the selected solution by checking its second derivative, while the A_k < 0 case follows similarly.