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Secure Wireless Communication via Intelligent Reflecting Surface

Miao Cui, Guangchi Zhang, Rui Zhang

arXiv:1905.10770v1cs.IT

TL;DR

The paper tackles limited secrecy rates caused by stronger, spatially correlated eavesdropping channels. It jointly designs AP transmit beamforming and IRS reflect beamforming using alternating optimization and semidefinite relaxation, and simulations show significant improvement over no IRS and a heuristic scheme.

  • Problem

    Highly correlated legitimate and eavesdropping channels, with the eavesdropper channel stronger, make secrecy rates very limited even with conventional techniques.

  • Method

    The paper jointly optimizes AP transmit beamforming and IRS reflect beamforming using alternating optimization and semidefinite relaxation.

  • Results

    Simulations show that the proposed IRS-assisted design significantly improves secrecy rate over no IRS and outperforms a heuristic scheme.

  • Takeaways & Limitations

    IRS-enabled power enhancement and interference suppression improve secrecy communication in the considered challenging setup.

Abstract

from arXiv · show

An intelligent reflecting surface (IRS) can adaptively adjust the phase shifts of its reflecting units to strengthen the desired signal and/or suppress the undesired signal. In this letter, we investigate an IRS-aided secure wireless communication system where a multi-antenna access point (AP) sends confidential messages to a single-antenna user in the presence of a single-antenna eavesdropper. In particular, we consider the challenging scenario where the eavesdropping channel is stronger than the legitimate communication channel and they are also highly correlated in space. We maximize the secrecy rate of the legitimate communication link by jointly designing the AP's transmit beamforming and the IRS's reflect beamforming. While the resultant optimization problem is difficult to solve, we propose an efficient algorithm to obtain high-quality suboptimal solution for it by applying the alternating optimization and semidefinite relaxation methods. Simulation results show that the proposed design significantly improves the secrecy communication rate for the considered setup over the case without using the IRS, and outperforms a heuristic scheme.

I. INTRODUCTION

The paper addresses secure communication when legitimate and eavesdropping channels are highly correlated and the eavesdropper’s channel is stronger. It proposes IRS-assisted joint beamforming to enhance the user’s signal and suppress the eavesdropper’s signal.

  • An IRS adaptively controls passive reflecting-unit phase shifts to improve wireless-network performance.
  • Highly correlated channels and a stronger eavesdropping channel leave conventional secrecy techniques with very limited achievable secrecy rate.
  • The considered system uses a multi-antenna AP, a single-antenna user, a single-antenna eavesdropper, and an IRS deployed near the receivers.
  • Jointly optimizing AP transmit beamforming and IRS reflect beamforming targets maximum secrecy rate despite non-convex, coupled variables.
  • The IRS strengthens the legitimate signal through constructive combining and suppresses the eavesdropping signal through destructive combining.

II. SYSTEM MODEL AND PROBLEM FORMULATION

The system model describes AP transmission assisted by an IRS with unit-modulus reflecting coefficients, and formulates secrecy-rate maximization over AP and IRS beamforming. The IRS phase design balances constructive combining at the user against destructive combining at the eavesdropper, while the resulting problem remains non-convex.

  • The model has an M-antenna AP, single-antenna user and eavesdropper, and an IRS with N reflecting units.
  • Perfect global CSI is assumed for jointly designing transmit and reflect beamforming under quasi-static flat-fading channels.
  • Each IRS coefficient is q_n=β_ne^jθ_n, with β_n=1 imposed so every unit has unit-modulus reflection.
  • The received signals include direct and once-reflected AP-to-receiver paths, while multiple IRS reflections are neglected because of severe path loss.
  • For fixed AP beamforming, IRS phases align the reflected user channel with the direct channel but oppose the eavesdropper channel, creating a design trade-off.
  • The objective jointly maximizes secrecy rate over AP beamformer w and IRS beamformer q, but its objective and unit-norm constraints are non-convex.

III. PROPOSED ALGORITHM FOR PROBLEM (8)

The proposed algorithm solves the joint design by alternating between AP transmit-beamforming optimization and IRS reflect-beamforming optimization. The two sub-problems are iterated, followed by convergence and complexity analysis.

  • Alternating optimization separates the problem into optimizing w with fixed q and optimizing q with fixed w.
  • The two sub-problems are solved iteratively to produce the overall algorithm, whose convergence and complexity are analyzed.

A. Sub-Problem 1: Optimizing w with Given q

With the IRS reflect beamforming vector fixed, the first sub-problem optimizes the AP transmit beamforming vector. Its optimal solution is obtained from the principal eigenvector of a matrix formed from the effective user and eavesdropper channels.

  • Sub-problem 1 constructs matrices from the effective user and eavesdropper channels for optimizing the AP beamformer.
  • The optimal AP beamformer is the normalized eigenvector associated with the largest eigenvalue of the specified matrix.
  • The secrecy objective can attain a non-negative optimum because setting w=0 raises any negative secrecy difference to zero without violating constraints.

B. Sub-Problem 2: Optimizing q with Given w

Sub-problem 2 optimizes the IRS reflect beamforming vector q while holding the AP transmit beamforming vector w fixed.

  • Sub-problem 2 formulates the optimization of q with given w.

E |(hIEQHAI + hAE)w|2 + 1 (13a)

The q-optimization is reformulated through quadratic expressions, then approximated using semidefinite relaxation and transformed into a convex SDP solvable by standard methods.

  • Substituting quadratic signal expressions yields a fractional optimization problem in s with non-convex quadratic equality constraints.
  • Semidefinite relaxation introduces S = ss^H and drops the rank(S) = 1 constraint to overcome the non-convexity.
  • The Charnes-Cooper transformation sets μ = 1/[tr(G_ES) + h_E + 1] and X = μS, producing an equivalent non-fractional formulation.
  • The transformed problem is a convex semidefinite program with constraints tr(G_EX) + μ(h_E + 1) = 1 and tr(E_nX) = μ.
  • Gaussian randomization obtains an approximate q after solving the relaxed SDP and addressing the omitted rank-one constraint.
  • Algorithm 1 initializes w and q, alternately updates them, records the objective R^(k), and repeats until convergence.

C. Overall Algorithm

The overall algorithm alternates AP transmit-beamforming and IRS reflect-beamforming updates, with convergence guaranteed by a non-decreasing bounded objective.

  • Each iteration updates w using a largest-eigenvalue eigenvector and updates q by solving the relaxed problem followed by Gaussian randomization.
  • The objective R^(k) is non-decreasing and bounded above, so the alternating algorithm is guaranteed to converge.
  • The algorithm complexity is O(N_ite(M^3 + (N + 1)^3.5)), with N_ite usually less than 10 for ε = 10^-3 in the simulations.

IV. SIMULATION RESULTS

Simulations compare the proposed joint beamforming design with heuristic, no-IRS, and upper-bound schemes under highly correlated AP-user and AP-eavesdropper channels. The proposed design achieves substantially better secrecy-rate behavior, approaching the upper bound and gaining more as IRS size increases.

  • The evaluation compares the proposed alternating-optimization design with AP MRT with IRS, without IRS, and an upper-bound scheme.
  • The setup uses M = 4 and colocates the AP, user, eavesdropper, and IRS at specified two-dimensional coordinates, with correlated Rician AP-user and AP-eavesdropper fading.
  • The simulation results average secrecy rates over 1000 random fading realizations with σ_E^2 = -80 dBm and ε = 10^-3.
  • With N = 64, the no-IRS secrecy rate increases slowly with P_AP, whereas both IRS schemes increase significantly as transmit power grows.
  • The proposed joint design is very close to its upper bound and significantly outperforms the heuristic AP MRT with IRS scheme.
  • At P_AP = 15 dBm, the proposed scheme exceeds AP MRT with IRS, and their performance gap increases with the number N of reflecting units.

V. CONCLUSION

The letter introduces an IRS-aided secure communication system and jointly optimizes active transmit and passive reflect beamforming to maximize secrecy rate. Simulations show significant improvement over the conventional system without an IRS by enhancing legitimate power and suppressing eavesdropper interference.

  • The proposed system jointly optimizes the AP’s active transmit beamforming and the IRS’s passive reflect beamforming for secrecy-rate maximization.
  • The evaluation targets a challenging setup where the conventional system without an IRS has very limited secrecy rate.
  • Simulations show significant performance improvement from IRS-enabled power enhancement at the legitimate receiver and interference suppression at the eavesdropper.
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