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Secure Wireless Communication in RIS-Aided MISO Systems with Hardware Impairments

Gui Zhou, Cunhua Pan, Hong Ren, Kezhi Wang, Zhangjie Peng

arXiv:2012.12733v3cs.ITeess.SP

TL;DR

The paper studies robust secrecy-rate maximization in RIS-aided secure communication when residual transceiver hardware impairments cause signal-dependent distortion noise. It alternately optimizes BS active beamforming and RIS passive beamforming using convex approximations, and simulations show greater robustness than a non-robust design that ignores impairments.

  • Problem

    The paper addresses robust transmission design for RIS-aided secure communication in the presence of residual transceiver hardware impairments and their distortion noise.

  • Method

    The method alternately updates BS active beamforming and RIS passive beamforming, solving the subproblems with SOCP/SCA and SDP-based optimization.

  • Results

    The proposed robust beamforming design is more effective than non-robust designs at compensating hardware-impairment performance loss in RIS-aided secure systems.

  • Takeaways & Limitations

    RIS-aided secure transmission benefits from explicitly accounting for transceiver hardware impairments in the beamforming design.

Abstract

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In practice, residual transceiver hardware impairments inevitably lead to distortion noise which causes the performance loss. In this paper, we study the robust transmission design for a reconfigurable intelligent surface (RIS)-aided secure communication system in the presence of transceiver hardware impairments. We aim for maximizing the secrecy rate while ensuring the transmit power constraint on the active beamforming at the base station and the unit-modulus constraint on the passive beamforming at the RIS. To address this problem, we adopt the alternate optimization method to iteratively optimize one set of variables while keeping the other set fixed. Specifically, the successive convex approximation (SCA) method is used to solve the active beamforming optimization subproblem, while the passive beamforming is obtained by using the semidefinite program (SDP) method. Numerical results illustrate that the proposed transmission design scheme is more robust to the hardware impairments than the conventional non-robust scheme that ignores the impact of the hardware impairments.

I. INTRODUCTION

The paper addresses secure RIS-aided communication under transceiver hardware impairments, a setting not covered by prior RIS security designs. It proposes jointly optimizing BS active beamforming and RIS passive beamforming for secrecy-rate enhancement.

  • I. INTRODUCTION: RIS elements can enhance legitimate-user signals constructively or suppress information leakage to eavesdroppers through controllable phase shifts.
  • I. INTRODUCTION: Prior RIS security studies considered multiple users, imperfect CSI, or artificial noise, but assumed perfect hardware at legitimate users.
  • I. INTRODUCTION: Residual transceiver impairments create additive Gaussian distortion noise whose variance scales with signal power, making perfect-hardware assumptions unrealistic.The cited impairments include phase noise, quantization errors, amplification noise, and nonlinearities.
  • I. INTRODUCTION: The paper jointly designs BS active beamforming and RIS passive beamforming for robust secrecy-rate maximization with transceiver hardware impairments.

A. Signal Transmission Model

The system models RIS-aided secure downlink transmission from a multi-antenna base station to a legitimate user in the presence of transmitter and receiver hardware impairments. An eavesdropper is modeled without residual hardware impairments under a worst-case assumption, and secrecy rate is defined from the legitimate and eavesdropper rates.

  • System model: The downlink uses an N-antenna base station, an M-element RIS, a single-antenna legitimate user, and a single-antenna eavesdropper.The RIS uses programmable phase shifters to improve physical-layer security.
  • Hardware impairments: Transmitter distortion is modeled as independent Gaussian noise whose per-antenna power is proportional to the corresponding transmit signal power.The proportionality factor is μ_t, the ratio of transmit distortion-noise power to transmit signal power.
  • Hardware impairments: Receiver distortion at the legitimate user is modeled as zero-mean Gaussian noise proportional to the undistorted received signal power, with ratio μ_r.The received signal also includes additive white Gaussian noise.
  • Eavesdropper model: The eavesdropper is assumed to have high-quality hardware without residual impairments because the base station lacks full eavesdropper hardware knowledge.The model assumes perfect channel-state information throughout the network.
  • Secrecy-rate model: The secrecy rate is formed from the legitimate-user rate minus the eavesdropper rate, with each receiver’s denominator including distortion and thermal noise.The legitimate-user and eavesdropper noise terms are denoted by U and E, respectively.

B. Problem Formulation

The paper formulates secrecy-rate maximization over the base-station beamforming vector and RIS reflection coefficients under transmit-power and unit-modulus constraints. Hardware-impairment-induced nonconcavity makes the resulting optimization problem difficult to solve in closed form.

  • Optimization problem: The optimization jointly maximizes secrecy rate over base-station beamforming and RIS passive beamforming.The formulation includes a maximum transmit-power constraint at the base station and unit modulus for each RIS coefficient.
  • Constraints: The RIS reflection vector imposes |e_m|^2 = 1 for each reflecting element, with the final augmented entry fixed to one.This constraint represents passive unit-modulus beamforming.
  • Objective property: The objective is always nonnegative because zero base-station beamforming yields zero secrecy rate whenever the legitimate-user rate is below the eavesdropper rate.Thus, the formulation can avoid a negative objective by setting the beamforming norm to zero.
  • Challenges: The problem is challenging because its objective is nonconcave, its RIS unit-modulus constraint is nonconvex, and hardware impairments complicate the secrecy-rate expression.Unlike a related impairment-free formulation, a closed-form beamforming solution is not straightforward here.

III. ALGORITHM DESIGN FOR SECURE WIRELESS

The algorithm design uses alternating optimization to decouple the base-station and RIS variables. Auxiliary variables reformulate the legitimate-user and eavesdropper rate constraints, producing an equivalent problem whose inequalities are tight at optimum.

  • Alternating optimization: Alternating optimization updates the base-station beamforming vector and RIS reflection beamforming in turn while holding the other variable fixed.This addresses the coupling between the two beamforming variables.
  • Auxiliary-variable reformulation: Four auxiliary variables are introduced to impose lower and upper bounds on the legitimate-user and eavesdropper rates.The reformulation requires RU ≥ p1 − p2 and RE ≤ p3 − p4.
  • Problem equivalence: The auxiliary constraints hold with equality at the optimum, so the reformulated problem is equivalent to the original secrecy-rate maximization problem.This equivalence follows from a contradiction argument.

A. Optimize f with fixed e

With e fixed, auxiliary variables and successive convex approximation transform the active beamforming subproblem into an SOCP solvable by CVX.

  • A. Optimize f with fixed e: Auxiliary variables make the non-convex constraints equivalent to a reformulated active beamforming subproblem.The vector rf contains four auxiliary variables associated with the reformulated constraints.
  • A. Optimize f with fixed e: First-order Taylor approximation handles the concave constraints while preserving a convex formulation for the active beamforming update.The reformulation also uses the equality yH g diag(xxH)y = xH g diag(yyH)x.
  • A. Optimize f with fixed e: Problem (13) can be solved using the CVX tool.

B. Optimize e with fixed f

With f fixed, the RIS update replaces the unit-modulus vector with a lifted matrix, approximates remaining non-convex constraints, and solves a relaxed SDP before projection and safeguarded updating.

  • B. Optimize e with fixed f: Semidefinite relaxation lifts e into eE = eeH and replaces the unit-modulus constraint with positive-semidefinite, rank-one, and diagonal conditions.The replacement is {eE ⪰ 0, rank(eE) = 1, g diag(eE) = IM+1}.
  • B. Optimize e with fixed f: First-order Taylor approximation is applied to the remaining non-convex constraints in the fixed-f RIS subproblem.
  • B. Optimize e with fixed f: The relaxed RIS subproblem is formulated as Problem (17) and further relaxed to a convex SDP solved with CVX tools.
  • B. Optimize e with fixed f: Gaussian randomization obtains a suboptimal RIS solution from eE, which is then projected onto the unit-modulus constraint set S.
  • B. Optimize e with fixed f: Because the SDR solution may reduce the objective, the algorithm uses an update rule and continues iterating until convergence.

C. Algorithm Analysis

The alternating-optimization objective sequence is non-decreasing and bounded, so the algorithm is guaranteed to converge, with SOCP and SDP complexity depending on N and M.

  • C. Algorithm Analysis: The AO objective sequence is non-decreasing and has a finite upper bound from the bounded transmit-power constraint, guaranteeing convergence.The non-decreasing property follows from the update rule and the globally optimal f update for fixed e.
  • C. Algorithm Analysis: The SOCP in Problem (13) has complexity O(N^3), while the SDP corresponding to Problem (17) has complexity O(M^3.5).

IV. NUMERICAL RESULTS AND DISCUSSIONS

Simulations evaluate RIS-aided secure communication under transceiver hardware impairments across transmit power and RIS size. Robust beamforming is particularly effective with RIS, while impairment levels limit gains from larger RISs.

  • Simulation setup: The evaluation uses four antennas at the BS and compares RIS-robust, NonRIS-robust, RIS-nonrobust, and NonRIS-nonrobust schemes.The simulated geometry places the BS at (0 m, 0 m), the RIS at (50 m, 0 m), the legitimate user at (50 m, 2 m), and the eavesdropper at (45 m, 2 m).
  • Transmit-power impact: The RIS-robust design is more effective at compensating hardware-impairment performance loss than robust beamforming without RIS.The secrecy rate becomes stable as Pmax increases because distortion noise is proportional to transceiver signal power.
  • RIS-size impact: Increasing the RIS size enhances secrecy rate, but the gain decreases as hardware-impairment levels increase.This comparison fixes Pmax = 30 dBm and N = 4.
  • RIS-size impact: Receive-side hardware impairments have a greater negative impact on secrecy rate than BS impairments.The receive distortion-noise proportion is much larger than the transmit distortion-noise proportion.

V. CONCLUSIONS

The paper maximizes secrecy rate in an RIS-aided secure system with transceiver hardware impairments by jointly optimizing BS active and RIS passive beamforming. Alternating SOCP and SDP subproblems yield the proposed design, whose simulations demonstrate a performance advantage.

  • V. CONCLUSIONS: Jointly optimizing BS active and RIS passive beamforming maximizes secrecy rate while accounting for hardware-impairment distortion noise.The two variables are updated alternately through approximate SOCP and SDP subproblems.
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