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Pinching-Antenna Systems (PASS)-enabled Secure Wireless Communications

Guangyu Zhu, Xidong Mu, Li Guo, Shibiao Xu, Yuanwei Liu, Naofal Al-Dhahir

arXiv:2504.13670v2eess.SP

TL;DR

The paper addresses how PASS can extend physical-layer security beyond conventional and earlier basic communication settings. It develops PA-position and baseband optimization methods for single- and multiple-waveguide systems, reporting stronger secrecy performance than conventional antennas, with WM strongest and WD competitive at lower complexity.

  • Problem

    Existing PASS research largely studies basic communications, leaving its integration with secure transmission limited despite the growing importance of physical-layer security.

  • Method

    The framework optimizes PA positions for single-waveguide PAST and combines AN with WD or WM architectures using PAST, SCA, AO, and PSO methods.

  • Results

    Numerical results show greater secrecy gains than conventional antennas; WM performs best, while WD offers competitive performance with lower complexity.

  • Takeaways & Limitations

    PASS provides a flexible physical-layer security framework spanning single-waveguide beamforming and multiple-waveguide joint signal designs.

Abstract

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A novel pinching-antenna systems (PASS)-enabled secure wireless communication framework is proposed. By dynamically adjusting the positions of dielectric particles, namely pinching antennas (PAs), along the waveguides, PASS introduces a novel concept of pinching beamforming to enhance the performance of physical layer security. A fundamental PASS-enabled secure communication system is considered with one legitimate user and one eavesdropper. Both single-waveguide and multiple-waveguide scenarios are studied. 1) For the single-waveguide scenario, the secrecy rate (SR) maximization is formulated to optimize the pinching beamforming. A PA-wise successive tuning (PAST) algorithm is proposed, which ensures constructive signal superposition at the legitimate user while inducing a destructive legitimate signal at the eavesdropper. 2) For the multiple-waveguide scenario, artificial noise (AN) is employed to further improve secrecy performance. A pair of practical transmission architectures are developed: waveguide division (WD) and waveguide multiplexing (WM). The key difference lies in whether each waveguide carries a single type of signal or a mixture of signals with baseband beamforming. For the SR maximization problem under the WD case, a two-stage algorithm is developed, where the pinching beamforming is designed with the PAST algorithm and the baseband power allocation among AN and legitimate signals is solved using successive convex approximation (SCA). For the WM case, an alternating optimization algorithm is developed, where the baseband beamforming is optimized with SCA and the pinching beamforming is designed employing particle swarm optimization.

I. INTRODUCTION

The paper introduces PASS-enabled physical-layer security, using reconfigurable pinching antennas to improve secrecy in single- and multiple-waveguide systems. It develops PAST, WD, and WM-based optimization methods for designing pinching and baseband beamforming.

  • Motivation and system concept: PASS uses movable dielectric particles along waveguides as reconfigurable radiation nodes for secure wireless transmission.These pinching antennas dynamically adjust the propagation environment and support pinching beamforming.
  • Motivation and system concept: The study addresses limited prior integration of PASS with secure transmission by considering a base station, legitimate user, and eavesdropper.Both single-waveguide and multiple-waveguide scenarios are analyzed.
  • Single-waveguide design: For a single waveguide, PAST first positions PAs to reduce Bob’s path loss, then tunes them for constructive reception at Bob and destructive interference at Eve.The method optimizes pinching beamforming for secrecy-rate maximization.
  • Multiple-waveguide design: For multiple waveguides, the paper introduces WD and WM architectures and uses AN to further improve secrecy performance.WD assigns signal types by waveguide, whereas WM supports joint baseband and pinching beamforming.
  • Results: Numerical results report greater secrecy gains than conventional antenna systems, with WM superior and WD offering competitive performance at lower complexity.The single-waveguide algorithm is especially efficient when the PA count is even or relatively large.

B. Problem Formulation

The single-waveguide problem maximizes secrecy rate by jointly optimizing transmit power and PA positions under power and spacing constraints. Because PA positions affect channels non-convexly, the problem is difficult to solve directly, while PASS makes full transmit power optimal under the stated channel-gain condition.

  • Problem formulation: The optimization maximizes secrecy rate by jointly designing transmit power P and PA positions x.The design is subject to a maximum transmit-power budget and minimum spacing between PAs.
  • Problem formulation: PA positions must remain ordered within the waveguide and satisfy the minimum-spacing constraint.The spacing prevents coupling effects between PAs.
  • Problem formulation: The resulting optimization is non-convex because channel characteristics depend complexly on PA positions.This positional dependence makes direct solution difficult.
  • Problem formulation: When proper pinching beamforming keeps Bob’s channel gain above Eve’s, secrecy rate increases with transmit power and the optimum uses P = Pmax.The subsequent analysis therefore focuses on optimizing the pinching beamforming vector.

C. Proposed PAST Algorithm

The PAST algorithm designs PA positions in two stages: first reducing Bob’s large-scale path loss, then enforcing constructive alignment at Bob and destructive alignment at Eve through successive refinements.

  • The SR objective is reduced to maximizing the channel-gain difference between Bob and Eve through path-loss reduction and phase alignment.
  • Phase-Constrained Beamforming: The phase strategy coherently combines legitimate signals at Bob while pairing phase terms oppositely to suppress the signal at Eve.For even PA counts, Eve’s signal can be almost completely canceled; for odd counts, one residual term remains.
  • Phase-Constrained Beamforming: The destructive-alignment condition decouples Eve suppression from the initial path-loss optimization, allowing the coarse stage to focus solely on Bob.
  • Coarse PA Distribution for Bob’s Large-Scale Path Loss Minimization: PA positions are initially distributed to maximize the sum of inverse distances from the PAs to Bob, without phase constraints.The coarse arrangement is a uniform symmetric placement centered at the midpoint under the stated distance condition.
  • Successive Fine-Tuning for Phase-Constrained Beamforming: PAST successively fine-tunes neighboring PA positions using first-order Taylor approximations while preserving feasibility of the phase constraints.A reference PA is selected near the center, and left and right positions are refined iteratively with feasible minimum step sizes.
  • Successive Fine-Tuning for Phase-Constrained Beamforming: The complete PAST algorithm has computational complexity O(N).

III. MULTIPLE-WAVEGUIDE PASS-ENABLED SECURE WIRELESS COMMUNICATIONS

The multiple-waveguide extension retains a single Bob and Eve while introducing a representative dual-waveguide configuration and joint channel modeling for PASS-enabled secure transmission.

  • The multiple-waveguide system introduces artificial noise at baseband to further enhance secrecy performance.The extension studies joint optimization of baseband signal processing and pinching beamforming through practical transmission architectures.
  • A dual-waveguide configuration with N PAs per waveguide is adopted as a representative case for extracting design insights.The waveguides are parallel, have identical length L, and are positioned at height H.
  • Each waveguide-to-user channel combines in-waveguide propagation from the feed point to a PA with free-space propagation from that PA to the user.The PA-to-user distance depends on the PA’s position, the user coordinates, and the waveguide height.
  • The end-to-end channel is constructed from the waveguide-specific channels for users k ∈ {b, e}.

A. Practical Transmission Architecture

The paper develops waveguide division and waveguide multiplexing as two practical architectures that combine PASS positioning with different forms of baseband signal processing.

  • The two architectures differ in whether waveguides carry separate signal types or multiplexed signals with baseband beamforming.
  • Waveguide Division: Waveguide division allocates power between the legitimate signal and artificial noise, then feeds the two streams to different waveguides.Each waveguide carries only one data stream, with the legitimate signal assigned to waveguide 1 in the stated simplification.
  • Waveguide Division: Under waveguide division, PA positions provide pinching beamforming while baseband processing performs power allocation subject to the BS transmit-power constraint.The resulting user rates are defined for both Bob and Eve.
  • Waveguide Multiplexing: Waveguide multiplexing combines the legitimate signal and artificial noise before transmission and assigns separate baseband beamforming coefficients to each waveguide.This architecture increases transmission flexibility through joint signal multiplexing and waveguide beamforming.

2) Waveguide Multiplexing:

The formulation incorporates transmit-power constraints and achievable rates into secrecy-rate optimization for the multi-waveguide setting. The resulting problem jointly accounts for baseband variables and pinching-antenna positions, creating substantial optimization complexity.

  • Problem Formulation: The secrecy-rate formulation includes maximum transmit-power constraints at the base station and achievable rates for both the legitimate user and eavesdropper.The rate is expressed in bit/s/Hz for users k ∈ {b, e}.
  • Problem Formulation: Multi-waveguide optimization jointly designs baseband power allocation or beamforming and pinching-antenna positions under spacing and transmit-power constraints.Waveguide division optimizes power coefficients, whereas waveguide multiplexing optimizes baseband beamforming vectors.
  • Problem Formulation: Additional baseband variables and cross-waveguide PA positioning tightly couple the design and make the resulting optimization problem highly challenging.The paper states that existing methods fail to address this problem effectively.

D. Proposed Two-Stage Algorithm for the WD Architecture

The WD architecture is solved through two stages: PAST determines pinching beamforming, then SCA optimizes baseband power allocation. Dedicated waveguides separate the legitimate signal and artificial noise, enabling independent PA-position design.

  • Two-Stage Algorithm: The WD solution first determines pinching beamforming and then optimizes baseband power allocation using SCA.The two stages respectively solve PA positioning and the power-allocation subproblem.
  • Two-Stage Algorithm: Because each WD waveguide carries one signal stream, PAST can determine pinching beamforming separately for the legitimate-signal and artificial-noise waveguides.Artificial noise is transmitted through a dedicated waveguide, decoupling PA-position design across the two waveguides.
  • Two-Stage Algorithm: The PA-position subproblems use transmission phase shifts and spacing constraints to obtain the positions on both waveguides.The phase variables distinguish links from each waveguide to Bob and Eve.
  • Two-Stage Algorithm: After pinching beamforming is fixed, the remaining WD problem becomes power allocation, whose non-convex objective is approximated by a convex lower bound using first-order Taylor expansion.The resulting convex problem can be solved with CVX.
  • Two-Stage Algorithm: Iteratively solving the SCA subproblem with the obtained pinching beamforming yields a stable solution, with complexity expressed in terms of SCA iterations and power-allocation variables.The paper sets the number of power-allocation variables to M = 2.

1) Pinching Beamforming Optimization:

For WM pinching-beamforming optimization, the paper uses PSO to search jointly over PA positions on both waveguides while enforcing position and spacing constraints. Particle updates balance personal and global search information.

  • Pinching Beamforming Optimization: Because the optimization variables are diverse and complex, the paper employs heuristic PSO to solve the WM pinching-beamforming subproblem.The particle swarm is initialized over the PA-position variables for both waveguides.
  • Pinching Beamforming Optimization: Each particle encodes the x-coordinates of PAs on both waveguides, with initialization designed to satisfy the position constraints.The particle coordinates represent PA locations on waveguide 1 and waveguide 2.
  • Pinching Beamforming Optimization: PSO updates particle positions using each particle’s historically best position and the swarm’s global best position.The update mechanism uses velocity iteration, inertia, and learning factors.
  • Pinching Beamforming Optimization: A linearly decreasing inertia weight balances global exploration and personal search across iterations.The inertia weight varies between α_min and α_max.
  • Pinching Beamforming Optimization: The fitness function uses secrecy rate and a penalty for PA-spacing violations, with a sufficiently large penalty factor enforcing the distance constraint.Particle best positions are updated until convergence.

2) Baseband Beamforming Optimization:

With PA positions fixed, WM optimization becomes a conventional physical-layer-security beamforming problem. The paper formulates it as an SDP, relaxes rank constraints, and applies SCA; alternating PSO-SCA updates converge to a stable solution.

  • Baseband Beamforming Optimization: Fixing the PA positions reduces the problem to conventional physical-layer-security beamforming with legitimate-signal and artificial-noise matrices.The beamforming matrices are defined as W = ww^H and V = vv^H.
  • Baseband Beamforming Optimization: The resulting beamforming subproblem is challenging because its objective is non-convex and includes rank-one constraints.These properties prevent direct solution in the original form.
  • Baseband Beamforming Optimization: The method omits the rank-one constraints using a relaxation whose solution remains consistent with the original problem, then approximates the objective with SCA.A first-order Taylor expansion provides a convex lower bound.
  • Baseband Beamforming Optimization: The relaxed SCA subproblem is convex and can be solved using CVX.The formulation is described as a standard convex problem.
  • Baseband Beamforming Optimization: Alternating PSO and SCA updates use the previous iteration’s solution and produce nondecreasing, bounded objectives, ensuring convergence to a stable solution.The PSO and SCA subproblems are updated from their latest optimal results.
  • Baseband Beamforming Optimization: The paper expresses the computational complexity of PSO, the relaxed SDP, and the overall alternating procedure in terms of particles, waveguides, and SCA iterations.The number of waveguides is set to M = 2.
  • Baseband Beamforming Optimization: Numerical results are provided to validate PASS-enabled secure communications in single-waveguide and multiple-waveguide scenarios.This validation covers the communication settings studied in the paper.

A. Simulation Setup

The simulations evaluate PASS secrecy performance under single- and multiple-waveguide settings using fixed system parameters, several baselines, and iterative optimization procedures. Results show that optimized PA positioning generally improves secrecy, while odd small PA counts can limit PAST performance.

  • Simulation Parameters: Simulations use H = 2 m, fc = 28 GHz, Pmax = 1 mW, σ_e^2 = −90 dBm, and minimum PA spacing Δ = λ/2.The effective refractive index is neff = 1.4, and convergence criteria are set to ε0 = ε1 = ε2 = 10^-3.
  • Multiple-Waveguide Procedure: The multiple-waveguide WM evaluation alternates particle-swarm optimization of PA positions with SCA updates of beamforming variables.The algorithm initializes particle positions and beamforming matrices, repeatedly solves the PA-position problem with PSO, and updates beamforming through SCA until convergence.
  • Baselines: The single-waveguide evaluation compares PAST with PSO, random PA positions, and a conventional antenna system using analog beamforming.The random-position result averages SR over 500 independent realizations.
  • Single-Waveguide Results: As N increases, optimized schemes improve SR by exploiting additional PA-position design DoFs, whereas random positioning provides no consistent secrecy enhancement.PASS consistently outperforms conventional antenna systems in the even-N comparison because flexible pinching beamforming mitigates large-scale path loss.
  • Single-Waveguide Results: At N = 3, PAST has a significant performance gap versus PSO, but the gap decreases as N increases.For odd N, one PA signal remains uncanceled at Eve; increasing N reduces each PA’s transmission power and weakens this effect.
  • Single-Waveguide Results: As L increases, secrecy performance generally decreases because users are farther from the BS, although PASS handles the resulting path loss more effectively than conventional antennas.The N = 3 PAST case is an exception whose curve fluctuates because Eve’s suppression is ineffective and Eve’s position changes randomly.

C. Secrecy Performance of the Multiple-Waveguide Scenario

The multiple-waveguide study compares WD and WM with conventional antenna baselines under varying PA counts, area sizes, and waveguide spacing. WM achieves the strongest secrecy performance, while WD offers a simpler competitive alternative and greater sensitivity to waveguide spacing.

  • Evaluation Setup: The study models two symmetric waveguides separated by D/2 and compares WM without AN, HB, FDB, and FDB without AN.The default separation is D = 0.5 m; HB and FDB use conventional antenna arrays with AN and different RF-chain configurations.
  • SR Versus PA Count: As N increases, all schemes improve SR, while WM achieves the highest SR by jointly exploiting PA positioning and baseband beamforming.WD has a simpler structure and achieves performance comparable to the stronger baselines.
  • SR Versus Area Size: As L expands, all schemes lose performance, but PASS experiences less degradation than conventional antenna systems.The area expansion generally increases communication distance, while PASS is more capable of handling the resulting path loss.
  • SR Versus Waveguide Spacing: Increasing D significantly degrades WD, whereas WM remains relatively stable with only slight SR fluctuations.WM jointly optimizes transmission across waveguides, producing more balanced legitimate-signal and AN design under spacing-induced channel variation.
  • SR Versus Waveguide Spacing: Deploying waveguides directly above the users achieves higher performance for both transmission architectures.This placement provides better channel conditions and is identified as an important consideration for PASS deployment.
  • Overall Comparison: The conclusion characterizes WM as superior to WD and WD as a complexity-efficient alternative with competitive performance.The corresponding algorithms are AO with PSO and SCA for WM, and a two-stage PAST-plus-SCA procedure for WD.

APPENDIX: PROOF OF LEMMA 1

The proof establishes that optimal pinching antennas are spaced by Δ and arranged symmetrically around Bob’s position. It derives these properties from monotonicity, path-loss symmetry, and the objective’s behavior under spacing changes.

  • Optimal spacing: The objective improves as neighboring-PA spacing decreases, so the optimal spacing is Δ.Equality holds only when the excess spacing is zero.
  • Symmetric placement: For two PAs, the optimal positions are x∗_1 = x_b − Δ/2 and x∗_2 = x_b + Δ/2.The two antennas are placed symmetrically around Bob.
  • General solution: For any N, optimal PA positions are symmetrically distributed around x_b with step size Δ.Odd and even antenna counts are obtained by extending or scaling the N = 2 construction.
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