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Pinching-Antenna Systems-enabled Secure ISAC: A Two-Timescale Optimization Framework

Haowen Song, Jingjing Zhao, Xidong Mu, Kaiquan Cai

arXiv:2609.02026v1eess.SP

TL;DR

The paper addresses secure ISAC with a moving Eve when PA activation overhead prevents real-time pinching-beamforming adaptation. It develops a two-timescale PASS framework that tracks Eve and updates pinching and baseband designs at different rates, achieving accurate tracking and higher secrecy rates than conventional antenna benchmarks.

Abstract

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A novel two-timescale optimization framework is proposed for pinching-antenna systems (PASS)-enabled secure integrated sensing and communications (ISAC). Specifically, a base station (BS) equipped with pinching antennas (PAs) transmits signals to a legitimate user under the existence of an eavesdropper (Eve), while employing leaky coaxial cables (LCXs) for receiving echo signals to track Eve's mobility states, i.e., locations and velocities. Considering the practical PAs activation overhead, the pinching beamforming and baseband processing are optimized in the large and small timescales, respectively. The multiple-waveguide scenario is first considered, where the BS can transmit the artificial noise together with communication signals for both jamming and sensing purposes. A joint baseband and pinching beamforming design problem is formulated to maximize the average secrecy rate. To address this problem, an alternating optimization algorithm is first invoked for jointly optimizing the pinching and baseband beamforming with predicted Eve's mobility states. With determined PAs positions, the baseband beamforming is updated with refined Eve's states obtained from real-time echo signal processing. The single-waveguide scenario is then considered. Since a single waveguide carries at most one independent data stream, an ISAC framework with separate communication and sensing phases is proposed. The element-wise algorithm proposed for the multiple-waveguide scenario is extended to solve the resultant pinching beamforming problem. Numerical results demonstrate that: 1) Eve's velocities and positions can be accurately tracked with the proposed two-timescale framework in both multiple- and single-waveguide scenarios; and 2) PASS achieves superior secrecy rate compared to conventional multiple-antenna benchmarks.

I. INTRODUCTION

The paper addresses secure ISAC with a moving eavesdropper when PA reconfiguration overhead prevents real-time pinching-beamforming adaptation. It proposes a two-timescale PASS framework combining Eve tracking, large-timescale pinching design, and real-time baseband updates.

Multiple-Waveguide Scenario

  • In the multiple-waveguide scenario, artificial noise accompanies communication signals for sensing and jamming, and AO jointly optimizes pinching and baseband beamforming using predicted Eve states.Source: B. Motivations and Contributions · p. 2

Single-Waveguide Scenario

  • In the single-waveguide scenario, separate communication and sensing phases support secrecy-rate maximization because one waveguide carries at most one independent data stream.Source: B. Motivations and Contributions · p. 2
  • Eve’s positions and velocities are tracked with high precision, while PASS outperforms conventional MIMO and massive MIMO in secrecy rate under PA activation overhead.Source: B. Motivations and Contributions · p. 3

A. Sensing Signal Model

The sensing model represents near-field, time-varying propagation between PASS transmit elements, Eve, and LCX receiving slots. Eve’s mobility produces nonuniform Doppler shifts across the large transmitting and receiving apertures.

  • The transmit model accounts for in-waveguide propagation from feed points to PAs and free-space propagation from PAs to Eve.Source: A. Sensing Signal Model · p. 4
  • The model assumes uniformly radiated transmit power across each waveguide’s PAs, neglects in-waveguide propagation loss, and defines the reference channel gain at 1 m.Source: A. Sensing Signal Model · p. 4
  • Near-field effects make Doppler shifts nonuniform across PAs and LCX slots as Eve moves.Source: A. Sensing Signal Model · p. 4
  • For each transmit waveguide, radial velocity and Doppler responses are represented across its PAs through time-varying phase-Doppler vectors.Source: A. Sensing Signal Model · p. 4
  • The reflected probing signal is received by LCXs, whose slots have corresponding radial velocities, Doppler responses, channel vectors, and received echo signals.Source: A. Sensing Signal Model · pp. 4–5
  • The combined LCX observations use per-LCX combination vectors and a block-diagonal combination matrix, with additive Gaussian noise included in the model.Source: A. Sensing Signal Model · p. 5

B. Communication Signal Model

The communication model describes transmission from PASS PAs to Bob and Eve, including the achievable rate at Bob, information leakage at Eve, and the resulting secrecy rate.

III. EKF-BASED EVE TRACKING SCHEME AND PROBLEM FORMULATION FOR MULTIPLE-WAVEGUIDE PASS

The paper uses an EKF-based framework to track Eve’s locations and velocities from echo signals, then formulates average secrecy-rate maximization for multiple-waveguide PASS.

III. EKF-BASED EVE TRACKING SCHEME AND PROBLEM FORMULATION FOR MULTIPLE-WAVEGUIDE PASS

  • The resulting formulation maximizes average secrecy rate in the multiple-waveguide PASS setting.Source: §III · p. 5

A. EKF Based Eve State Tracking

1) State Transition and Observation Model:

A. EKF Based Eve State Tracking

1) State Transition and Observation Model:

2) Prior Prediction:

The EKF predicts Eve’s next state from the kinematic model and refines it using received echoes, supplying mobility information for a constrained secrecy-rate optimization.

2) Prior Prediction:

  • The prior prediction feeds the current mobility state into the transition function to estimate the next state.Source: 2) Prior Prediction · p. 6
  • The prediction covariance uses the kinematic-model Jacobian and the previous state-error covariance.Source: 2) Prior Prediction · p. 6

3) Posterior Update:

  • After receiving each CPI’s echo signal, the prior estimate is updated with the refined mobility state.Source: 3) Posterior Update · p. 6
  • The Kalman gain is computed from the state-transition uncertainty, observation Jacobian, and residual covariance.Source: 3) Posterior Update · p. 6

B. Problem Formulation

  • The BS uses tracked locations and velocities to support subsequent pinching and baseband beamforming designs.Source: B. Problem Formulation · p. 6
  • The optimization maximizes average secrecy rate subject to transmit-power, echo-power, waveguide-length, and PA-spacing constraints.Source: B. Problem Formulation · p. 6
  • Pinching beamforming uses predicted Eve locations, whereas baseband beamforming uses positions refined from echo signals.Source: B. Problem Formulation · p. 6

IV. PROPOSED TWO-TIMESCALE SOLUTION FOR MULTIPLE-WAVEGUIDE PASS

The proposed solution alternates between large-timescale PA-position optimization and small-timescale baseband optimization, using element-wise search and convexified covariance design.

IV. PROPOSED TWO-TIMESCALE SOLUTION FOR MULTIPLE-WAVEGUIDE PASS

  • The algorithm jointly optimizes PA positions and baseband beamforming at each time block, then updates baseband beamforming during each CPI.Source: §IV · p. 6

A. Large-timescale Pinching Beamforming Optimization

B. Small-timescale Baseband Beamforming Optimization

A. Large-timescale Pinching Beamforming Optimization

B. Small-timescale Baseband Beamforming Optimization

C. Overall Two-Timescale Optimization Algorithm Design and Property Analysis

Algorithm 2 applies alternating optimization at the beginning of each time block and updates baseband beamforming with refined Eve CSI during each CPI.

C. Overall Two-Timescale Optimization Algorithm Design and Property Analysis

1) Convergence Analysis:

The proposed alternating optimization and sequential timescale updates produce non-decreasing objective values and converge under the feasible-set and power constraints, with complexity split between large- and small-timescale processing.

  • Each alternating-optimization iteration non-decreasingly improves the original objective through element-wise pinching updates and SCA beamforming updates.Source: 1) Convergence Analysis · p. 8
  • Convergence is guaranteed because the sum secrecy rate is bounded by the feasible set and total transmit-power constraint.Source: 1) Convergence Analysis · p. 8
  • The two-timescale algorithm performs pinching beamforming at the beginning of each time block and baseband beamforming updates within each CPI.Source: 2) Complexity Analysis · p. 8, 1) Convergence Analysis · p. 8
  • The large-timescale complexity combines element-wise pinching beamforming with interior-point processing, while the small-timescale stage updates baseband beamforming separately.Source: 2) Complexity Analysis · p. 8
  • The overall Algorithm 2 complexity is expressed by combining the large-timescale AO cost with the small-timescale baseband-update cost.Source: 2) Complexity Analysis · p. 8

V. TWO-TIMESCALE ISAC-ENABLED SECURE COMMUNICATIONS FRAMEWORK FOR SINGLE-WAVEGUIDE PASS

In the single-waveguide setting, rank-one transmission limits the system to one independent data stream, so the framework separates communication and sensing phases while updating power across CPIs.

  • A single waveguide provides one effective spatial dimension, yielding a rank-one channel that supports at most one independent data stream.Source: §V · p. 8
  • Each time block contains separate communication and sensing phases in the proposed two-timescale framework.Source: §V · p. 9, Figure 2 · p. 9
  • Large-timescale pinching beamforming maximizes average secrecy rate subject to a minimum echo-signal-power requirement in the sensing phase.Source: §V · p. 9
  • Small-timescale baseband power allocation is updated across different CPIs.Source: §V · p. 9
  • The sensing-phase duration is assumed not to exceed one CPI, while communication–sensing time allocation is left for future study.Source: A. Signal Model · p. 9

B. Problem Formulation

The single-waveguide problem maximizes block-average secrecy rate through joint power and pinching-beamforming design, then uses an element-wise solution with CPI-level power updates and feasibility checks.

B. Problem Formulation

  • The optimization jointly selects sensing power, communication powers, and the pinching-beamforming vector to maximize average secrecy rate over each time block.Source: B. Problem Formulation · p. 9
  • Transmit-power constraints limit communication power and received echo power is characterized through the round-trip channel vector.Source: B. Problem Formulation · p. 9
  • Setting sensing power to Pmax enlarges the feasible region because sensing power appears only in constraints and not in the secrecy-rate objective.Source: B. Problem Formulation · p. 9

C. Proposed Solution

  • When Bob has an effective channel-quality advantage over Eve, the secrecy rate increases monotonically with communication power.Source: C. Proposed Solution · p. 9
  • The algorithm initializes pinching beamforming and updates it through element-wise one-dimensional searches over the feasible deployment set.Source: C. Proposed Solution · p. 10
  • Small-timescale power allocation is performed in each CPI, with communication power set according to the secrecy-rate condition.Source: C. Proposed Solution · p. 10
  • Because predicted Eve states may be inaccurate, the secrecy condition is rechecked using refined CSI; if it fails, communication power is set to zero.Source: C. Proposed Solution · p. 10
  • Pinching beamforming is optimized only at each time block’s beginning, and Algorithm 3 has complexity O(I1NT NtMt).Source: C. Proposed Solution · p. 10

VI. SIMULATION RESULTS

Numerical experiments evaluate the proposed two-timescale ISAC-enabled secure communications framework in both multiple- and single-waveguide PASS scenarios under specified system parameters.

  • The numerical study verifies the effectiveness of the proposed framework in both multiple- and single-waveguide scenarios.Source: §VI · p. 10
  • The multiple-waveguide setup uses Nt = 2 waveguides, Mt = 8 PAs per waveguide, and Nr = 2 LCXs for echo reception.Source: A. Simulation Setup · p. 10
  • Waveguides and LCXs have length L = 10 m, height d = 3 m, and both inter-waveguide and inter-LCX spacing equal 5 m.Source: A. Simulation Setup · p. 10
  • The simulation parameters include a velocity-related value of vy = 0.02 (m/s)2.Source: A. Simulation Setup · p. 10

B. Multiple-Waveguide Scenario

In the multiple-waveguide scenario, the proposed framework tracks Eve’s mobility and jointly optimizes pinching and baseband beamforming to improve secrecy performance. PASS outperforms conventional MIMO benchmarks and benefits from additional waveguides and PAs.

Evaluation setup

  • The BS compares PASS with fully digital MIMO, hybrid massive MIMO, and random-position baselines for secrecy-rate evaluation.The multiple-waveguide setup includes dedicated RF chains and considers Eve trajectory tracking alongside secrecy-rate optimization.Source: B. Multiple-Waveguide Scenario · pp. 10–11

Eve-state tracking

  • Eve’s estimated trajectory closely matches the ground truth, while position errors are much smaller than velocity errors.Unmodeled velocity variances limit velocity tracking and data fusion, whereas position estimation is less affected over one CPI.Source: B. Multiple-Waveguide Scenario · p. 11

Optimization convergence

  • The AO algorithm’s average secrecy rate improves sharply in the first iterations and stabilizes after about five iterations.This behavior indicates relatively low iterative overhead for the proposed two-timescale optimization.Source: B. Multiple-Waveguide Scenario · p. 11, Figure 4 · p. 11

Secrecy-rate performance

  • 10.3 bps/Hz: PASS at Nt = 2 and Pmax = 20 dBm, versus 5.8 bps/Hz for MIMO and 7.6 bps/Hz for massive MIMO.Across the considered schemes, average secrecy rate increases monotonically with BS maximum transmit power, while PASS significantly outperforms both benchmarks.Source: B. Multiple-Waveguide Scenario · p. 11, Figure 5 · p. 11

Impact of PA number

  • 26 %: PASS’s average secrecy rate increases when the number of PAs per waveguide grows from 2 to 10.The improvement is attributed to additional spatial degrees of freedom, while PASS avoids the larger phase-shifter count generally required by hybrid MIMO.Source: B. Multiple-Waveguide Scenario · p. 11, Figure 6 · p. 12

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