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Sensing-Driven Secure Transmission with Mobile Eavesdropper Tracking in RIS-Assisted ISAC

Jie Li, Ning Wang, Zhendong Li, Ze Li, Lingfeng Shen, Zhongyun Li, Jiakang Zheng

arXiv:2610.23437v1eess.SP

TL;DR

Mobile Eve motion makes eavesdropping channels time-varying and can leave security decisions based on outdated information. The paper combines multi-view RIS-assisted sensing and motion prediction with joint transmission design; simulations report improved tracking and secure transmission against mobile Eves.

  • Problem

    Mobile Eve motion changes the eavesdropping channel, making timely and accurate Eve position and motion information important for secure transmission.

    Source: §I · p. 2

  • Method

    The framework uses multi-view BS/RIS sensing to localize and predict Eve motion, then jointly optimizes BS beamforming and RIS phases using the predicted Eve state.

    Source: §I · pp. 4–5

  • Results

    Numerical evaluations report lower tracking errors with delay-aware IMM tracking and benefits from sensing and trajectory prediction for secure transmission against mobile Eves.

    Source: §I · p. 5, §V · p. 24

  • Takeaways & Limitations

    The simulations support using sensing and trajectory prediction to adapt secure transmission in scenarios with mobile Eves.

    Source: §I · p. 5

Abstract

from arXiv · show

The mobility of potential eavesdroppers (Eves) poses a critical challenge to physical-layer security (PLS) in integrated sensing and communication (ISAC) systems, since rapidly varying Eve positions lead to time-varying eavesdropping channels and outdated security decisions. To address this challenge, this paper investigates sensing-driven secure transmission for reconfigurable intelligent surface (RIS)-assisted ISAC systems with a maneuvering Eve. To this end, by exploiting the dual functionality of the ISAC waveform, a multi-view angle estimation method jointly exploiting the base station (BS) and RIS is developed based on MUSIC and maximum likelihood estimation (MLE), enabling three-dimensional (3D) Eve localization, whose accuracy is characterized by the Cramer-Rao lower bound (CRLB). Subsequently, an interacting multiple model extended Kalman filter (IMM-EKF) with out-of-sequence measurement (OOSM) compensation is employed to track and predict the maneuvering Eve. Based on the predicted trajectory, the time-varying eavesdropping channel is updated, and the transmit beamforming and RIS phase shifts are jointly optimized subject to a sensing CRLB constraint. Furthermore, an alternating optimization (AO) algorithm integrating fractional programming, semidefinite relaxation (SDR), and Riemannian manifold optimization is developed to solve the resulting non-convex problem. Finally, numerical results demonstrate the effectiveness of the proposed approach in accurately tracking maneuvering Eves and enhancing secure transmission in dynamic ISAC environments.

I. INTRODUCTION

The introduction frames mobile-Eve channel aging as a security challenge and proposes sensing-driven RIS-assisted ISAC to localize, track, and predict Eve motion for adaptive transmission. It also outlines the system assumptions and evaluates localization, tracking, and secrecy performance.

I. INTRODUCTION

  • Mobile Eve motion can make acquired Eve CSI outdated and degrade security, while integrating sensing uncertainty, delayed observations, and motion prediction into joint beamforming and RIS design remains largely unexplored.Earlier RIS-assisted security studies commonly assume Eve locations or CSI are known or unchanged during transmission.Source: §I · pp. 2–4
  • The proposed framework reuses the downlink waveform and RIS configurations for multi-view 3D Eve localization, then uses estimated motion to update the eavesdropping channel and jointly design beamforming and RIS phases.Localization accuracy is characterized by a CRLB, and transmission design has communication-quality and sensing-accuracy constraints.Source: §I · pp. 4–5
  • MUSIC and maximum likelihood estimation extract angular parameters, IMM-EKF with OOSM compensation tracks maneuvering Eve, and AO with SDR and manifold optimization solves the coupled design.The paper also analyzes the proposed algorithm’s convergence and computational complexity.Source: §I · p. 5
  • Simulations evaluate localization against benchmark methods, tracking under different motion patterns and sensing delays, and secrecy performance against representative benchmarks.The reported comparisons demonstrate benefits from exploiting sensing and trajectory prediction for secure transmission against mobile Eves.Source: §I · p. 5

Notation:

  • Bold lowercase and uppercase letters denote vectors and matrices, while transpose, conjugate transpose, conjugate, trace, and Frobenius norm have designated notation.The notation section also defines diagonal matrices, number sets, complex Gaussian distributions, real and imaginary parts, expectation, and vector norms.Source: Notation · pp. 5–6

II. SYSTEM MODEL

  • The system comprises a multi-antenna BS, an RIS, Bob, and a mobile UAV Eve whose channel varies over time and is reconstructed from sensing-assisted location estimates.The RIS applies unit-modulus phase shifts, and the fixed BS-RIS channel and cooperative Bob CSI are assumed accurately obtainable.Source: §II · pp. 6–7

III. RADAR SENSING AND ANGULAR PARAMETER ESTIMATION

The sensing stage reuses the downlink waveform and changes RIS phase configurations to obtain spatially diverse observations. These observations support angular estimation by separating direct and RIS-dependent echo components.

III. RADAR SENSING AND ANGULAR PARAMETER ESTIMATION

  • The BS reuses the downlink communication waveform for radar sensing, with TDD channel reciprocity assumed for the uplink Eve-to-BS echo.The beamforming vector is power-limited and the transmitted waveform has unit energy.Source: §III · p. 8

A. Angular Parameter Estimation

  • Changing RIS phase configurations provides spatially diverse sensing observations with different spatial signatures for estimating Eve’s direction from BS and RIS observations.The received echo includes a target scattering coefficient treated as constant within a coherent processing interval and independently varying between intervals.Source: A. Angular Parameter Estimation · p. 8, §III · p. 8
  • Orthogonal RIS phase coding, including DFT-based patterns, separates the RIS-independent direct echo from RIS-dependent echo information in the collected snapshots.The snapshots are collected after matched filtering.Source: §III · p. 8, A. Angular Parameter Estimation · p. 9

1) BS-Eve Direction Estimation:

The method estimates Eve directions from both direct BS echoes and RIS-dependent echoes, then uses those complementary angular observations for localization.

1) BS-Eve Direction Estimation:

  • The direct BS-Eve direction is estimated by maximizing a MUSIC spatial spectrum built from the direct-echo noise subspace.The direct channel is modeled with the BS array response and Eve’s azimuth and elevation angles.Source: 1) BS-Eve Direction Estimation · p. 9

2) RIS-Eve Direction Estimation:

  • RIS-dependent echoes provide additional angular information, with least-squares estimates of linear echo coefficients reducing MLE to a two-dimensional search over RIS direction.The echo model includes cross-path and RIS-mediated round-trip components.Source: 2) RIS-Eve Direction Estimation · pp. 9–10

B. Joint Angle-Based Position Estimation

The section combines BS and RIS angular estimates to localize Eve in 3D, characterizes localization accuracy with a CRLB, and describes delay-aware tracking and model initialization.

B. Joint Angle-Based Position Estimation

  • Geometric constraints from the BS and RIS convert their estimated azimuth and elevation angles into Eve’s position through nonlinear least squares.The angular observation vector contains four angles, two observed from each site.Source: B. Joint Angle-Based Position Estimation · pp. 10–11

C. CRLB-Based Localization Accuracy Analysis

  • Under a small-error Gaussian angular measurement model, the Fisher information matrix characterizes the position estimate’s CRLB.The model relates measured angles to Eve’s position through a theoretical angle function.Source: C. CRLB-Based Localization Accuracy… · p. 11

D. Delay-Aware IMM-EKF Tracking Model

  • The delay-aware tracking model uses a 10-dimensional state and CV, CA, and CT motion modes; delayed observations have bounded, known latency after timestamping.The state comprises 3D position, velocity, acceleration, and horizontal yaw rate.Source: D. Delay-Aware IMM-EKF Tracking Model · pp. 11–12

1) Model Initialization:

  • Initial motion models are fitted to preliminary position estimates, while BIC compares relative fit and initial IMM model probabilities remain uniform.The initialization passage describes linear or quadratic position-polynomial fits for CV and CA models.Source: 1) Model Initialization · p. 12

2) Delay-Aware IMM Filtering:

The IMM filter propagates mode-specific state estimates and combines them through model mixing and parallel prediction, retaining recent posteriors for delayed measurements.

2) Delay-Aware IMM Filtering:

  • Each mode evolves with its own transition matrix and process-noise covariance, with the nonlinear CT dynamics linearized in the EKF framework.The process noise represents uncertainty from unmodeled dynamics and random maneuvers.Source: 2) Delay-Aware IMM Filtering · p. 13

3) Model Mixing & Parallel Prediction:

  • Mode mixing probabilities form each model’s mixed initial condition before independent prediction, measurement updates, and storage in a finite buffer sized for allowable latency.Each model uses its corresponding Kalman or extended Kalman update.Source: 3) Model Mixing & Parallel Prediction · p. 13

4) OOSM Update & Forward Propagation:

The tracking procedure compensates delayed observations at their historical time, propagates corrected estimates forward, updates mode probabilities, and fuses the state for channel updating.

4) OOSM Update & Forward Propagation:

  • For each motion hypothesis, OOSM compensation updates the historical posterior with the delayed measurement and propagates the corrected state to the current step.The forward transition operator spans the delay interval, using mode-specific transitions for CV, CA, or CT.Source: 4) OOSM Update & Forward Propagation · pp. 13–14

5) Likelihood Evaluation and Model Probability Update:

6) Final State Fusion:

  • The fused IMM estimate yields Eve’s predicted position, which updates the time-varying Eve channel for subsequent secure-transmission optimization.Source: 6) Final State Fusion · pp. 14–15

E. Computational Complexity Analysis

The framework optimizes transmit beamforming and RIS phases using the predicted Eve location, maximizing secrecy rate subject to sensing accuracy. Alternating optimization addresses the coupled non-convex design, with fractional programming, SCA, and SDR used for beamforming.

E. Computational Complexity Analysis

  • The sensing and tracking framework’s complexity is dominated by angular estimation and IMM tracking, with separate complexity terms for angle estimation, 3D position fitting, and tracking.The BS-Eve MUSIC stage has complexity O(M 2Q + M 3 + GBSM 2), RIS-Eve angular fitting has complexity O(GRISQMN), and 3D position fitting has complexity O(Ipos).Source: E. Computational Complexity Analysis · p. 15

IV. JOINT TRANSMIT BEAMFORMING AND RIS PHASE SHIFT OPTIMIZATION ALGORITHM

  • Using the predicted Eve location, the design jointly optimizes transmit beamforming and RIS phase shifts for secrecy rate while satisfying a sensing-accuracy requirement.The Eve-related channels are reconstructed from the IMM tracker’s predicted position.Source: §IV · p. 15

A. Transmit Beamforming Optimization with Fixed RIS Phase

  • With RIS phases fixed, Dinkelbach fractional programming handles the secrecy-rate objective, while SCA and SDR address the non-convex beamforming objective and CRLB constraint.The stated sources of non-convexity include an indefinite matrix objective and the inverse-FIM CRLB constraint.Source: A. Transmit Beamforming Optimization… · p. 17

1) SCA Approximation of CRLB Constraint:

The beamforming procedure locally linearizes the CRLB constraint, solves an SDR problem iteratively within the Dinkelbach update, and recovers a beamforming vector from the resulting matrix.

1) SCA Approximation of CRLB Constraint:

  • At each SCA iteration, the CRLB metric Ψ(W) is locally approximated around the previous matrix iterate, replacing the original constraint with a linearized constraint.The approximation uses the gradient of the CRLB metric with respect to the Hermitian matrix variable W.Source: 1) SCA Approximation of CRLB Constraint · p. 17

2) SDR-Based Beamforming Optimization:

  • The SDR step temporarily removes the rank-one constraint, and SCA iterations continue until convergence before the Dinkelbach parameter is updated.The Dinkelbach iteration terminates when successive parameter values differ by no more than ϵη.Source: 2) SDR-Based Beamforming Optimization · pp. 17–18

3) Beamforming Vector Recovery:

  • If the optimized matrix is rank one, its beamforming vector is recovered directly; otherwise, Gaussian randomization generates candidate vectors for selection.The passage also describes eigenvalue decomposition as a recovery route and candidate scaling to satisfy the transmit-power constraint.Source: 3) Beamforming Vector Recovery · p. 18

B. RIS Phase Shift Optimization via Riemannian Manifold Optimization

With the beamformer fixed, the RIS phase problem is optimized over the complex circle manifold. Equivalent-channel expressions support the objective and its manifold gradient calculation.

B. RIS Phase Shift Optimization via Riemannian Manifold Optimization

  • With the beamforming vector fixed, RIS phase optimization imposes unit modulus on each element, placing the phase vector on the complex circle manifold.The optimization subproblem is formulated for the RIS phase-shift vector under those elementwise constraints.Source: B. RIS Phase Shift Optimization via… · p. 18

1) Equivalent Channel Representation:

  • For fixed beamforming, channel projection vectors express Bob’s and Eve’s received signals in equivalent-channel form, yielding the objective used for phase optimization.The passage defines the projection vectors using the direct and RIS-reflected channel terms.Source: 1) Equivalent Channel Representation · pp. 18–19

2) Riemannian Gradient Calculation:

  • Wirtinger calculus gives the Euclidean gradient, which is projected onto the tangent space to obtain the Riemannian gradient on the complex circle manifold.The passage defines zB and zE from the direct terms and channel projections before calculating the Euclidean gradient.Source: 2) Riemannian Gradient Calculation · p. 19

3) Riemannian Conjugate Gradient (RCG) Algorithm:

The joint procedure alternates beamforming optimization and RIS phase optimization. The RIS step uses a Riemannian conjugate-gradient iteration with manifold line search and retraction.

3) Riemannian Conjugate Gradient (RCG) Algorithm:

  • The Riemannian conjugate-gradient step uses vector transport, Armijo backtracking, and retraction to update the RIS phase vector on the complex circle manifold.The step size is chosen by Armijo backtracking to guarantee sufficient decrease, and the iteration stops when the objective change is below ϵRIS.Source: 3) Riemannian Conjugate Gradient (RCG)… · pp. 19–20
  • Algorithm 1 alternates between constructing channels for fixed RIS phases, optimizing the beamformer, and optimizing RIS phases with the RCG algorithm.The algorithm initializes the RIS phase vector and repeats the alternating updates until the outer stopping condition is met.Source: 3) Riemannian Conjugate Gradient (RCG)… · p. 20
  • Within each beamforming update, the algorithm iterates the SCA semidefinite program and Dinkelbach parameter update, then recovers a beamformer by eigenvalue decomposition or Gaussian randomization.The inner loops stop using their respective SCA and Dinkelbach tolerances.Source: 3) Riemannian Conjugate Gradient (RCG)… · p. 20

C. Computational Complexity Analysis

The paper reports accurate mobile-Eve tracking and improved secrecy versus schemes using static or outdated Eve information. Simulations also examine algorithm convergence, secrecy-rate trends, and tracking accuracy as system parameters vary.

C. Computational Complexity Analysis

  • Active beamforming and passive RIS phase-shift subproblems are the main sources of AO complexity; each RCG iteration for the RIS subproblem requires O(NM) operations.The beamforming subproblem uses SDR, while the RIS subproblem computes channel projection vectors and Euclidean gradients at each RCG iteration.Source: C. Computational Complexity Analysis · pp. 20–21

V. NUMERICAL RESULTS

  • The AO algorithm converges in approximately 10 iterations under different system configurations, while secrecy rate increases with transmit power.The reported power trend is attributed to power margins remaining after the radar sensing constraint is satisfied.Source: §V · p. 21, Figure 2 · p. 22
  • At the same transmit power, BS arrays with more antennas achieve higher secrecy rates than smaller arrays.Secrecy rate also increases monotonically with transmit power across the considered BS array configurations.Source: §V · p. 21, Figure 3 · p. 22
  • A larger BS array aperture improves angular resolution, Eve localization accuracy, and state information for subsequent secure transmission.The larger array also provides spatial gains and beamforming degrees of freedom to enhance Bob's link and suppress Eve under sensing constraints.Source: §V · pp. 22–23
  • As transmit power increases, the estimated 3D trajectory approaches ground truth and trajectory-estimation error decreases monotonically.The paper presents the trajectory comparison and error trend in Figs. 4 and 5, respectively.Source: §V · pp. 23–24, Figure 4 · p. 23, Figure 5 · p. 23
  • Secrecy performance improves as the number of RIS elements increases.The paper attributes this trend to greater passive beamforming gain and finer spatial degrees of freedom for focusing signals toward Bob while suppressing Eve's communication rate.Source: Figure 6 · p. 24, §V · p. 24
  • The delay-aware IMM achieves lower tracking errors than conventional IMM throughout the observation period, despite slight degradation during initial motion-model switching.The initial degradation is attributed to transient effects from delayed updates and forward propagation.Source: §V · p. 24, Figure 7 · p. 25

VI. CONCLUSION

  • The approach achieves accurate Eve tracking under different motion patterns and sensing delays, with improved secrecy versus schemes using static or outdated Eve information.The conclusion identifies multiple mobile Eves and learning-based trajectory prediction as future work.Source: §VI · p. 25

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