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Sensing-Assisted Eavesdropper Estimation: An ISAC Breakthrough in Physical Layer Security

Nanchi Su, Fan Liu, Christos Masouros

arXiv:2210.08286v1eess.SP

TL;DR

The paper tackles the practical difficulty that PLS needs information about potential eavesdroppers, especially their directions. It uses ISAC sensing and CAML estimation, then jointly optimizes secrecy rate, CRB, beamforming, and artificial noise under uncertainty. The resulting iterative design improves sensing-security performance and reaches secrecy rates of 7.5 bit/s/Hz and 7.8 bit/s/Hz at the reported SNRs.

  • Problem

    PLS often requires difficult-to-obtain eavesdropper information, such as CSI, SNR, or direction, limiting its practicality in ISAC systems.

  • Method

    The BS estimates eavesdropper directions with an omnidirectional waveform and CAML, then jointly optimizes secrecy rate and CRB using beamforming, artificial noise, and uncertainty-aware wide-main-beam constraints.

  • Results

    7.5 bit/s/Hz at SNR=-22 dB and 7.8 bit/s/Hz at SNR=-15 dB, outperforming isotropical AN methods.

  • Takeaways & Limitations

    The results demonstrate mutual benefits between sensing accuracy and communication security in single- and multi-eavesdropper scenarios.

Abstract

from arXiv · show

In this paper, we investigate the sensing-aided physical layer security (PLS) towards Integrated Sensing and Communication (ISAC) systems. A well-known limitation of PLS is the need to have information about potential eavesdroppers (Eves). The sensing functionality of ISAC offers an enabling role here, by estimating the directions of potential Eves to inform PLS. In our approach, the ISAC base station (BS) firstly emits an omni-directional waveform to search for potential Eves' directions by employing the combined Capon and approximate maximum likelihood (CAML) technique. Using the resulting information about potential Eves, we formulate secrecy rate expressions, that are a function of the Eves' estimation accuracy. We then formulate a weighted optimization problem to simultaneously maximize the secrecy rate and minimize the CRB with the aid of the artificial noise (AN), and minimize the CRB of targets'/Eves' estimation. By taking the possible estimation errors into account, we enforce a beampattern constraint with a wide main beam covering all possible directions of Eves. This implicates that security needs to be enforced in all these directions. By improving estimation accuracy, the sensing and security functionalities provide mutual benefits, resulting in improvement of the mutual performances with every iteration of the optimization, until convergence. Our results avail of these mutual benefits and reveal the usefulness of sensing as an enabler for practical PLS.

I. INTRODUCTION

The paper addresses the difficulty of applying physical layer security in ISAC when eavesdropper information is unavailable. It uses sensing to estimate eavesdropper directions and jointly designs sensing and security objectives so their performance improves iteratively.

  • I. INTRODUCTION: ISAC security is challenging because wireless broadcasting and shared sensing-communication waveforms expose confidential data, while mmWave channels can correlate sensing and communication links.The paper also notes that conventional PLS requires information such as eavesdropper CSI, SNR, or direction, which is difficult to obtain.
  • I. INTRODUCTION: The proposed system uses sensing to assist PLS, addressing prior secure-ISAC designs in which sensing and communication pursue separate objectives.The stated goal is cooperation between sensing and communication for improved security.
  • I. INTRODUCTION: An omnidirectional waveform first estimates potential eavesdropper angles using reflected echoes, known cooperative-user angles, and the CRB as the estimation-performance measure.Known CU locations allow their angles to be removed from the received echoes.
  • I. INTRODUCTION: A weighted optimization minimizes target/eavesdropper CRB and maximizes secrecy rate under beampattern and transmit-power constraints, jointly designing beamforming and artificial noise.The paper also analyzes CRB lower bounds and secrecy-rate upper bounds under the power budget.
  • I. INTRODUCTION: The design widens the sensing main beam according to estimation uncertainty, while iterative accuracy improvements update secrecy and sensing objectives until convergence.The wide beam covers the possible angular region where an eavesdropper may appear.

II. SYSTEM MODEL

The system is a colocated-antenna mmWave ISAC base station that communicates with known users while detecting targets or eavesdroppers whose information is unavailable. Its dual-functional waveform combines user-directed beamforming, data streams, and artificial noise.

  • II. SYSTEM MODEL: The base station has Nt transmit and Nr receive antennas, serves I communication users, detects K targets or eavesdroppers, and knows CU channels but not Eve information.The system uses colocated antennas.
  • II. SYSTEM MODEL: The transmit waveform X ∈ C^Nt×L contains L time-domain snapshots and is formed from dual-functional waveforms sent to the communication users.The rows of X represent transmit waveforms.
  • II. SYSTEM MODEL: The received communication signal includes additive white Gaussian noise, whose entries have variance σ^2.
  • II. SYSTEM MODEL: Communication channels are modeled as slow-fading block Rician channels with line-of-sight and non-line-of-sight components.The LoS component uses an array steering vector associated with the user’s departure angle.
  • II. SYSTEM MODEL: The beamforming matrix W has one beamformer per communication user, while S contains unit-power user data streams and N is transmitter-generated artificial noise.The artificial-noise covariance RN is designed and is positive semidefinite.

B. Radar Signal Model

The radar signal model describes echoed Eve signals using transmit and receive steering vectors, Eve amplitudes, and interference-plus-noise terms. The model is recast in matrix form for subsequent estimation and analysis.

  • Radar echo model: The reflected echo from K Eves is modeled as a sum of transmit waveforms weighted by Eve amplitudes and transmit and receive steering vectors.The steering vectors correspond to colocated uniform linear arrays with half-wavelength antenna spacing.
  • Array model: The receive steering vector uses the ULA geometry, with the array center selected as the reference point.This reference choice simplifies the steering-vector representation.
  • Noise model: The echo model includes interference and AWGN represented by independent circularly symmetric complex Gaussian columns with covariance Q = σ2_R I.The noise covariance is specified for the received radar signal.
  • Security metric: The eavesdropping SNR is defined from the received signal model for each Eve.This quantity supports the later secrecy-rate formulation.
  • Matrix representation: The reflected echo is compactly rewritten using receive steering matrix A(θ), transmit steering matrix B(θ), and diagonal amplitude matrix Λ = diag(βk).This matrix representation collects the directions and complex amplitudes of all Eves.

C. CRB and Secrecy Rate

This section evaluates sensing and security through the CRB and secrecy rate. The CRB characterizes estimation uncertainty, while secrecy rate compares legitimate-user and eavesdropper communication rates.

  • CRB metric: The CRB is used to measure target and Eve estimation performance as a lower bound on unbiased-estimator variance.For multiple Eves, the unknown parameters include their angles and complex amplitudes.
  • CRB metric: The Fisher information matrix contains angle parameters and the real and imaginary parts of Eve amplitudes.Its block structure is specified through the matrix elements used to form the CRB.
  • CRB computation: The CRB matrix is obtained from the Fisher information matrix and the transmit-signal covariance matrix.The covariance matrix of the transmitted waveform enters the sensing-performance calculation.
  • Secrecy-rate metric: The worst-case secrecy rate is defined as the difference between achievable rates at legitimate receivers and eavesdroppers.The corresponding CU and Eve rates are specified separately.

III. BENCHMARK SCHEMES: ISOTROPIC AN-AIDED SECURE BEAMFORMING AND EVE-AWARD AN DESIGN

The benchmark scheme uses artificial noise when Eve-channel information is unavailable. Noise is placed in the orthogonal complement of the communication-user channels so it interferes with Eves without interfering with legitimate users.

  • Isotropic AN-aided secure beamforming: When Eve channels are unknown, artificial noise is isotropically transmitted in the orthogonal-complement subspace of the CU channels.A portion of the transmit power is allocated to this artificial noise.
  • Isotropic AN-aided secure beamforming: The artificial-noise vector is generated from a zero-mean colored-noise vector through the CU-channel orthogonal-complement projector.The projector is V = I_Nt − H^H(HH^H)^−1H.
  • Isotropic AN-aided secure beamforming: The resulting transmit covariance combines the beamformed data covariance with the projected artificial-noise covariance.The covariance includes the term V R̄_n V^H.
  • Performance metrics: The legitimate-user received signal is formed from the designed beamforming and noise components.The benchmark then evaluates the resulting CU SINR and Eve SNR.
  • Benchmark assumptions: The colored-noise covariance is set to the identity matrix when the ISAC BS lacks Eve-channel information.This assumption defines the unknown-channel benchmark setting.

A. AN Refinement Based on Eves’ Information

This scheme refines artificial-noise design using Eve information and estimates Eve parameters with CAML. It begins with omnidirectional probing, then updates the sensing beamwidth using the optimized CRB.

  • AN refinement: With instantaneous Eve-channel realizations known, the transmitter can refine artificial-noise design and formulate a secrecy-rate maximization problem.The benchmark assumes an extreme comparison setting with Gk = σ2_g,k > 0 and i.i.d. Eve channels and data.
  • AN refinement: The resulting secrecy-rate maximization problem is non-convex only in its objective function and is treated using an efficient benchmark formulation.Simulation results are used for comparison with the proposed approach.
  • CAML estimation: CAML estimates Eve directions by applying Capon first for peak directions and AML afterward for Eve amplitudes.This separates direction detection from amplitude estimation.
  • CAML estimation: The initial probing stage uses an omnidirectional waveform, with covariance R̃_X = P0/Nt I_Nt.The corresponding CRBs for target angles and amplitudes are obtained by substituting this covariance into the CRB expressions.
  • Iterative beamwidth design: The Eve angle-estimation error is modeled as zero-mean Gaussian with variance determined by the initial CRB.The initial radar-beampattern main-lobe width is then iteratively updated using the optimized CRB.
  • CAML estimation: With two Eves and three CUs, CAML is evaluated at SNR = 20dB and SNR = -15dB using known CU directions and specified complex amplitudes.The corresponding spatial spectra are shown in Fig. 2.

V. BOUNDS FOR CRB AND SECRECY RATE

This section establishes bounds for the sensing and secrecy objectives so they can be normalized in the later weighted optimization. CRB minimization is expressed through Fisher Information Matrix maximization, while secrecy-rate maximization is treated separately under perfect CSI.

  • The weighted design requires normalizing CRB and secrecy rate because they have different units and magnitudes.Their respective bounds are obtained from separate minimization and maximization problems.
  • The resulting upper bounds on FIM determinant and secrecy rate are used to normalize the two metrics in the weighted objective.
  • Minimizing the CRB matrix inverse is equivalent to maximizing the Fisher Information Matrix determinant.The CRB matrix is the inverse of the FIM matrix.
  • The CRB-bound problem uses the system power budget and is convex, enabling efficient solution with a CVX toolbox.Substituting the optimal beamforming and artificial-noise variables yields the upper bound on the FIM determinant.

B. Secrecy Rate Bound

The secrecy-rate bound is incorporated into a weighted design that jointly accounts for Eve-angle uncertainty, sensing accuracy, secrecy, and transmit power. A wide main beam covers each Eve’s possible directions, while iterative updates link improved estimation to secrecy performance.

  • Problem formulation: The weighted optimization exposes the tradeoff between communication secrecy and Eve-parameter estimation.
  • Problem formulation: Eve-angle uncertainty is represented by an interval around each initially estimated direction, and the sensing main beam covers all possible Eve directions.The main-beam width reflects estimation uncertainty.
  • Problem formulation: The weighting factor ρ controls the relative emphasis on Eve-estimation performance and secrecy rate, while α specifies the wide-main-beam fluctuation.The possible Eve directions are indexed by ϑ_k,n, with ϑ_k,0 denoting the estimated angle.
  • Iterative optimization: The algorithm iteratively updates the optimization variables and repeats until convergence.
  • Performance connection: Secrecy rate depends on Eve-parameter estimation accuracy, so improved sensing performance directly improves secrecy performance.

B. Efficient Solver

The proposed solver transforms the weighted problem through auxiliary variables, fractional programming, and convex reformulations. It then combines CVX-based optimization with a one-dimensional search to obtain the optimized CRB and secrecy rate.

  • Problem reformulation: The secrecy-rate term is recast using auxiliary variables to simplify the weighted objective.
  • Problem reformulation: Fractional programming replaces the fraction term with a coefficient z, producing a reformulated optimization problem.
  • Problem reformulation: The substitution c = 1 b enables an equivalent reformulation in which the optimal y_i variables have a closed form.
  • Numerical solution: The reformulated constraints are solved using the CVX toolbox, while a one-dimensional line search over c uses uniform sampling or golden search.
  • CRB optimization: The CRB determinant minimization is recast with a selection matrix P and Schur-complement conditions, yielding a convex determinant-maximization problem.The matrix P selects the activated Eves’ parameters for CRB minimization.

VII. NUMERICAL RESULTS

Numerical results evaluate the sensing-aided secure ISAC design across beampattern shaping, iterative convergence, Eve-location uncertainty, power budgets, and CU load. The results show improved secrecy and estimation performance under iterative optimization, while uncertainty and system load create trade-offs and feasibility limits.

  • Beampattern evolution: The proposed beampattern narrows its main beam toward a single estimated Eve over successive iterations and handles overlapping main lobes when estimating two Eves.The single-Eve case uses an initial angle of −25°; the two-Eve case uses −25° and 15° with overlapping lobes at the first iteration.
  • Beampattern evolution: The ISAC BS begins with an omnidirectional waveform and CAML-based Eve estimation, then updates the main-beam width from the previous iteration’s CRB.Iterative CRB updates progressively narrow the main lobes toward the Eves’ directions.
  • Iterative convergence: The performance metrics converge after five iterations at SNR=-22 dB, with fewer iterations required at higher SNR.The metrics include root-CRB for amplitude and angle estimation and secrecy rate.
  • Iterative convergence: 7.5 bit/s/Hz and 7.8 bit/s/Hz are the converged secrecy rates at SNR=-22 dB and SNR=-15 dB, respectively, outperforming isotropical AN methods.The convergence figure tracks root-CRB and secrecy-rate behavior across iterations.
  • Uncertainty and power: Secrecy rate first increases and then decreases as Eve-location uncertainty expands, while the proposed algorithm outperforms benchmark AN designs without requiring Eve information.The benchmarks use known G_k or no Eve-channel information, and the proposed weighted optimization uses no Eve information.
  • Uncertainty and power: At P0 = 25 dBm, secrecy rate decreases monotonically with uncertainty width and the weighted optimization is infeasible when ∆θ exceeds 5 degrees.Wider beams require security across a wider angular range and allocate more power to Eve estimation.
  • Security–sensing trade-off: Expanding the uncertain angular interval deteriorates both metrics, while increasing secrecy rate raises CRB and reduces Eve angle-estimation accuracy.The angle difference between the CU and Eve also affects the security–sensing trade-off.

VIII. CONCLUSION

The paper develops sensing-aided secure ISAC in which a dual-functional BS estimates potential Eves while transmitting confidential data. Its weighted design jointly optimizes normalized CRB and secrecy rate to promote cooperation between sensing and communication.

  • Conclusion: The dual-functional BS estimates potential Eves’ amplitudes and directions while simultaneously transmitting confidential data to cooperative users.The conclusion frames sensing and communication as cooperating rather than individual functionalities.
  • Conclusion: The proposed weighted optimization jointly optimizes normalized CRB and secrecy rate for sensing and communication performance.CRB measures estimation performance, while secrecy rate measures security performance.
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