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Waveform Randomization for Secure ISAC

Zexin Fang, Bin Han, Shuangyang Li, Hans D. Schotten

arXiv:2610.07994v1eess.SP

TL;DR

ISAC reuses radio resources for sensing and communication, but repeated sensing references can expose activity to unauthorized tracking. This paper randomizes the sensing waveform with phase keys and tangent AN, while coordinated legitimate receivers use a shared reference. The reported results indicate that Eve's sensing capability remains strongly suppressed under favorable geometry, including when she observes direct and reflected paths, while key reconstruction remains limited by residual mismatch and imperfect AN removal.

  • Problem

    ISAC's reuse of resources for sensing and communication can expose sensing activity and repeated references to unauthorized tracking or identification.

    Source: §I · p. 1

  • Method

    The design combines a phase-keyed Fourier-curve waveform with tangent AN so legitimate nodes can recover the reference while Eve observes a randomized waveform.

    Source: §I · p. 1

  • Results

    The proposed design strongly suppresses Eve's sensing capability under favorable geometry, including when she exploits both direct- and reflected-path observations.

    Source: §V · p. 6

  • Takeaways & Limitations

    Residual key mismatch and imperfect AN removal still limit Eve's coherent sensing after phase-key reconstruction, while accurate recovery incurs high computational complexity.

    Source: §V · p. 6

    Multi-target and multi-Eve scenarios closer to practical B5G/6G deployments remain for future validation.

    Source: §V · p. 6

Abstract

from arXiv · show

This paper studies waveform-level security for Integrated Sensing and Communication (ISAC). Instead of relying on spatial beamforming or power allocation, we randomize the sensing waveform itself using phase keys and tangent Artificial Noise (AN) applied to a Fourier-curve constellation. Coordinated legitimate nodes know the key and recover the sensing reference, while Eve observes only a randomized waveform and cannot construct the correct coherent matched reference. We consider an Unmanned Aerial Vehicle (UAV)-mounted Eve with a dominant Line-of-Sight (LOS) link who fully exploits favorable geometry, including a bypass scenario where Eve listens to both the direct and echo sides to circumvent our design. We further consider a stronger Eve that attempts phase-key reconstruction from long-term observations; even then, residual key mismatch structurally degrades correlation and AN cancellation, while accurate key recovery incurs high computational complexity. Numerical results show that the proposed design reduces Eve's probability of detecting the sensing reference using non-coherent detection and, in the bypass case, substantially suppresses her correct-delay lock probability, while the legitimate receiver reliably locks onto the reference through echo accumulation.

I. INTRODUCTION

ISAC reuses radio resources for communication and sensing, but its repeated sensing references can expose activity to unauthorized tracking. The paper protects the waveform itself with phase keys and tangent AN, using a Fourier-curve constellation whose harmonic components are determined by one phase index.

I. INTRODUCTION

  • A UAV-borne Eve can reposition for a dominant LOS link, while ghost-target ambiguity designs do not hide the true echo or sensing activity from prolonged observation.The paper therefore asks how to hide the sensing reference from Eve while keeping it decodable to a cooperating receiver.Source: §I · p. 1
  • The proposed waveform-level defense uses phase keys and tangent AN so legitimate nodes recover the sensing reference while an Eve without the phase key sees a randomized waveform.Unlike spatial-domain defenses, this approach protects what waveform is observed.Source: §I · p. 1

A. Fourier-Curve Modulator

  • Each coded-bit group selects one phase index, which maps to a k-dimensional harmonic symbol vector whose components are jointly determined by that index.The vector's components can map to parallel subcarriers, orthogonal signaling dimensions, or successive resource elements.Source: A. Fourier-Curve Modulator · pp. 1–2
  • Differentiating the Fourier-curve symbol vector with respect to its phase traces the curve's local direction, and the tangent perturbation is purely rotational.The tangent has no component along the symbol vector itself.Source: A. Fourier-Curve Modulator · p. 2

B. Tangent AN and Channel

A shared phase-key vector is applied across the Fourier-curve harmonics before tangent AN is added. The key makes the legitimate receiver's codebook match the transmitted symbol geometry, while an unintended receiver without the key faces a mismatch.

B. Tangent AN and Channel

  • Before AN injection, the transmitter applies a shared phase-key vector across the k harmonic components to form the keyed Fourier-curve symbol vector.The legitimate receiver knows the key and builds the keyed codebook directly; without it, an unintended receiver faces a geometry mismatch even before AN.Source: B. Tangent AN and Channel · p. 2
  • For each transmission, one real Gaussian scalar is shared across all k harmonic components, while its signed amplitude is drawn independently for each symbol vector.The tangent direction is deterministic for a fixed index, and the symbol vector and tangent are unit-norm and orthogonal.Source: B. Tangent AN and Channel · p. 2
  • After synchronization and channel equalization, the receiver works with a real-valued received symbol vector.Source: B. Tangent AN and Channel · p. 2

C. QPSK Sensing-Waveform Design

The sensing sequence uses QPSK phases mapped to weighted OFDM subcarrier vectors, with a discrete search optimizing sidelobe behavior. Cooperating base stations share the schedule and key–AN pair and correlate a known reference, reducing residual timing uncertainty through echo accumulation.

C. QPSK Sensing-Waveform Design

  • The QPSK sensing sequence is mapped to weighted subcarrier vectors and transformed into time-domain OFDM bursts, with subcarrier-vector correlation equivalent to burst correlation.Inactive subcarriers are set to zero before the inverse OFDM transform.Source: C. QPSK Sensing-Waveform Design · p. 2
  • The discrete QPSK phase-sequence objective penalizes total sidelobe energy and peak sidelobe, with λ = 10 emphasizing Peak Sidelobe Ratio.The combinatorial optimization uses discrete coordinate descent with random restarts, repeated for each harmonic order k.Source: C. QPSK Sensing-Waveform Design · p. 2
  • The cooperating base stations share the burst schedule and key–AN pair over secure backhaul, then correlate the known reference over the expected delay window.After compensating known front-end and channel distortions, echo accumulation further reduces remaining timing uncertainty.Source: C. QPSK Sensing-Waveform Design · p. 2
  • Algorithm 1 searches QPSK phase sequences through coordinate updates across random or structured restarts and returns the best sequence found.Each chip is set to the phase that minimizes the objective while the other chips remain fixed; a restart stops when a sweep makes no improvement.Source: C. QPSK Sensing-Waveform Design · p. 2

1) Unknown-AN Maximum Likelihood Receiver:

Because the communication receiver does not know the candidate symbol's tangent direction, it marginalizes the random AN rather than estimating it. Its covariance-aware metric accounts for candidate-dependent AN covariance, and soft demapping supports coded control and payload while sensing remains uncoded.

1) Unknown-AN Maximum Likelihood Receiver:

  • The receiver marginalizes the random AN because the candidate symbol is unknown and its tangent direction is not known until that candidate is decided.The AN raises variance along the tangent expected under each candidate.Source: 1) Unknown-AN Maximum Likelihood… · p. 2
  • The candidate metric combines an ordinary Euclidean penalty with a correction for candidate-dependent covariance, accounting for AN along the candidate's expected tangent.The hard decision selects the candidate with the smallest metric; the Euclidean baseline omits this covariance correction.Source: 1) Unknown-AN Maximum Likelihood… · pp. 2–3
  • The soft demapper uses log-sum-exp, and rate-1/2 LDPC decoding is applied to coded control and payload while the sensing waveform remains uncoded.The sensing receiver instead correlates with the known reference.Source: 1) Unknown-AN Maximum Likelihood… · p. 3

III. THREAT MODEL

The threat model gives Eve favorable LOS geometry and considers both ordinary non-coherent detection and a bypass using direct- and reflected-path observations. It also allows Eve to exploit long-term observations and search for phase keys.

III. THREAT MODEL

  • Eve is assumed to use non-coherent detection on both paths, exploit long-term observations for cross-burst reference reconstruction, and search the phase-key space.If her key estimate is sufficiently accurate, she can recover the nominal sensing sequence and form a coherent reference.Source: §III · p. 3
  • The LOS-only, single-tap channel model is explicitly a best case for Eve and favors her detection performance.The passage attributes this setting to UAV links at typical altitudes and frequencies, where multipath is attenuated below the direct path.Source: §III · p. 3
  • In the bypass model, Eve uses the direct path as a surrogate and cross-correlates it with the reflected-path observation over candidate delays.The direct and reflected signals are modeled as scaled, delayed copies of the transmitted burst plus independent AWGN; the null and target-present hypotheses are tested at a threshold set for the required false-alarm rate.Source: §III · p. 3
  • Eve searches candidate delay bins because the echo delay is unknown and need not align with the grid; the detection threshold applies to correlation magnitude.The threat model focuses on delay-only detection.Source: §III · p. 3

1) Noise Model:

The noise model treats Eve's statistic as a correlation of two noisy signals, with its null-versus-target asymmetry arising from a signal-noise cross-term under the target-present hypothesis.

1) Noise Model:

  • The shared noise cross-term contributes under both hypotheses, so any statistic-variance asymmetry must come from the target-present signal-noise cross-term.Under the strong-direct-link approximation, the direct observation acts as a quasi-clean reference and this cross-term is negligible, leaving echo-channel noise variance as the dominant term.Source: 1) Noise Model · p. 3
  • With the cross-term neglected, the noise variance is σ_w^2 E_s, recovering the standard complex-Gaussian form.This conclusion is stated for the strong-direct-link regime.Source: 1) Noise Model · p. 3

2) Correct-Bin and False-Lock Probabilities:

Mainlobe alignment bounds correct-bin detection, but the bound is not the actual correct-lock probability except under ideal direct-link and waveform conditions.

3) Role of the Mainlobe:

  • The mainlobe alignment |χ[0]|^2 bounds correct-bin detection, reducing to the classical matched-filter result only with a perfectly clean direct link and ideal waveform.The authors characterize it as an upper bound rather than the true Pcorr.Source: 3) Role of the Mainlobe · p. 4

4) Role of the Sidelobes:

Sidelobes can create false detection crossings without improving ranging accuracy, so detection probability alone does not fully characterize ranging reliability. The section also reports communication-security results for keyed waveforms and demodulators.

4) Role of the Sidelobes:

  • A large off-peak autocorrelation sidelobe can cross the threshold at an incorrect delay, raising Pfalse and PD without improving ranging accuracy.Consequently, a lower-sidelobe waveform can have lower PD while maintaining equal or higher Pcorr; PSR alongside mainlobe magnitude characterizes ranging reliability more fully than PD alone.Source: 4) Role of the Sidelobes · p. 4

A. Validation of Secure Communication

  • With phase keying, Eve's BER remains high even with covariance-aware demapping, while the keyed legitimate receiver sees no performance degradation.As harmonic dimension k increases, BER decreases for both demodulators, and the covariance-aware advantage widens; higher k trades spectral efficiency for lower BER.Source: A. Validation of Secure Communication · p. 4
  • For 1/2 LDPC-coded 64-PSK at 4 and 8 dB, the overall trends match the uncoded QPSK case, while Euclidean decoding performs worse than in the QPSK scenario because the higher-order constellation has smaller neighboring-symbol distances.The Euclidean metric is therefore more sensitive to noise and AN perturbation, independently of keying.Source: A. Validation of Secure Communication · p. 4

B. Validation of waveform design and legitimate sensing

The optimized waveform improves legitimate sensing quality, and echo accumulation supports reconstruction despite residual impairments. Key refresh and tangent AN reduce Eve’s detection and correct-delay lock, including under favorable bypass geometry and attempted key recovery.

B. Validation of waveform design and legitimate sensing

  • The optimized waveform achieves higher PSR than the random baseline, with PSR around 20 dB for most harmonic dimensions.The QPSK alphabet causes dips at k = 4 and k = 8 because the harmonic sum can vanish at those orders, reducing waveform diversity.Source: B. Validation of waveform design and… · p. 4
  • Across accumulated echoes, reconstruction error converges toward the no-AN baseline despite residual timing error and channel distortion.The receiver uses the shared key-AN realization and compensates known front-end and channel distortions.Source: B. Validation of waveform design and… · p. 4, Figure 3 · p. 5

C. validation of secure sensing

  • Keying lowers the optimized sequence’s PC from 1.0 to 0.386; adding AN drives it below the unprotected-random baseline near β ≈ 0.3 and to 0 from β ≈ 0.6.With independent AN but the same phase key, the optimized sequence retains high PC, indicating that key updates—not AN alone—are essential to suppression.Source: C. validation of secure sensing · p. 4, Table II · p. 5
  • When Eve estimates phase keys with average error σφ = 0.25π, she can barely identify the sequence through waveform-based detection.A residual key mismatch degrades correlation and AN cancellation; at σφ = 0.1π, exhaustive search requires about 3.20 × 10^6 key hypotheses per burst.Source: C. validation of secure sensing · pp. 5–6
  • Eve’s symbol-wise key-search detector requires CEve = 4N⌈2/σφ⌉^k metric evaluations per burst, rather than enumerating all key-and-symbol-sequence hypotheses.The attack evaluates four constellation metrics per QPSK symbol.Source: C. validation of secure sensing · p. 5
  • In the bypass case, optimized and random keyed-AN sequences have similar Pcorr and PD because keying and AN disrupt the optimized sequence’s sensitive phase alignment.The comparison assumes Eve has line of sight to both transmitter and target, with the direct path 4–8 dB stronger than the reflected path.Source: C. validation of secure sensing · p. 5, Figure 4 · p. 6
  • At 1 dB average reflected signal, Eve’s Pcorr remains below 0.1, while the legitimate receiver reaches 0.92 after 10 echoes.The comparison assumes Eve knows the legitimate receiver’s location and exploits its beamforming gain.Source: Figure 4 · p. 6, C. validation of secure sensing · p. 6

V. DISCUSSION AND CONCLUSION

Waveform randomization with Fourier-curve modulation, phase keys, and tangent AN suppresses Eve’s sensing capability even when she exploits direct and reflected paths under favorable geometry. Residual phase-key mismatch and imperfect AN removal constrain coherent sensing, while future work targets joint optimization and broader validation.

  • Eve’s sensing capability is strongly suppressed even when she exploits both direct- and reflected-path observations under favorable geometry.Source: §V · p. 6
  • Table III reports Eve’s symbol-estimation SER after key mismatch for N = 64, k = 5, β = 0.5, and SNR = 1 dB; zero mismatch is the legitimate exact-key reference.It gives Eve’s symbol-wise complexity as CEve = 4NQ5.Source: Table III · p. 6
  • Residual phase-key mismatch and imperfect AN removal still limit Eve’s coherent sensing, while accurate key recovery incurs high computational complexity.Source: §V · p. 6
  • Future work will jointly optimize the phase key, tangent-AN power, and harmonic dimension k under sensing-accuracy and communication-reliability constraints, and validate multi-target and multi-Eve scenarios.The stated validation target is closer to practical B5G/6G deployments.Source: §V · p. 6
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