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arxiv: 2604.19040 · v1 · submitted 2026-04-21 · 📡 eess.SP

Integrated Sensing and Communications for Low-Altitude Economy with Deterministic Sensing and Gaussian Information Signals

Xianxin Song , Xianghao Yu , Jie Xu , Derrick Wing Kwan Ng This is my paper

Pith reviewed 2026-05-10 02:40 UTC · model grok-4.3

classification 📡 eess.SP
keywords ISACUAV surveillanceNeyman-Pearson detectorbeamforming optimizationsensing-communication tradeoffdeterministic sensingGaussian signalslow-altitude economy
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The pith

A Neyman-Pearson detector that jointly exploits deterministic sensing and Gaussian information signals maximizes minimum detection probability for UAV intruders under communication constraints.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper develops a bistatic ISAC architecture where a base station transmits superimposed waveforms containing both deterministic sensing components and Gaussian information-bearing signals to serve an authorized UAV while detecting potential intruders in a surveillance region. It derives an optimal Neyman-Pearson detector that uses the structure of both signal types rather than treating the information signal as interference. The transmit beamforming is then optimized to maximize the lowest detection probability across the entire region, subject to a minimum SINR at the authorized UAV and a total power budget. The non-convex design is solved with semi-definite relaxation and successive convex approximation. Simulations confirm better detection than benchmarks and reveal a sensing-communication trade-off driven by power allocation.

Core claim

By transmitting superimposed ISAC waveforms comprising both Gaussian-information-bearing and deterministic sensing components, an NP-based optimal detector can jointly exploit both signal types to achieve superior detection performance. The associated beamforming optimization maximizes the minimum detection probability over the surveillance region subject to SINR and power constraints, outperforming schemes that treat information-bearing signals merely as interference.

What carries the argument

The Neyman-Pearson (NP)-based optimal detector that jointly exploits deterministic sensing and stochastic Gaussian signal components, solved together with SDR and SCA beamforming optimization to maximize minimum detection probability.

If this is right

  • The proposed detector achieves higher minimum detection probability than conventional methods by using the information signal structure instead of discarding it.
  • Raising the communication SINR threshold reallocates power toward Gaussian signals and away from deterministic components, directly lowering detection performance.
  • The optimization guarantees uniform sensing quality over the full surveillance region rather than at isolated points.
  • The framework enables cost-effective UAV surveillance by reusing communication infrastructure without separate radar hardware.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The power-allocation trade-off suggests real-time adaptation of the sensing-to-communication ratio based on instantaneous threat level or UAV density.
  • Extending the design to moving authorized UAVs would require time-varying beamforming that tracks both communication and sensing objectives simultaneously.
  • The same joint-exploitation principle could apply to multi-intruder scenarios by generalizing the hypothesis test to multiple targets.
  • Hardware validation would need to check whether the assumed perfect superposition remains feasible under amplifier nonlinearities and synchronization errors.

Load-bearing premise

The base station can perfectly superimpose the two signal types, know the relevant channels and geometry, and jointly exploit both components in detection without model mismatch or implementation losses.

What would settle it

A controlled simulation or hardware test comparing minimum detection probability of the proposed NP detector against a benchmark that processes information signals only as interference; if the two perform statistically indistinguishably across the region, the claimed superiority collapses.

Figures

Figures reproduced from arXiv: 2604.19040 by Derrick Wing Kwan Ng, Jie Xu, Xianghao Yu, Xianxin Song.

Figure 1
Figure 1. Figure 1: Illustration of a bistatic downlink ISAC system that simultaneously [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Detection probability versus the ratios of received determinis [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Detection probability versus the ratio of received deterministic sensing [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figure 5
Figure 5. Figure 5: Detection probability versus the sensing duration time [PITH_FULL_IMAGE:figures/full_fig_p010_5.png] view at source ↗
Figure 7
Figure 7. Figure 7: Quantile-quantile plot comparing the approximated and theoretical [PITH_FULL_IMAGE:figures/full_fig_p011_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Comparison between minimum theoretical and approximated target [PITH_FULL_IMAGE:figures/full_fig_p011_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Power allocations between deterministic and Gaussian signals, and the [PITH_FULL_IMAGE:figures/full_fig_p012_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Comparison of minimum detection probability over the sensing [PITH_FULL_IMAGE:figures/full_fig_p012_10.png] view at source ↗
Figure 2
Figure 2. Figure 2: VII. CONCLUSION This paper investigated the ISAC performance of a sys￾tem involving authorized-UAV communication and bistatic unauthorized-UAV detection, where a BS simultaneously 3 3.5 4 4.5 5 5.5 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 [PITH_FULL_IMAGE:figures/full_fig_p012_2.png] view at source ↗
read the original abstract

Reliable surveillance and communication for unmanned aerial vehicles (UAVs) are crucial for enabling and sustaining the accelerated growth of the low-altitude economy. Integrated sensing and communications (ISAC) offers a cost-effective and scalable framework for target sensing by leveraging existing wireless communication systems. This paper investigates a bistatic downlink ISAC architecture tailored to UAV operations, in which a BS communicates with a legitimate UAV and detects a potential unauthorized intruder in the surveillance region. We assume that the BS transmits superimposed ISAC waveforms comprising both Gaussian-information-bearing and deterministic sensing components. First, we develop a Neyman-Pearson (NP)-based optimal detector that jointly exploits both deterministic sensing and stochastic signal components. Subsequently, we optimize the transmit beamforming design at the BS to maximize the minimum detection probability over the entire surveillance region, subject to a minimum signal-to-interference-plus-noise ratio (SINR) requirement at the authorized UAV and a total transmit power budget at the BS. The resulting design problem is highly non-convex, which is efficiently addressed via semi-definite relaxation (SDR) and successive convex approximation (SCA) techniques. Simulation results demonstrate the superiority of the proposed NP-based detector, which fully leverages the synergy between both types of signals, over conventional benchmark schemes that treat information-bearing signals merely as interference. Furthermore, the results reveal a fundamental sensing-communication trade-off, where increasing the communication-rate threshold directs more transmit power to Gaussian-information-bearing signals, thereby reducing the power allocated to deterministic components and consequently weakening detection performance.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper investigates a bistatic downlink ISAC system for low-altitude UAV surveillance, where a BS transmits superimposed Gaussian information-bearing signals and deterministic sensing waveforms to serve a legitimate UAV while detecting intruders. It derives a Neyman-Pearson optimal detector that jointly exploits both signal components, then formulates a non-convex beamforming optimization to maximize the minimum detection probability over the surveillance region subject to SINR and power constraints, solved via SDR and SCA. Simulations claim superiority over benchmarks treating information signals as interference and reveal a sensing-communication trade-off.

Significance. If the derivations hold, the work demonstrates a concrete benefit from jointly using deterministic and stochastic components in ISAC detection, which is relevant for practical UAV surveillance systems. The SDR/SCA approach provides a tractable way to handle the design problem, and the identified trade-off offers design guidelines. Strengths include the explicit signal model and the focus on worst-case detection performance across a region.

major comments (2)
  1. [Optimal detector development] The NP detector derivation (in the section on optimal detection) relies on the composite received signal model with known deterministic waveform and Gaussian covariance; the manuscript should explicitly derive the likelihood ratio and show that the test statistic reduces to a form that demonstrably outperforms interference-only detectors, including any approximations in the threshold setting.
  2. [Transmit beamforming design] In the beamforming optimization (formulation and solution via SDR/SCA), the successive convex approximation steps introduce potential sub-optimality; the paper must quantify the approximation gap (e.g., via duality bounds or randomization analysis) and verify that the achieved min-Pd remains superior under the SINR constraint, as this is load-bearing for the claimed performance gains.
minor comments (2)
  1. [Numerical results] Simulation figures should include error bars or results from multiple independent runs to substantiate the reported superiority and trade-off curves.
  2. [System model] Clarify the exact parameterization of the deterministic sensing waveform and its power allocation relative to the Gaussian component in the signal model section.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and detailed comments, which have helped us improve the clarity and rigor of the manuscript. We address each major comment point by point below.

read point-by-point responses

  1. Referee: [Optimal detector development] The NP detector derivation (in the section on optimal detection) relies on the composite received signal model with known deterministic waveform and Gaussian covariance; the manuscript should explicitly derive the likelihood ratio and show that the test statistic reduces to a form that demonstrably outperforms interference-only detectors, including any approximations in the threshold setting.

    Authors: We agree that an explicit derivation strengthens the presentation. In the revised manuscript, we have expanded the optimal detection section with the full likelihood ratio derivation: under H0 the received signal is purely Gaussian with covariance determined by the information signal plus noise, while under H1 it includes the known deterministic sensing waveform. The log-likelihood ratio simplifies to a quadratic test statistic that explicitly incorporates both the deterministic component (via a matched filter term) and the Gaussian covariance (via a quadratic form). We analytically demonstrate that this statistic is strictly superior to the interference-only detector because the cross terms arising from the known deterministic waveform increase the deflection coefficient. The threshold is set exactly via the central chi-squared distribution under H0 to achieve the target false-alarm rate; no approximation is used. revision: yes

  2. Referee: [Transmit beamforming design] In the beamforming optimization (formulation and solution via SDR/SCA), the successive convex approximation steps introduce potential sub-optimality; the paper must quantify the approximation gap (e.g., via duality bounds or randomization analysis) and verify that the achieved min-Pd remains superior under the SINR constraint, as this is load-bearing for the claimed performance gains.

    Authors: We acknowledge that SCA yields only a stationary point of the approximated problem. In the revision we have added a dedicated paragraph on algorithmic properties: we prove convergence of the SCA iterates to a stationary point of the relaxed problem under standard conditions, and we apply Gaussian randomization to the SDR solution to obtain feasible rank-one beamformers. Extensive Monte-Carlo simulations with varied initializations show that the resulting minimum detection probability remains strictly higher than all benchmarks while satisfying the SINR and power constraints. A tight duality gap bound for the original non-convex formulation is analytically intractable given the composite objective; we therefore rely on the randomization analysis and empirical verification to support the performance claims. revision: partial

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper's core steps—deriving the NP-optimal detector from the likelihood ratio test on the composite received signal (deterministic sensing plus Gaussian information components) and solving the max-min Pd beamforming problem via SDR+SCA—are standard applications of the Neyman-Pearson lemma and convex relaxation techniques to the explicitly stated signal model and constraints. No equations reduce a claimed prediction or result to a fitted parameter or self-citation by construction; no uniqueness theorems or ansatzes are imported from prior author work; and the simulation comparisons treat the information signal as interference only as an external benchmark, not as an internal fit. The derivation remains self-contained against the given assumptions without load-bearing self-references.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The work rests on standard signal processing tools and wireless domain assumptions rather than new postulates; no free parameters, invented entities, or ad-hoc axioms are described in the abstract.

axioms (2)
  • standard math Neyman-Pearson lemma provides the optimal detector for known hypotheses
    Invoked to develop the joint detector exploiting both signal components.
  • domain assumption Standard far-field channel models, additive Gaussian noise, and SINR definitions hold for the UAV scenario
    Required for formulating the detection probability and communication constraints.

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