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arxiv: 2606.28940 · v1 · pith:MSMPWJNWnew · submitted 2026-06-27 · 💻 cs.IT · math.IT

Modeling and Analysis of Sensing Assisted UAV Networks for Urban Vehicular Communications

Kaushlendra Pandey , Nithin V Sabu , Abhishek K. Gupta This is my paper

Pith reviewed 2026-06-30 08:18 UTC · model grok-4.3

classification 💻 cs.IT math.IT
keywords UAV networksvehicular communicationssensing assistedManhattan Poisson line processdetection probabilitycoverage probabilityrate coverageblockage model
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The pith

Sensing radius in UAV vehicular networks is limited by both signal strength and elevation-dependent blockages.

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

The paper models urban roads using a Manhattan Poisson line process and places vehicles and UAVs as Poisson point processes to analyze a sensing-assisted network. UAVs at fixed altitude sense vehicles before providing connectivity, with sensing radius set by detection probability under an elevation dependent blockage model. The work derives detection probability, the Laplace transform of interference accounting for sensing activity, coverage probability, and rate coverage, revealing that higher altitudes reduce sensing and coverage performance while rate coverage first falls then rises.

Core claim

In a three-dimensional setup with UAVs at fixed altitude modeled as homogeneous PPP, roads as MPLP, and vehicles as 1D PPP, the sensing radius is jointly limited by signal strength and blockage effects. The detection probability is derived to characterize the typical UAV's sensing region, the Laplace transform of aggregate interference is obtained considering directional patterns and sensing-driven activity, and the coverage probability and rate coverage of sensed vehicles are analyzed, showing specific trends with altitude.

What carries the argument

Elevation dependent blockage model used to define sensing radius based on detection probability, combined with the Laplace transform of aggregate interference that accounts for directional antenna patterns and sensing-driven activity.

If this is right

  • Higher UAV altitude degrades sensing performance due to increased blockages and path loss.
  • Communication coverage probability decreases as altitude increases.
  • Rate coverage probability exhibits a non-monotonic trend, decreasing initially then increasing with altitude.
  • The sensing region is characterized within reliability requirements for detection probability.

Where Pith is reading between the lines

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

  • Optimal UAV altitude may exist that balances the trade-off between sensing degradation and rate coverage improvement.
  • Deployment strategies could involve altitude adaptation based on vehicle density or urban density.
  • Extensions to mobile UAVs or multi-UAV coordination might build on the derived interference Laplace transform.

Load-bearing premise

The elevation-dependent blockage model accurately represents urban signal obstruction for both sensing detection probability and communication coverage.

What would settle it

Measurement of detection probability and rate coverage as a function of UAV altitude in a real urban setting with known vehicle locations to check if the non-monotonic rate coverage trend holds.

Figures

Figures reproduced from arXiv: 2606.28940 by Abhishek K. Gupta, Kaushlendra Pandey, Nithin V Sabu.

Figure 1
Figure 1. Figure 1: System model illustrating active UAVs with their sensing zone, inactive [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: UAV-mounted RADAR sensing model with antenna orientation [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Sense-then-communicate cycle of a UAV with [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Analytical and simulation results for the sensing load and the CDF [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: (a) Activation probability pa versus vehicular density λv for H ∈ {50, 100, 150} m in dense urban environment (a = 9.61, b = 0.16), with dashed lines indicating the asymptotic limit as λ → ∞. (b) pa with UAV altitude H at λ = 1 vehicle/km, compared against a no-blockage. Distance r (m) 0 200 400 600 800 D e t e c tio n p r o b a bilit y P d(r) 0 0.05 0.1 0.15 Ana Sim . = 60 / ; 30 / ; 15 / ; 8 / ; 4 / (a) … view at source ↗
Figure 6
Figure 6. Figure 6: (a) DP Pd(r) under dense urban blockage (a = 9.61, b = 0.16) versus ground distance r at fixed altitude H = 100 m; (b)Pd(r) versus UAV altitude H at fixed ground distance r = 500 m. B. Impact of altitude on activation probability [PITH_FULL_IMAGE:figures/full_fig_p010_6.png] view at source ↗
Figure 8
Figure 8. Figure 8: a presents the LT of interference at the kth nearest vehicle located at Rk = 100 m. As UAV altitude increases, the LoS probability improves over a wider area, raising the activation probability pa and consequently the density of active interferers, resulting in higher resultant interference and a lower LT. Fig. 8b shows that narrowing the beamwidth from γ = π/3 to γ = π/12 improves CP across the entire 10 … view at source ↗
Figure 9
Figure 9. Figure 9: CP and UAV activation probability with UAV altitude [PITH_FULL_IMAGE:figures/full_fig_p012_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: (a) RC (b) the typical RC with UAV altitude for different UAV [PITH_FULL_IMAGE:figures/full_fig_p012_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Diagram illustrating the (A) horizontal and the (B) vertical chord [PITH_FULL_IMAGE:figures/full_fig_p013_11.png] view at source ↗
read the original abstract

Urban vehicular networks (VNs) demand seamless connectivity and situational awareness within road-constrained environments, motivating the deployment of unmanned aerial vehicles (UAVs) platforms capable of simultaneously sensing vehicles and establishing communication with them. In this paper, we present a sensing-assisted UAV network that provides connectivity to the vehicles in an urban area. The road network of the urban area is modeled as Manhattan Poisson line process (MPLP), and the random location of vehicles on each road is modeled as one dimensional Poisson point processes (PPPs). UAVs are distributed in the urban area at a fixed altitude and provide connectivity after sensing the vehicles. Their locations are modeled as a two-dimensional homogeneous PPP. Combined with the fixed altitude, this results in a three-dimensional spatial configuration. We incorporate an elevation dependent blockage model and define the sensing radius based on detection probability (DP), showing that it is jointly limited by signal strength and blockage effects. We derive the DP and characterize the typical UAV's sensing region within the reliability requirements. We also derive the Laplace transform (LT) of aggregate interference accounting for directional patterns and sensing-driven activity, and analyze the resulting coverage probability (CP). Finally, we obtain the rate coverage (RC) of sensed vehicles falling within the UAV's sensing zone. Numerical results shows that increasing altitude degrades sensing and coverage performance, whereas RC exhibits a non-monotonic trend, first decreasing and then increasing with altitude.

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 develops a stochastic geometry model for sensing-assisted UAV networks serving urban vehicular communications. Roads are modeled as a Manhattan Poisson line process, vehicles as 1D PPPs on each road, and UAVs as a 2D homogeneous PPP at fixed altitude, yielding a 3D setup. An elevation-dependent blockage model is incorporated to define the sensing radius via detection probability (DP). The work derives the DP, the Laplace transform of aggregate interference (accounting for directional patterns and sensing-driven activity), coverage probability (CP), and rate coverage (RC) of sensed vehicles. Numerical results claim that increasing altitude degrades sensing and coverage performance while RC exhibits a non-monotonic trend (first decreasing, then increasing).

Significance. If the derivations hold, the paper supplies analytical expressions for key metrics in an integrated sensing-communication UAV setting under a realistic urban blockage model, enabling performance evaluation and altitude optimization. The application of standard PPP properties (LT of interference, CP) to the sensing-driven activity model is a strength in analytical tractability; the reported non-monotonic RC behavior, if robust, offers a concrete design insight.

major comments (2)
  1. [Abstract and modeling section] Abstract and modeling section: The elevation-dependent blockage model is used both to define the sensing radius via DP and inside the LT of interference and CP expressions; because blockage probability is an explicit function of elevation angle (hence altitude), any inaccuracy in its functional form propagates directly into the three performance metrics and can produce or eliminate the claimed non-monotonic RC trend. The manuscript provides no cross-validation against measured urban data or sensitivity analysis to alternative blockage functions.
  2. [Numerical results section] Numerical results section: The headline claims (sensing/CP degrade with altitude; RC non-monotonic) rest on the specific blockage model and chosen parameter values (UAV density, vehicle density, detection threshold); without reported sensitivity checks or alternative blockage functions, it is unclear whether the non-monotonic RC is a general feature or an artifact of the chosen model.
minor comments (2)
  1. [Abstract] The abstract states that the sensing radius is 'jointly limited by signal strength and blockage effects' but does not specify the exact functional form or threshold used for DP; adding the governing equation would improve clarity.
  2. [Numerical results] Figure captions in the numerical results should explicitly list the parameter values (densities, altitude range, detection probability threshold) used to generate each curve.

Simulated Author's Rebuttal

2 responses · 1 unresolved

We thank the referee for the constructive feedback. We address each major comment below and indicate the changes planned for the revised manuscript.

read point-by-point responses

  1. Referee: [Abstract and modeling section] Abstract and modeling section: The elevation-dependent blockage model is used both to define the sensing radius via DP and inside the LT of interference and CP expressions; because blockage probability is an explicit function of elevation angle (hence altitude), any inaccuracy in its functional form propagates directly into the three performance metrics and can produce or eliminate the claimed non-monotonic RC trend. The manuscript provides no cross-validation against measured urban data or sensitivity analysis to alternative blockage functions.

    Authors: The referee is correct that the blockage model directly influences the derived metrics. We adopted the elevation-dependent form because it is standard in the UAV literature for capturing the geometry of urban LoS probability as a function of elevation angle. Cross-validation against measured urban data is not present in the manuscript, as the work is analytical rather than measurement-driven. However, we agree that sensitivity analysis is needed to confirm robustness. In the revision we will add a dedicated subsection comparing results under the original model, a parameter variation of the same model, and an alternative distance-dependent blockage function, to show that the non-monotonic RC trend persists. revision: yes

  2. Referee: [Numerical results section] Numerical results section: The headline claims (sensing/CP degrade with altitude; RC non-monotonic) rest on the specific blockage model and chosen parameter values (UAV density, vehicle density, detection threshold); without reported sensitivity checks or alternative blockage functions, it is unclear whether the non-monotonic RC is a general feature or an artifact of the chosen model.

    Authors: The numerical claims are obtained under the stated model and parameters. The non-monotonic RC arises analytically from the opposing effects of increasing path loss versus decreasing blockage probability with altitude; this trade-off is embedded in the closed-form expressions rather than being a numerical coincidence. To strengthen the claim, the revised version will include sensitivity plots varying UAV/vehicle densities, detection threshold, and an alternative blockage model, demonstrating that the non-monotonic behavior is preserved across these cases. revision: yes

standing simulated objections not resolved
  • Cross-validation of the blockage model against measured urban data, which would require external empirical datasets outside the scope of the present analytical study.

Circularity Check

0 steps flagged

No circularity: derivations apply standard PPP tools to new sensing model

full rationale

The paper models roads via MPLP and vehicles/UAVs via PPPs, incorporates an elevation-dependent blockage model to define sensing radius from detection probability, then derives the Laplace transform of interference and coverage probability expressions directly from the point-process properties and directional patterns; rate coverage follows from the same. No equation reduces a derived quantity to a fitted input by construction, no self-citation chain bears the central claims, and the altitude trends are outputs of the explicit model rather than tautological inputs.

Axiom & Free-Parameter Ledger

4 free parameters · 4 axioms · 0 invented entities

The central claim rests on standard stochastic-geometry modeling assumptions plus several free parameters for densities, thresholds, and altitude that are not derived from first principles.

free parameters (4)
  • UAV density
    Intensity parameter of the 2D PPP for UAV locations
  • Vehicle density per road
    Intensity of the 1D PPP for vehicles on each line
  • Altitude
    Fixed height parameter varied in numerical analysis
  • Detection probability threshold
    Value used to define the sensing radius
axioms (4)
  • domain assumption Urban road network is modeled as Manhattan Poisson line process
    Abstract states this models the road network of the urban area
  • domain assumption Vehicles on each road follow independent 1D Poisson point processes
    Abstract states random location of vehicles on each road
  • domain assumption UAV locations form 2D homogeneous PPP at fixed altitude
    Abstract states UAVs distributed as 2D homogeneous PPP resulting in 3D configuration
  • domain assumption Elevation dependent blockage model governs signal obstruction
    Abstract states incorporation of this model for sensing radius

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discussion (0)

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