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arxiv: 1906.10909 · v1 · pith:QU2NZDAMnew · submitted 2019-06-26 · 📡 eess.SP · cs.SY· eess.SY

Probabilistic Two-Ray Model for Air-to-Air Channel in Built-Up Areas

Zhuangzhuang Cui , Ke Guan , C\'esar Briso , Danping He , Bo Ai , Zhangdui Zhong This is my paper

Pith reviewed 2026-05-25 15:38 UTC · model grok-4.3

classification 📡 eess.SP cs.SYeess.SY
keywords air-to-air propagationpath loss modelingtwo-ray modelurban environmentsray tracingshadowingWeibull distributionaerial platforms
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The pith

A probabilistic two-ray model predicts path loss for air-to-air links in built-up areas using Weibull and Normal distributions fitted to ray-tracing data.

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

This paper introduces a probabilistic two-ray path loss model tailored for air-to-air propagation in built-up areas ranging from suburban to high-rise urban environments. The model relies on statistical representations of city layouts to determine the likelihood of line-of-sight and reflected paths. Path loss values are fitted to a Weibull distribution while fluctuations follow a Normal distribution, as validated through ray-tracing simulations. An extension extracts an altitude-dependent shadowing model that aligns closely with measurement-based results. These elements together offer a practical method for rapid channel prediction in aerial scenarios without requiring extensive computational simulations.

Core claim

The central discovery is that the air-to-air path loss in built-up areas follows a Weibull distribution under the probabilistic two-ray framework derived from city deployment statistics, with its fluctuation modeled as Normal, and that this leads to an altitude-dependent shadowing model consistent with measurements.

What carries the argument

The probabilistic two-ray (PTR) model, which uses city statistical deployment to probabilistically account for direct and ground-reflected rays in path loss calculations.

If this is right

  • The PTR model applies to suburban, urban, dense urban, and high-rise urban areas.
  • Path loss predictions show good agreement with ray-tracing simulations.
  • The shadowing model derived from the PTR framework matches measurement-based models.
  • Both provide tools for accurate and quick prediction for aerial platforms.

Where Pith is reading between the lines

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

  • If the city statistical model is representative, the approach could extend to other frequencies or antenna heights not simulated.
  • Integration into drone network planning tools would allow faster coverage estimates than full ray-tracing.
  • Validation against additional real-world measurements at different altitudes could confirm generality.

Load-bearing premise

The statistical model of city deployment accurately represents real built-up areas from suburban to high-rise.

What would settle it

A direct comparison of the PTR model's predicted path loss distributions against measured data from flights over a real city at multiple altitudes would test the claim.

Figures

Figures reproduced from arXiv: 1906.10909 by Bo Ai, C\'esar Briso, Danping He, Ke Guan, Zhangdui Zhong, Zhuangzhuang Cui.

Figure 1
Figure 1. Figure 1: Propagation description: (a) Built-up areas with three conditions: (1) [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Ground reflection probability vs. elevation angle for four environments. [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Validation by the ray-tracing simulations from [9] in urban scenario. [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figure 5
Figure 5. Figure 5: Path loss results for the FSPL, our proposed model, and the ray-tracing [PITH_FULL_IMAGE:figures/full_fig_p004_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: CDFs and fits (when h = 100 m): (a) Path loss; (b) Shadow fading. 50 100 150 200 250 300 350 Altitude (m) 1.4 1.6 1.8 2 2.2 2.4 2.6 (a) 50 100 150 200 250 300 350 Altitude (m) 1.2 1.3 1.4 1.5 1.6 1.7 1.8 (b) 50 100 150 200 250 300 350 Altitude (m) 1.2 1.4 1.6 1.8 2 2.2 2.4 (c) 50 100 150 200 250 300 350 Altitude (m) 1 2 3 4 5 6 (d) [PITH_FULL_IMAGE:figures/full_fig_p005_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Shadowing factor σ with respect to the altitude in different environ￾ments: (a) Suburban; (b) Urban; (c) Dense Urban; and (d) High-rise Urban. where p1, q1 and r1 are parameters that related to the char￾acteristics of environments. Based on our proposed model, we simulated the path loss at various altitudes in different environments and thereby obtain the shadowing factors shown in [PITH_FULL_IMAGE:figure… view at source ↗
read the original abstract

In this paper, we present a probabilistic two-ray (PTR) path loss model for air-to-air (AA) propagation channel in built-up areas. Based on the statistical model of city deployment, the PTR path loss model can be applied to suburban, urban, dense urban, and high-rise urban. The path loss is optimally fitted as the Weibull distribution and its fluctuation is fitted as the Normal distribution in ray-tracing simulations. The good agreements between our model and ray tracing indicate the proposed model can provide a useful tool for accurate and quick prediction for aerial platforms. As an extended research of PTR model, we extract the shadowing factor by numerous simulations and propose the altitude-dependent shadowing model. The result shows that the proposed shadowing model has very good consistent with the measurement-based model, which indicates that our research performs well in the extensibility and generality.

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 / 1 minor

Summary. The manuscript proposes a probabilistic two-ray (PTR) path loss model for air-to-air propagation in built-up areas (suburban to high-rise urban) derived from a statistical city deployment model. Path loss is fitted to a Weibull distribution and fluctuations to a Normal distribution via ray-tracing simulations, with reported agreement to those simulations supporting its use for quick prediction; an extension extracts altitude-dependent shadowing parameters that are compared to a measurement-based model.

Significance. If the circularity between fitting and validation can be resolved, the PTR model would offer a computationally lightweight probabilistic alternative to deterministic ray-tracing for aerial platform channel prediction across urban categories, with the shadowing extension adding practical generality by aligning with measurements.

major comments (2)
  1. [Abstract] Abstract: the central claim that the PTR model 'can provide a useful tool for accurate and quick prediction' rests on 'good agreements between our model and ray tracing' after the path loss 'is optimally fitted as the Weibull distribution and its fluctuation is fitted as the Normal distribution in ray-tracing simulations.' Because the distributions and parameters are obtained directly from the same simulation ensemble used for the agreement check, the reported match does not constitute independent validation or demonstrate generalization; a hold-out test set, cross-validation, or comparison against separate measurements is needed to support the prediction claim.
  2. [Abstract] Abstract: the statistical city deployment model is asserted to enable application across suburban, urban, dense urban, and high-rise categories, yet no quantitative description of the building-height or density distributions, their calibration sources, or sensitivity analysis is supplied. Without these, it is unclear whether the Weibull/Normal fits are tied to the specific simulated environments or hold more broadly.
minor comments (1)
  1. [Abstract] Abstract: 'has very good consistent with the measurement-based model' is grammatically incorrect and should read 'has very good consistency with the measurement-based model.'

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive feedback on our manuscript. We address the two major comments point by point below, indicating planned revisions where appropriate.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the central claim that the PTR model 'can provide a useful tool for accurate and quick prediction' rests on 'good agreements between our model and ray tracing' after the path loss 'is optimally fitted as the Weibull distribution and its fluctuation is fitted as the Normal distribution in ray-tracing simulations.' Because the distributions and parameters are obtained directly from the same simulation ensemble used for the agreement check, the reported match does not constitute independent validation or demonstrate generalization; a hold-out test set, cross-validation, or comparison against separate measurements is needed to support the prediction claim.

    Authors: We acknowledge that fitting the distributions and parameters from the ray-tracing ensemble and then reporting agreement on the same data constitutes a goodness-of-fit demonstration rather than fully independent validation. The PTR model itself is constructed from the deterministic two-ray mechanism augmented by probabilistic parameters drawn from the statistical city model; the simulations are used to select and parameterize the Weibull and Normal distributions. The reported agreements confirm that these choices reproduce the simulated statistics. To address the concern about generalization, we will add a cross-validation procedure in the revised manuscript by partitioning the ray-tracing results into fitting and held-out test sets and reporting predictive performance on the test portion. We also note that the altitude-dependent shadowing extension already provides comparison against an independent measurement-based model. revision: yes

  2. Referee: [Abstract] Abstract: the statistical city deployment model is asserted to enable application across suburban, urban, dense urban, and high-rise categories, yet no quantitative description of the building-height or density distributions, their calibration sources, or sensitivity analysis is supplied. Without these, it is unclear whether the Weibull/Normal fits are tied to the specific simulated environments or hold more broadly.

    Authors: Quantitative descriptions of the building-height and density distributions for each urban category, together with their calibration sources, appear in Section II of the manuscript. We will revise the abstract to include a brief reference to these distributions and will add a short sensitivity analysis subsection showing how moderate variations in building density and height statistics affect the resulting Weibull and Normal parameters. revision: yes

Circularity Check

1 steps flagged

Path-loss and fluctuation distributions are fitted directly to ray-tracing ensemble then validated by agreement with that same ensemble

specific steps
  1. fitted input called prediction [Abstract]
    "The path loss is optimally fitted as the Weibull distribution and its fluctuation is fitted as the Normal distribution in ray-tracing simulations. The good agreements between our model and ray tracing indicate the proposed model can provide a useful tool for accurate and quick prediction for aerial platforms."

    Distributions are fitted to the ray-tracing outputs; the subsequent claim of agreement with ray tracing therefore compares the fitted model to the data that defined its parameters, making the reported predictive performance a restatement of the fit rather than an independent test.

full rationale

The paper states that the PTR model is obtained by optimally fitting Weibull to path loss and Normal to fluctuation inside the ray-tracing simulations, then reports 'good agreements between our model and ray tracing'. This reduces the claimed predictive accuracy to a goodness-of-fit on the identical data used to determine the distributional parameters, satisfying the fitted-input-called-prediction pattern. The shadowing extension is compared to an external measurement-based model and does not inherit the same reduction. No self-citation load-bearing or self-definitional steps are present in the provided text.

Axiom & Free-Parameter Ledger

3 free parameters · 2 axioms · 0 invented entities

The central claim rests on fitted distribution parameters extracted from simulations and domain assumptions about city statistics and simulation accuracy. No independent evidence or machine-checked elements are described.

free parameters (3)
  • Weibull distribution parameters for path loss
    Optimally fitted to ray-tracing simulations for different urban categories
  • Normal distribution parameters for fluctuation
    Fitted from ray-tracing simulations
  • Altitude-dependent shadowing parameters
    Extracted by numerous simulations to match measurement-based model
axioms (2)
  • domain assumption Statistical model of city deployment is representative for suburban, urban, dense urban, and high-rise urban environments
    Invoked to generalize the PTR model across area types
  • domain assumption Ray-tracing simulations accurately capture real propagation effects in built-up areas
    Used as the basis for fitting and agreement claims

pith-pipeline@v0.9.0 · 5691 in / 1565 out tokens · 31753 ms · 2026-05-25T15:38:36.005525+00:00 · methodology

discussion (0)

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Reference graph

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