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arxiv: 1907.04299 · v1 · pith:KMSFVOEEnew · submitted 2019-07-09 · 💻 cs.IT · cs.NI· math.IT

On the 3-D Placement of Airborne Base Stations Using Tethered UAVs

Mustafa A. Kishk , Ahmed Bader , Mohamed-Slim Alouini This is my paper

Pith reviewed 2026-05-24 23:54 UTC · model grok-4.3

classification 💻 cs.IT cs.NImath.IT
keywords tethered UAVairborne base stationpath loss minimization3D placementinclination angleline-of-sight probabilityUAV tether optimization
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The pith

Bounds on tether length and inclination angle for tethered UAV base stations keep average path-loss within 0-3 dB of the optimum.

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

The paper formulates an optimization problem for placing a tethered UAV base station to minimize average path-loss to a ground receiver, subject to a maximum tether length from a rooftop launch point and a minimum inclination angle to avoid building tangling. It derives upper and lower bounds on the optimal tether length and angle, plus a closed-form suboptimal solution that maximizes line-of-sight probability, and the probability distribution of the minimum safe inclination angle whose mean ranges from 10 degrees in suburban settings to 31 degrees in high-rise urban ones. A reader would care because the results show that these simple bounds deliver near-optimal performance without needing exhaustive numerical search, enabling practical energy-unlimited airborne base stations.

Core claim

The central claim is that the derived upper and lower bounds on the optimal values of the tether length and inclination angle lead to tight suboptimal values of the average path-loss that are only 0-3 dBs above the minimum value, while a closed-form solution based on maximizing the line-of-sight probability serves as a practical alternative and the minimum inclination angle follows an environment-dependent distribution with means between 10 and 31 degrees.

What carries the argument

Upper and lower bounds on the optimal tether length and inclination angle under maximum length and minimum-angle constraints from building-height statistics and probabilistic line-of-sight path-loss models.

If this is right

  • The bounds yield average path-loss values only 0-3 dB above the true minimum across environments.
  • A closed-form tether length and angle solution is available by maximizing line-of-sight probability.
  • The mean minimum inclination angle ranges from 10 degrees in suburban to 31 degrees in high-rise urban environments.
  • The probability distribution of the minimum inclination angle can be derived directly from building height statistics.

Where Pith is reading between the lines

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

  • The same bounding approach could be adapted to time-varying receiver locations by updating the inclination bounds periodically.
  • City planners could use the environment-specific angle statistics to set default tether safety rules without per-rooftop surveys.
  • The closed-form solution might serve as an initial guess for iterative optimizers in larger networks of multiple tethered UAVs.

Load-bearing premise

The probabilistic line-of-sight probability and path-loss models that depend only on environment type and building-height statistics accurately capture real-world conditions without site-specific measurements.

What would settle it

A direct numerical comparison, in a given environment, of the average path-loss achieved by placements using the derived bounds versus the true minimum obtained by exhaustive search over feasible tether lengths and angles.

Figures

Figures reproduced from arXiv: 1907.04299 by Ahmed Bader, Mohamed-Slim Alouini, Mustafa A. Kishk.

Figure 1
Figure 1. Figure 1: The system setup considered in this paper. [PITH_FULL_IMAGE:figures/full_fig_p009_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: The effect of Propositions 2, 3, and 4 on the hovering region. [PITH_FULL_IMAGE:figures/full_fig_p011_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: As explained in Theorem 2, PLp is always greater than PLp ∗ . where H1 = n (t, θ) : θmin ≤ θ ≤ π 2 , t = Tmaxo , (12) and H2 = {(t, θ) : θ = θmin, 0 < t < Tmax} . (13) When d < Tmaxcos(θmin), the optimal values of (tp, θp) belong to the following set Hˆ = Hˆ 1 ∪ Hˆ 2 ∪ Hˆ 3, (14) where Hˆ 1 =  (t, θ) : cos−1  d Tmax ≤ θ ≤ π 2 , t = Tmax , (15) Hˆ 2 =  (t, θ) : θ = θmin, 0 < t ≤ d cos(θmin)  , (16) Hˆ… view at source ↗
Figure 4
Figure 4. Figure 4: The regions we should search for the optimal location of the TUAV [PITH_FULL_IMAGE:figures/full_fig_p015_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: The CDF of θmin for different environments. Remark 3. As described in detail in Appendix C, the event θmin < θ takes place when every building at distance L, for any L ≤ Tmax cos(θ), has a height less than hb + L tan(θ). In other words, we only care for the heights of the buildings inside the ball B [PITH_FULL_IMAGE:figures/full_fig_p018_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: The optimal and suboptimal locations of the TUAV as we increase the value of [PITH_FULL_IMAGE:figures/full_fig_p019_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: The optimal value of θ is always within the bounds derived in Theorem 3. 0 50 100 150 200 250 300 Distance in meters (d) 0 50 100 150 topt min=45 min=30 min=15 min=45 min=30 min=15 [PITH_FULL_IMAGE:figures/full_fig_p020_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: The optimal value of t is always within the bounds derived in Theorem 3. the approach used to compute the suboptimal locations, which is maximizing the LoS probability PLoS. Given that θmin = 0◦ , the values of topt and θopt should be within the bounds provided in Corollary 2, which can be easily verified using the values of (xopt, zopt) provided in [PITH_FULL_IMAGE:figures/full_fig_p020_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Optimal and suboptimal values of θ for different values of d. 50 100 150 200 250 300 Distance in meters (d) 40 45 50 55 60 65 70 75 Optimal Average Path Loss (PL) Optimal PL Suboptimal PL Increasing Tmax= [50 100 150] [PITH_FULL_IMAGE:figures/full_fig_p021_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Optimal and suboptimal values of PL for different values of [PITH_FULL_IMAGE:figures/full_fig_p021_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: The PL range against different values of [PITH_FULL_IMAGE:figures/full_fig_p022_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: For a given value of θ, only the heights of the buildings inside the ball B(0, Tmax cos(θ)) affect the value of P(θmin ≤ θ). APPENDIX B PROOF OF LEMMA 2 Given that 0 < θp < π 2 , we can easily observe that R2 p in (31) in Appendix A is an increasing function of θp. As stated in Appendix A, PLoS is an increasing function of the fraction zp xp , which means that we only need to prove the concavity of zp xp … view at source ↗
read the original abstract

One of the main challenges slowing the deployment of airborne base stations (BSs) using unmanned aerial vehicles (UAVs) is the limited on-board energy and flight time. One potential solution to such problem, is to provide the UAV with power supply through a tether that connects the UAV to the ground. In this paper, we study the optimal placement of tethered UAVs (TUAVs) to minimize the average path-loss between the TUAV and a receiver located on the ground. Given that the tether has a maximum length, and the launching point of the TUAV (the starting point of the tether) is placed on a rooftop, the TUAV is only allowed to hover within a specific hovering region. Beside the maximum tether length, this hovering region also depends on the heights of the buildings surrounding the rooftop, which requires the inclination angle of the tether not to be below a given minimum value, in order to avoid tangling and ensure safety. We first formulate the optimization problem for such setup and provide some useful insights on its solution. Next, we derive upper and lower bounds for the optimal values of the tether length and inclination angle. We also propose a suboptimal closed-form solution for the tether length and its inclination angle that is based on maximizing the line-of-sight probability. Finally, we derive the probability distribution of the minimum inclination angle of the tether length. We show that its mean value varies depending on the environment from 10 degrees in suburban environments to 31 degrees in high rise urban environments. Our numerical results show that the derived upper and lower bounds on the optimal values of the tether length and inclination angle lead to tight suboptimal values of the average path-loss that are only 0-3 dBs above the minimum value.

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

0 major / 3 minor

Summary. The paper formulates a constrained optimization problem for the 3-D placement of a tethered UAV base station to minimize average path loss to a ground receiver, subject to a maximum tether length and a minimum inclination angle derived from surrounding building heights. It derives analytic upper and lower bounds on the optimal tether length and inclination angle, proposes a suboptimal closed-form solution based on maximizing LoS probability, derives the distribution of the minimum inclination angle (means ranging from 10° suburban to 31° high-rise urban), and shows numerically that the bounds yield average path-loss values only 0-3 dB above the true minimum under the environment-specific LoS and path-loss model.

Significance. If the bounds and numerical tightness hold, the work supplies practical, near-optimal closed-form placement rules for energy-constrained tethered UAV BSs that avoid the need for exhaustive search over the hovering region. The explicit derivation of the inclination-angle distribution from building-height statistics and the environment-dependent performance guarantees are useful for system design in suburban-to-urban settings.

minor comments (3)
  1. The abstract states that the LoS probability and path-loss model depend on environment type but does not cite the specific prior references used for the suburban-to-high-rise parameters; these should be added in §II or the model section for reproducibility.
  2. The hovering-region boundary conditions (maximum tether length and minimum inclination) are described qualitatively; a diagram or explicit coordinate definition of the feasible set would clarify the optimization domain in §III.
  3. The numerical results claim a 0-3 dB gap, but the text does not specify the number of Monte-Carlo realizations or the exact environment parameter sets used for each curve; adding these details would strengthen the validation section.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive assessment of our work on the 3-D placement of tethered UAV base stations and for recommending acceptance. The referee's summary accurately captures the contributions regarding bounds, the suboptimal closed-form solution, and the inclination-angle distribution.

Circularity Check

0 steps flagged

No significant circularity; derivation is self-contained

full rationale

The paper formulates a constrained optimization over tether length and inclination angle using geometric hovering-region constraints and an environment-specific LoS/path-loss model taken from prior literature. It then derives analytic upper/lower bounds on the optima, a closed-form suboptimal solution via LoS maximization, and the distribution of the minimum inclination angle from building-height statistics. None of these steps reduce by construction to fitted parameters, self-citations, or renamed inputs; the central tightness claim (0-3 dB) is obtained by direct numerical evaluation under the stated model. No load-bearing self-citation chain or self-definitional reduction is present.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central results rest on standard wireless propagation models (path loss and LoS probability) and geometric constraints; no new free parameters are introduced or fitted, and no invented entities are postulated.

axioms (2)
  • domain assumption Standard probabilistic LoS and path loss models for urban environments apply directly to the TUAV setup.
    Invoked to formulate the objective and the suboptimal solution based on maximizing LoS probability.
  • domain assumption Building height statistics allow derivation of the minimum inclination angle distribution without site-specific data.
    Used to obtain the reported mean values (10° suburban to 31° high-rise).

pith-pipeline@v0.9.0 · 5862 in / 1183 out tokens · 21387 ms · 2026-05-24T23:54:10.310704+00:00 · methodology

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