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arxiv: 1907.07158 · v1 · pith:4CNLRDUSnew · submitted 2019-07-16 · 💻 cs.NI · eess.SP

On the Performance of Renewable Energy-Powered UAV-Assisted Wireless Communications

Silvia Sekander , Hina Tabassum , Ekram Hossain This is my paper

Pith reviewed 2026-05-24 20:25 UTC · model grok-4.3

classification 💻 cs.NI eess.SP
keywords UAVrenewable energy harvestingsolar powerwind powerenergy outageSNR outageharvest-store-consumewireless communications
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The pith

Statistical models of solar and wind harvesting yield closed-form outage expressions and optimization solutions for UAV-assisted wireless links.

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

The paper develops statistical models for energy harvested from solar and wind sources at UAVs under a harvest-store-consume architecture. It derives closed-form PDFs, CDFs, and moment generating functions for the harvested power in solar-only, wind-only, and hybrid cases. These expressions are inverted via the Gil-Pelaez technique to obtain energy outage probability at the UAV and SNR outage probability at ground users. The authors then formulate and solve an SNR-outage minimization problem that returns closed-form expressions for the UAV's transmit power and flight time. A sympathetic reader would care because the results replace simulation with direct analytical evaluation of performance under stochastic renewable supply.

Core claim

The paper establishes closed-form expressions for the PDF and CDF of harvested solar and wind power, their moment generating functions, and the moments of those powers. It applies Gil-Pelaez inversion to compute energy outage at the UAV and SNR outage at ground users, then obtains closed-form solutions for transmit power and flight time that minimize the SNR outage. Additional metrics such as battery charging probability within flight time, average charging time, and eventual energy outage probability over finite duration are also derived from the same statistical models.

What carries the argument

Moment generating functions of harvested solar and wind power together with Gil-Pelaez inversion applied to the harvest-store-consume architecture.

If this is right

  • Energy and SNR outage probabilities can be evaluated in closed form for any given solar irradiance and wind-speed statistics.
  • Optimal UAV transmit power and flight duration that minimize SNR outage follow directly from the derived expressions.
  • Moments of harvested power supply explicit formulas for battery charging time and charging success probability.
  • Eventual energy outage probability over any finite interval can be computed without Monte-Carlo simulation.

Where Pith is reading between the lines

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

  • The same MGF framework could be reused to incorporate additional renewable sources such as vibration or thermal harvesting.
  • The closed-form outage expressions enable rapid sensitivity analysis of network coverage to seasonal weather statistics.
  • Embedding the derived charging-time metric into trajectory planners could reduce the frequency of forced landings.
  • The optimization solutions suggest that hybrid solar-wind UAVs may sustain longer continuous service than single-source designs under the same average power.

Load-bearing premise

The chosen statistical distributions for solar irradiance, wind speed, and UAV energy consumption accurately capture real variability without significant unmodeled losses or hardware constraints.

What would settle it

Comparison of the derived PDF of harvested power and the resulting energy-outage probability against direct long-term measurements from a UAV operating under measured solar and wind conditions.

Figures

Figures reproduced from arXiv: 1907.07158 by Ekram Hossain, Hina Tabassum, Silvia Sekander.

Figure 1
Figure 1. Figure 1: System model. in a straight line trajectory from the charging station, Tb is set as Tb = Rm/vd. The UAV travels with the speed vd (in m/sec) and is equipped with the fixed back-up battery power Pb to support the UAV flight (in case if the harvested power is not enough). The UAV performs data transmission to the cellular users in the downlink using transmit power Pd for the time duration Tb − Tf given that … view at source ↗
Figure 2
Figure 2. Figure 2: Distribution of the harvested power from solar energy [PITH_FULL_IMAGE:figures/full_fig_p010_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: SNR outage of the user and energy outage at the UAV [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗
Figure 6
Figure 6. Figure 6: Energy outage and rate outage as a function of the [PITH_FULL_IMAGE:figures/full_fig_p011_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: SNR outage as a function of the transmission power [PITH_FULL_IMAGE:figures/full_fig_p011_7.png] view at source ↗
Figure 10
Figure 10. Figure 10: Energy outage and rate outage as a function of the [PITH_FULL_IMAGE:figures/full_fig_p012_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Eventual energy outage as a function of the transmis [PITH_FULL_IMAGE:figures/full_fig_p012_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Energy outage as a function of the transmission power [PITH_FULL_IMAGE:figures/full_fig_p013_12.png] view at source ↗
read the original abstract

We develop novel statistical models of the harvested energy from renewable energy sources (such as solar and wind energy) considering harvest-store-consume (HSC) architecture. We consider three renewable energy harvesting scenarios, i.e. (i) harvesting from the solar power, (ii) harvesting from the wind power, and (iii) hybrid solar and wind power. In this context, we first derive the closed-form expressions for the probability density function (PDF) and cumulative density function (CDF) of the harvested power from the solar and wind energy sources. Based on the derived expressions, we calculate the probability of energy outage at UAVs and signal-to-noise ratio (SNR) outage at ground cellular users. We derive novel closed-form expressions for the moment generating function (MGF) of the harvested solar power and wind power. Then, we apply Gil-Pelaez inversion to evaluate the energy outage at the UAV and signal-to-noise-ratio (SNR) outage at the ground users. We formulate the SNR outage minimization problem and obtain closed-form solutions for the transmit power and flight time of the UAV. In addition, we derive novel closed-form expressions for the moments of the solar power and wind power and demonstrate their applications in computing novel performance metrics considering the stochastic nature of the amount of harvested energy as well as energy arrival time. These performance metrics include the probability of charging the UAV battery within the flight time, average UAV battery charging time, probability of energy outage at UAVs, and the probability of eventual energy outage (i.e. the probability of energy outage in a finite duration of time) at UAVs.

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 / 2 minor

Summary. The paper develops statistical models for harvested energy from solar, wind, and hybrid sources under a harvest-store-consume architecture for UAV-assisted wireless communications. It derives closed-form PDF and CDF expressions for the harvested power, novel MGF expressions, applies Gil-Pelaez inversion to obtain energy outage at the UAV and SNR outage at ground users, formulates and solves an SNR outage minimization problem yielding closed-form solutions for UAV transmit power and flight time, and derives moments of the harvested power to evaluate metrics including battery charging probability within flight time, average charging time, and probabilities of energy outage and eventual energy outage.

Significance. If the derivations hold, the closed-form expressions and optimization solutions provide useful analytical tools for performance evaluation and design in renewable-energy UAV systems, explicitly accounting for stochastic energy arrival. The application of standard MGF and inversion techniques to the HSC model, combined with the optimization results, represents a solid contribution to energy-harvesting wireless networks.

minor comments (2)
  1. The abstract and introduction would benefit from explicit statements of the underlying channel model (e.g., path-loss exponent, fading distribution) used when deriving the SNR outage expressions, as this is central to interpreting the closed-form solutions.
  2. Notation for the random variables representing harvested solar and wind power (and their hybrid combination) should be introduced consistently and early to avoid ambiguity when moving between PDF/CDF, MGF, and moment derivations.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive review, accurate summary of our contributions on statistical modeling of renewable energy harvesting under the HSC architecture, and recommendation for minor revision. No specific major comments were raised.

Circularity Check

0 steps flagged

No significant circularity identified

full rationale

The paper's derivation chain consists of standard statistical modeling steps: deriving closed-form PDF and CDF expressions for harvested solar/wind power under the HSC architecture from assumed distributions, computing the MGF from those expressions, applying the Gil-Pelaez inversion theorem to obtain outage probabilities, and solving the resulting SNR outage minimization problem to yield closed-form expressions for transmit power and flight time. These steps are mathematically independent and do not reduce to fitted parameters, self-definitions, or self-citation chains; the models are taken as inputs and the outputs follow directly from them without circular equivalence. No load-bearing uniqueness theorems or ansatzes imported via self-citation are present.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Central claim rests on standard probability theory for deriving distributions and applying inversion techniques; no free parameters, ad-hoc axioms, or invented entities are indicated in the abstract.

axioms (1)
  • standard math Standard mathematical techniques such as deriving PDFs/CDFs from energy models and applying Gil-Pelaez inversion for outage probabilities hold without additional constraints.
    Invoked for evaluating energy and SNR outage probabilities from the derived MGFs.

pith-pipeline@v0.9.0 · 5827 in / 1304 out tokens · 23358 ms · 2026-05-24T20:25:54.965331+00:00 · methodology

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