Energy Efficiency Optimization for UAV-assisted Backscatter Communications

JianMing Zhou; Shengzhi Yang; Xuanxuan Tang; Yansha Deng; Yuan Ding

REVIEW 3 major objections 5 minor 18 references

Energy Efficiency Optimization for UAV-assisted Backscatter Communications

T0 review · 3 major / 5 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read A UAV collecting data from backscatter tags has a unique hover point that maximizes energy efficiency, and that point moves closer to the tags when the UAV transmits at lower power.

desk verdict A fresh UAV-backscatter system model, but the main outage derivation multiplies two events that share the same channel gain, overestimating outage and shifting the claimed optimal hover location. read the letter →

arxiv 1908.01339 v1 pith:IA2552HF submitted 2019-08-04 eess.SP

Shengzhi Yang , Yansha Deng , Xuanxuan Tang , Yuan Ding , Jianming Zhou This is my paper · ORCID

classification eess.SP

keywords UAV-assistedbackscattercommunicationsenergyefficiencyoptimizationaverageoutageprobabilityNakagami-mfadingdatacollectionlocationGoldenSectionmethodInternetofThingstimedivisionmultipleaccess

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper considers a UAV that hovers over a field of terrestrial backscatter tags, collects data from them one by one, then flies to a base station to upload what it gathered. It derives a closed-form expression for the system's average outage probability in Nakagami-m fading with line-of-sight and non-line-of-sight components, and uses that expression to optimize the UAV's data-collection location for maximum energy efficiency under a finite energy budget. The central result is that the optimal hover location exists and is unique, and that it shifts closer to the tags as the UAV transmit power decreases. A sympathetic reader would care because this gives a simple design rule for extending energy-efficient IoT connectivity to remote areas.

What carries the argument

The load-bearing object is the closed-form average outage probability in Eq. (10), built by writing the joint successful-delivery probability as a product of three terms: the complementary CDF of the tag-to-UAV SNR, the complementary CDF of the UAV-to-BS SNR, and the complementary energy-outage probability. Each term is evaluated under Nakagami-m fading with LoS/NLoS probabilities from Eq. (2). The optimization mechanism is the Golden Section method, a one-dimensional line search, applied to the energy efficiency objective in Eq. (12); it supplies the unique $x_1^*$ without computing derivatives of the complicated outage expression.

What would settle it

Run a Monte Carlo simulation with fixed parameters from the paper, drawing the tag-to-UAV channel and using it simultaneously for the backscattered signal and the energy-harvest outage, then compare the measured joint outage probability with Eq. (10); a systematic gap that grows with channel correlation would show the factorization in Eq. (8) does not hold.

Watch

Extended reading notes

Core claim

The paper's central claim is that the system average outage probability in Eq. (10) accurately captures the behavior of the proposed UAV-assisted backscatter system, and that maximizing the energy efficiency in Eq. (12) yields a unique optimal data collection location $x_1^*$. The outage model combines three events: the tag fails to harvest enough energy, the backscattered tag-to-UAV signal falls below threshold, or the UAV-to-BS upload falls below threshold. Using Golden Section search on the one-dimensional feasible region, the paper shows that the optimal hover point moves closer to the tags for lower UAV transmit power, because weaker excitation requires shorter backscatter links to keep outage low; higher transmit power instead lets the UAV hover closer to the base station and spend less energy on flight. The paper verifies the analytical expression with Monte Carlo simulation over the full range of hover locations and finds the optimal transmit power for maximum energy efficiency.

Load-bearing premise

The whole outage calculation in Eq. (8) multiplies together the probabilities of three separate outage events as if they were independent; the tag-to-UAV signal quality and the tag's energy harvest both depend on the same random channel, so if that dependence is strong the predicted outage probability and optimal hover location will be off.

Editorial extensions

If this is right

The optimal hover location can be computed directly from closed-form expressions, so system designers can avoid exhaustive simulation when positioning a collector UAV.
Lower UAV transmit power forces the collector closer to the tags; higher power relaxes that requirement and lets the UAV hover nearer the base station, saving flight energy.
For any fixed hover location, there is an optimal UAV transmit power that maximizes bits per joule, so power and position should be chosen together.
Per-tag outage grows with the horizontal distance between tag and UAV, so the scheme implicitly treats tags near the center of the collection zone more favorably.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The outage formula multiplies marginal probabilities for tag-to-UAV signal quality and energy harvesting even though both depend on the same tag-to-UAV channel; a joint outage treatment would be a natural extension and could shift the optimal hover point.
If the UAV operates half-duplex instead of full-duplex, the collection phase doubles or the schedule changes, which would alter the energy-efficiency trade-off in a straightforward way from the same model.
The same Golden Section optimization can be extended to multiple UAVs or non-uniform tag distributions, though the objective may then lose its unimodal shape.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Two things to know before you read it. First, the system model—a UAV hovering over terrestrial backscatter tags, collecting via TDMA, then flying to a BS to upload—is new relative to the cited work, and the per-tag energy harvesting/backscatter split is cleanly expressed. Second, the main analytical result, the average outage probability in Eqs. (8) and (10), rests on an unstated independence assumption that is wrong.

The claimed factorization in Eq. (8) treats the events “tag has enough energy” and “tag-to-UAV SNR exceeds threshold” as independent. Both depend on the same channel gain |g_VUm|². The energy event is |g|²≥A_m; conditioning on that makes the SNR stochastically larger, so the true joint success probability is higher than the product of the two marginals. The stress-test note works through the exact conditional integral and is correct. The error propagates directly into the energy-efficiency objective (12) and the claimed optimal location x1*, which is the paper's main design conclusion.

Smaller quibbles: Theorem 1 says “closed-form,” but the expression still contains an integral over y. Convexity of the outage probability in x1 is asserted as “obvious” but not proven; the Golden Section search only needs unimodality, which is also unproven. There is no comparison with any baseline, such as a fixed collector or a non-UAV backscatter system.

Credit where due: the energy-outage Lemma is correctly derived, the unconditional CDF in Eq. (14) is right, and the Monte-Carlo match in Fig. 2 presumably follows because the simulator samples the two events independently. No parameters are fitted to the conclusions; the paper is a serious design-tradition analysis, not a toy.

If you have to decide on this paper, the independence error is fixable: replace the product with a single integral over y≥A_m. But as it stands, the quantitative claims do not hold. I would not cite the outage or energy-efficiency numbers. If it crosses your desk, send it back for major revision rather than desk reject—the system model is worth keeping.

Referee Report

3 major / 5 minor

Summary. The paper proposes a UAV-assisted backscatter communication system in which a UAV hovers at a location x1 to collect data from multiple terrestrial backscattering tags via TDMA, then flies to a location x2 near a base station to upload the collected data. The authors derive an expression for the system average outage probability (Theorem 1) and formulate an energy efficiency maximization problem over the data collection location x1, solved by Golden Section search under a UAV energy constraint. They report that the optimal location x1* moves closer to the tags as the UAV transmit power decreases. Monte Carlo simulations are presented to validate the analytical outage probability.

Significance. The system model is timely and the optimization framework is relevant for IoT applications in remote areas. The paper provides explicit analytical expressions and includes Monte Carlo validation, which is a strength. However, the correctness of the main analytical derivation is undermined by an unjustified independence assumption in Eq. (8), and the optimality claim relies on an unproven unimodality assumption. If the technical issues are resolved, the results would be a useful contribution to UAV-assisted backscatter communications.

major comments (3)

[Section II-C, Eq. (8)] Eq. (8) factorizes the joint event of tag energy sufficiency and tag-to-UAV SNR success as the product of the marginal probabilities. However, both events depend on the same channel power |g_VUm|^2: the energy event is |g_VUm|^2 >= A_m (from Eq. (6)), and the SNR event, conditioned on |g_VUm|^2 = y, is |g'_VUm|^2 >= gamma^m_th (y sigma^2_Um + sigma^2_V) / (eta_R P_V y). Since |g_VUm|^2 and |g'_VUm|^2 are independent, the exact joint success probability is a single integral over y >= A_m. The product form is not equal to this integral in general, and because the conditional survival probability is increasing in y, the product systematically underestimates the joint success probability and overestimates Pin,m. This error propagates into the closed-form expression in Eq. (10) and into the energy efficiency objective in Eq. (12). The Monte Carlo match in Fig. 2 does not resolve the issue unless the simulator explicitly generates the joint event; the paper does not state the simulation procedure.
[Section III, feasible region] The feasible region for x1 is derived incorrectly. From the constraint (x2 - x1) P_F / v + (T_B + T_U) P_V <= E_total, the correct lower bound is x1 >= x2 - v (E_total - (T_B + T_U) P_V) / P_F, not x1 >= v (E_total - (T_B + T_U) P_V) / P_F as written in the text. This changes the search interval for the Golden Section method and may lead to infeasible or overly restrictive optimization results.
[Section III, unimodality and convexity] The optimization uses the Golden Section method, which requires the objective function to be unimodal over the search interval. The paper asserts that Pin(x1) is 'obviously convex' based on a single simulation figure, but no proof is provided, and convexity of Pin(x1) does not imply unimodality of eta_en(x1), which also has a location-dependent denominator. The claimed global optimum x1* is therefore not rigorously established. The authors should either provide a proof of unimodality for the considered parameter regimes or explicitly restrict the claim to the numerical examples.

minor comments (5)

[Theorem 1, Eq. (10)] The expression in Eq. (10) is called 'closed-form' in the abstract and Theorem 1, but it still contains an integral; please rephrase as an analytical expression with a single integral.
[Section II-A, system model] The tags are described as 'randomly scattered with uniform distribution within a range of 20 meters,' but Eq. (9) treats the tag locations as fixed without averaging over the spatial distribution; clarify whether the analysis is for a given realization or averages over the tag positions.
[Section IV, simulation parameters] The simulation parameters do not specify the UAV total energy E_total; adding this value would improve reproducibility.
[Section III, text near Eq. (12)] The text says 'the problem in Eq. (10) is convex,' but Eq. (10) is an expression, not an optimization problem; please rephrase.
[Section III, feasible-region formula] The formula for the feasible region is ambiguous because of missing parentheses; write it as x1 >= x2 - v(E_total - (T_B + T_U) P_V) / P_F to avoid confusion.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: outage and energy-efficiency results are derived from stated channel/energy models without fitted inputs or load-bearing self-citations.

full rationale

The derivation chain is self-contained and non-circular. The outage expression in Eq. (8) and Theorem 1, Eq. (10), are obtained from the stated channel and energy models (Nakagami-m fading, LoS/NLoS probabilities, backscatter SNR in Eq. (4), and tag energy in Eq. (6)) using standard probability calculations; no parameter is fitted to the outage or energy-efficiency results being reported. The optimal data-collection location x1* in Section III is produced by a Golden Section search over the objective in Eq. (12), whose ingredients are the same derived outage formulas and the flight/energy constraint; the observation that x1* moves closer to the tags at lower UAV transmit power follows from evaluating that objective, not from imposing the conclusion. The paper's references are to prior external work on channels and UAV models, and no load-bearing claim is supported only by a self-citation. The only notable issue, the product factorization in Eq. (8) of events that both depend on |gVUm|^2, is a possible modeling approximation; even if it were inaccurate, it is a correctness concern, not circularity, because the formula is not fitted to the Monte-Carlo points and the simulation validation does not define the analytical result. Therefore the circularity score is 0.

Assumptions & free parameters 7 free parameters · 5 assumptions · 0 invented entities

The analysis rests on standard channel models and a set of hand-selected system parameters. No parameter is fitted to the reported outage or efficiency results, so the ledger mainly records modeling assumptions and the unstated independence assumption in Eq. (8).

free parameters (7)

LoS probability constants c and q = c=11.95, q=0.136
Environment-dependent constants from Al-Hourani's model [15], chosen by hand; they set the LoS/NLoS mixing probabilities in Eq. (2) and affect every link probability.
Nakagami shape factor k_{a,b} = 2 for all links
Modeling choice for fading severity; used in Eq. (1) and all outage CDFs.
Reflection coefficient eta_R = 0.5
Fraction of incident power reflected by the tag; chosen as a common assumption, affects SNR in Eq. (4) and energy harvesting in Eq. (6).
Energy conversion efficiency eta_C = 0.5
Tag circuit conversion efficiency in Eq. (6); chosen by hand.
NLoS attenuation factors eta_VB and eta_VUm = 0.5
Extra path loss for non-line-of-sight links; chosen from common assumptions in Eq. (7) and Eq. (10).
Path loss exponent alpha = 2
Free-space path loss; from [14], affects all distances.
UAV flight power PF = 100 W
Consumed power during flight; chosen by hand, directly enters the energy efficiency objective and constraint.

assumptions (5)

domain assumption All channels follow i.i.d. Nakagami-m fading with shape factor k_{a,b} and mean Omega = omega beta0 d^{-alpha}.
Eq. (1); standard but unverified for UAV links; the i.i.d. assumption simplifies the product factorization.
domain assumption LoS probability follows p_{a,LOS} = 1/(1 + c exp[-q(theta - c)]).
Eq. (2), empirical model from [15]; parameters c and q are environment constants.
domain assumption The UAV operates in full-duplex mode with perfect signal separation, so no self-interference remains.
Footnote 1; required for the clean SNR expression in Eq. (4).
ad hoc to paper SNR outage, uplink outage, and tag energy outage events factor into independent probabilities in Eq. (8).
Not proven; gamma_UmV and the energy outage both depend on |gVUm|^2, so the factorization is an approximation unless conditional independence holds.
ad hoc to paper The energy efficiency objective is unimodal over the feasible x1 region, so Golden Section search converges to the global optimum.
Asserted from Fig. 2; no proof of convexity or unimodality is provided.

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Cite this review

Pith. "Pith review of Energy Efficiency Optimization for UAV-assisted Backscatter Communications." pith.science (2026). https://pith.science/paper/IA2552HF

@misc{pith2026190801339,
  author       = {Pith},
  title        = {Pith review of: Energy Efficiency Optimization for UAV-assisted Backscatter Communications},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/IA2552HF}},
  note         = {Machine review of arXiv:1908.01339}
}

read the original abstract

Future Internet-of-Things (IoT) has high demand for energy-saving communications, especially in remote areas and smart cities. To meet this demand, we propose novel Unmanned Aerial Vehicle-assisted backscatter communications, where a UAV first collects data from multiple terrestrial backscattering tags via time division multiple access, and then flies into the coverage region of a terrestrial base station to upload its collected data to its associated base station. To determine the optimal UAV data collection location, we first analyze the system average outage probability, and then optimize the energy efficiency with the optimal backscattering location through Golden Section method under UAV energy constraint. Our analytical and simulation results illustrate that there is a trade-off between UAV data collection location and the outage probability, and the optimal UAV data collection location to achieve maximum energy efficiency needs to be closer to the tags for lower UAV transmit power.

Figures

Figures reproduced from arXiv: 1908.01339 by the authors.

**Figure 2.** System average outage probability Pin v.s. UAV data collection location x1 [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗

**Figure 3.** Energy efficiency optimization with different variables [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗

Discussion (0). Continue with ORCID to comment.

Reference graph

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Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.

[1] [1]

Wirelessly powered backscatter communication networks: Modeling, coverage, and capacity,

K. Han and K. Huang, “Wirelessly powered backscatter communication networks: Modeling, coverage, and capacity,” IEEE Trans. Wireless Commun., vol. 16, no. 4, pp. 2548–2561, Apr. 2017

work page 2017

[2] [2]

Wireless-powered device-to-device communications with ambient backscattering: Performance modeling and analysis,

X. Lu, H. Jiang, D. Niyato, D. I. Kim, and Z. Han, “Wireless-powered device-to-device communications with ambient backscattering: Performance modeling and analysis,” IEEE Trans. Wireless Commun. , vol. 17, no. 3, pp. 1528–1544, Mar. 2018

work page 2018

[3] [3]

Wi-Fi backscatter: Internet connectivity for RF-powered devices,

B. Kellogg, A. Parks, S. Gollakota, J. R. Smith, and D. Wetherall, “Wi-Fi backscatter: Internet connectivity for RF-powered devices,” in Proc. ACM SIGCOMM 2014 , ser. SIGCOMM ’14. New York, NY , USA: ACM, Aug. 2014, pp. 607–618

work page 2014

[4] [4]

LoRa backscatter: Enabling the vision of ubiquitous connectivity,

“LoRa backscatter: Enabling the vision of ubiquitous connectivity,” in Proc. ACM Interact. Mob. Wearable Ubiquitous Technol. , vol. 1, no. 3. New York, NY , USA: ACM, Sep. 2017, pp. 105:1–105:24

work page 2017

[5] [5]

Wireless charging technologies: Fundamentals, standards, and network applications,

X. Lu, P. Wang, D. Niyato, D. I. Kim, and Z. Han, “Wireless charging technologies: Fundamentals, standards, and network applications,” IEEE Commun. Surveys Tuts. , vol. 18, no. 2, pp. 1413–1452, 2016

work page 2016

[6] [6]

LoRea: A backscatter architecture that achieves a long communication range,

A. Varshney, O. Harms, C. Perez-Penichet, C. Rohner, F. Hermans, and T. V oigt, “LoRea: A backscatter architecture that achieves a long communication range,” in ACM SENSYS 2017 , Nov. 2017, pp. 1–14

work page 2017

[7] [7]

Survey on unmanned aerial vehicle networks for civil applications: A communications viewpoint,

S. Hayat, E. Yanmaz, and R. Muzaffar, “Survey on unmanned aerial vehicle networks for civil applications: A communications viewpoint,” IEEE Commun. Surveys Tuts. , vol. 18, no. 4, pp. 2624–2661, 2016

work page 2016

[8] [8]

Cellular-connected UA V: Potential, challenges, and promising technologies,

Y . Zeng, J. Lyu, and R. Zhang, “Cellular-connected UA V: Potential, challenges, and promising technologies,” IEEE Wireless Commun. , vol. 26, no. 1, pp. 120–127, Feb. 2019

work page 2019