Simultaneous Harvest-and-Transmit Ambient Backscatter Communications under Rayleigh Fading

Byung Moo Lee; Furqan Jameel; Imran Khan; Tapani Ristaniemi

arxiv: 1906.09888 · v1 · pith:6C4A7MQBnew · submitted 2019-06-24 · 📡 eess.SP · cs.SY· eess.SY

Simultaneous Harvest-and-Transmit Ambient Backscatter Communications under Rayleigh Fading

Furqan Jameel , Tapani Ristaniemi , Imran Khan , Byung Moo Lee This is my paper

Pith reviewed 2026-05-25 17:29 UTC · model grok-4.3

classification 📡 eess.SP cs.SYeess.SY

keywords ambient backscatterRayleigh fadingoutage probabilitypower splittingenergy harvestingdata rate tradeoffwireless poweredIoT

0 comments

The pith

Ambient backscatter model yields closed-form outage probability under Rayleigh fading for optimal power split

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

The paper formulates a model for wireless-powered ambient backscatter devices that can harvest energy and transmit data simultaneously. It derives a closed-form expression for the outage probability when signals fade according to the Rayleigh distribution. This expression is used to determine the power-splitting factor that trades off between the energy harvested and the rate at which data can be sent. A reader would care because it gives an exact way to predict and optimize performance for low-power, battery-free devices in IoT applications without needing extensive simulations.

Core claim

The authors formulate a model for wireless-powered ambient backscatter devices and derive a closed-form expression of outage probability under Rayleigh fading. Based on this expression, the article provides the power-splitting factor that balances the tradeoff between energy harvesting and achievable data rate. The results shed light on the complex interplay of a power-splitting factor, amount of harvested energy, and the achievable data rates.

What carries the argument

Closed-form outage probability expression for the simultaneous harvest-and-transmit ambient backscatter system under Rayleigh fading.

If this is right

The outage probability can be calculated analytically for any given parameters.
The power-splitting factor can be chosen to achieve the desired balance between energy and rate.
System designers gain insight into how fading impacts the energy-data tradeoff.
Performance can be predicted for various device configurations in fading environments.

Where Pith is reading between the lines

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

The derivation technique might apply to other fading models with appropriate modifications.
Adaptive power splitting could be implemented if channel state information is available.
Integration with other ambient energy sources could improve overall efficiency.
Field tests with actual hardware would be a natural next step to verify the model.

Load-bearing premise

The model of how the device splits power between harvesting and backscatter transmission, and the resulting signal model, accurately describes real device operation.

What would settle it

An experiment measuring the actual outage probability of an ambient backscatter prototype in Rayleigh fading conditions and finding it does not match the closed-form expression.

Figures

Figures reproduced from arXiv: 1906.09888 by Byung Moo Lee, Furqan Jameel, Imran Khan, Tapani Ristaniemi.

**Figure 1.** Figure 1: System model. Eh ≥ Eb + Es + Em. (1) In the above expression Eh, Eb, Es, Em denotes the harvested energy, energy consumed for backscatter communication, energy consumed for spectrum sensing and the energy consumed by micro-controller/ sensor for data gather and processing. Some of the key symbols used throughout this paper are provided in Table I. Symbol Definition Eh Harvested energy Eb Energy consumed fo… view at source ↗

**Figure 2.** Figure 2: Circuit design of the ambient backscatter device. [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 3.** Figure 3: Time schedule and power splitting. yi,1 = s βP Pl,1 hi,1s1 + ni,1, (2) where yi,1 is the received signal, s1 denotes the normalized signal, P represents the transmit power, and Pl,1 = d θ 1 is the path loss experienced by the backscatter device and θ is the path loss exponent. Furthermore, hi,1 represents the channel gain between the ambient RF source and backscatter device which is assumed to be Rayleigh … view at source ↗

**Figure 4.** Figure 4: Outage probability as a function of SNR. [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗

**Figure 5.** Figure 5: Achievable rate against different values of [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗

**Figure 6.** Figure 6: Harvested energy against increasing values of [PITH_FULL_IMAGE:figures/full_fig_p009_6.png] view at source ↗

**Figure 7.** Figure 7: Achievable rate and harvested energy versus increasing values of [PITH_FULL_IMAGE:figures/full_fig_p010_7.png] view at source ↗

read the original abstract

Ambient backscatter communications is an emerging paradigm and a key enabler for pervasive connectivity of low-powered wireless devices. It is primarily beneficial in the Internet of things (IoT) and the situations where computing and connectivity capabilities expand to sensors and miniature devices that exchange data on a low power budget. The premise of the ambient backscatter communication is to build a network of devices capable of operating in a battery-free manner by means of smart networking, radio frequency (RF) energy harvesting and power management at the granularity of individual bits and instructions. Due to this innovation in communication methods, it is essential to investigate the performance of these devices under practical constraints. To do so, this article formulates a model for wireless-powered ambient backscatter devices and derives a closed-form expression of outage probability under Rayleigh fading. Based on this expression, the article provides the power-splitting factor that balances the tradeoff between energy harvesting and achievable data rate. Our results also shed light on the complex interplay of a power-splitting factor, amount of harvested energy, and the achievable data rates.

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.

Desk Editor's Note private letter to a colleague

Closed-form outage and power-split optimization for harvest-and-transmit ambient backscatter, but the single-Rayleigh assumption looks questionable given the cascaded links.

read the letter

The main point is that the paper sets up a power-splitting model for wireless-powered ambient backscatter devices and derives a closed-form outage probability under Rayleigh fading, then uses that expression to pick the splitting factor that balances harvested energy against rate. They also show how the three quantities interact. This is a direct application of standard outage analysis to the simultaneous harvest-and-transmit case, and the closed form plus the optimization rule are the concrete outputs. For the subfield that cares about analytical expressions in energy-harvesting IoT, that is useful work and worth having on record. The derivation appears to follow the usual Rayleigh steps without obvious fitting or circularity. The abstract is clear about what is claimed. The soft spot is the channel model. Ambient backscatter uses two independent links, so the effective SNR follows the product of two Rayleigh random variables rather than a single Rayleigh. The abstract says the result holds “under Rayleigh fading” but does not say whether the integration used the correct double-Rayleigh PDF or an approximation. If the composite link was treated as ordinary Rayleigh, the closed-form expression and the resulting optimal split are not exact. That needs checking in the full derivation. This paper is for researchers already working on backscatter and RF energy harvesting. It is narrow enough that most readers outside that niche will not need it, but the analytical result could save time for those who do. It shows straightforward engagement with the problem and prior techniques, so it is coherent on its own terms. I would send it to referees with a specific request to verify the fading distribution used in the outage integral.

Referee Report

1 major / 0 minor

Summary. The paper formulates a model for wireless-powered ambient backscatter devices operating in simultaneous harvest-and-transmit mode and derives a closed-form expression for outage probability under Rayleigh fading. This expression is then used to determine the power-splitting factor that balances the tradeoff between harvested energy and achievable data rate.

Significance. If the derivation is correct and accounts for the composite channel, the closed-form outage result and optimized splitting factor would provide a useful analytical framework for performance evaluation and design of ambient backscatter IoT systems under fading. The work addresses a relevant practical constraint in battery-free communications.

major comments (1)

[Abstract / Model section] The abstract states that the outage expression is derived 'under Rayleigh fading' but does not clarify whether the cascaded (product) channel formed by the ambient-source-to-tag and tag-to-reader links is modeled. Ambient backscatter channels are typically double-Rayleigh; treating the effective link as single Rayleigh would invalidate the closed-form integration unless an explicit approximation or transformation is justified in the derivation.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the detailed review and constructive feedback. We address the major comment below.

read point-by-point responses

Referee: [Abstract / Model section] The abstract states that the outage expression is derived 'under Rayleigh fading' but does not clarify whether the cascaded (product) channel formed by the ambient-source-to-tag and tag-to-reader links is modeled. Ambient backscatter channels are typically double-Rayleigh; treating the effective link as single Rayleigh would invalidate the closed-form integration unless an explicit approximation or transformation is justified in the derivation.

Authors: We agree that the abstract and model section would benefit from explicit clarification. In the manuscript, both the ambient source-to-tag and tag-to-reader links are modeled as independent Rayleigh fading channels, so the effective backscatter link is the product (double-Rayleigh) channel. The closed-form outage probability is obtained by integrating the SNR expression over the PDF of the product of two independent Rayleigh random variables (which yields a modified Bessel function of the second kind). We will revise the abstract to state 'under cascaded Rayleigh fading' and expand the model section with the explicit PDF derivation and integration steps to justify the closed-form result. revision: yes

Circularity Check

0 steps flagged

No circularity: derivation proceeds from formulated model to closed-form expression without reduction to inputs

full rationale

The paper states it formulates a model for wireless-powered ambient backscatter devices, derives a closed-form outage probability under Rayleigh fading from that model, and then obtains the power-splitting factor from the resulting expression. No quoted steps exhibit self-definition of variables in terms of the target result, renaming of fitted parameters as predictions, or load-bearing reliance on self-citations whose content reduces to the present claims. The chain is presented as standard derivation from stated assumptions and is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract supplies no explicit free parameters, axioms, or invented entities; the device model itself is treated as an input without further breakdown.

pith-pipeline@v0.9.0 · 5729 in / 967 out tokens · 18605 ms · 2026-05-25T17:29:33.898477+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

yi,1 = √(βP/Pl,1) hi,1 s1 + ni,1; Eh,i = ρη(1-α)T βΩ1 |hi,1|²/Pl,1 (Rayleigh hi,1)

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

25 extracted references · 25 canonical work pages

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F. Jameel, Z. Chang, and T. Ristaniemi, “Intercept probability analysis of wireless powered relay system in kappa-mu fading,” in 2018 IEEE 87th V ehicular Technology Conference (VTC Spring) , June 2018, pp. 1–6

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Exploiting interference for energy harvesting: A survey, research issues, and challenges,

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Distributed resource allocation for energy efﬁciency in ofdma multicell networks with wireless power transfer,

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Ambient backscatter: wireless communication out of thin air,

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

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

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Ambient backscatter communications: A contemporary survey,

N. Van Huynh, D. T. Hoang, X. Lu, D. Niyato, P. Wang, and D. I. Kim, “Ambient backscatter communications: A contemporary survey,” IEEE Communications Surveys & Tutorials , 2018

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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 Transactions on Wireless Communications , vol. 17, no. 3, pp. 1528–1544, 2018

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Cooperative receiver for ambient backscatter communications with multiple antennas,

G. Yang, Y .-C. Liang, and Q. Zhang, “Cooperative receiver for ambient backscatter communications with multiple antennas,” in IEEE International Conference on Communications (ICC) . IEEE, 2017, pp. 1–6

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G. Wang, F. Gao, R. Fan, and C. Tellambura, “Ambient backscatter communication systems: Detection and performance analysis,” IEEE Transactions on Communications , vol. 64, no. 11, pp. 4836–4846, 2016

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Noncoherent detections for ambient backscatter system,

J. Qian, F. Gao, G. Wang, S. Jin, and H. Zhu, “Noncoherent detections for ambient backscatter system,” IEEE Transactions on Wireless Communications , vol. 16, no. 3, pp. 1412–1422, 2017

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Modeling and performance analysis of wireless networks with ambient backscatter devices,

D. Darsena, G. Gelli, and F. Verde, “Modeling and performance analysis of wireless networks with ambient backscatter devices,” IEEE Transactions on Communications, vol. 65, no. 4, pp. 1797–1814, 2017

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Riding on the primary: A new spectrum sharing paradigm for wireless-powered IoT devices,

X. Kang, Y .-C. Liang, and J. Yang, “Riding on the primary: A new spectrum sharing paradigm for wireless-powered IoT devices,” in IEEE International Conference on Communications (ICC) . IEEE, 2017, pp. 1–6

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Outage probability for ambient backscatter system with real source,

Y . Zhang, J. Qian, F. Gao, and G. Wang, “Outage probability for ambient backscatter system with real source,” in IEEE 18th International Workshop on Signal Processing Advances in Wireless Communications (SPA WC) . IEEE, 2017, pp. 1–5

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Outage analysis of ambient backscatter communication systems,

W. Zhao, G. Wang, S. Atapattu, C. Tellambura, and H. Guan, “Outage analysis of ambient backscatter communication systems,” IEEE Communications Letters, 2018

work page 2018

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Overlay RF-powered backscatter cognitive radio networks: A game theoretic approach,

D. T. Hoang, D. Niyato, P. Wang, D. I. Kim, and L. B. Le, “Overlay RF-powered backscatter cognitive radio networks: A game theoretic approach,” in Communications (ICC), 2017 IEEE International Conference on . IEEE, 2017, pp. 1–6

work page 2017

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Hybrid backscatter communication for wireless-powered heterogeneous networks,

S. H. Kim and D. I. Kim, “Hybrid backscatter communication for wireless-powered heterogeneous networks,” IEEE Transactions on Wireless Communications, vol. 16, no. 10, pp. 6557–6570, 2017. Furqan Jameel received his BS in Electrical Engineering (under ICT R&D funded Program) in 2013 from the Lahore Campus of COMSATS Institute of Information Technology (CI...

work page 2017