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arxiv: 1907.05469 · v1 · pith:DQ7EDVXTnew · submitted 2019-07-11 · 💻 cs.IT · cs.NI· math.IT

Coverage Probability Analysis Under Clustered Ambient Backscatter Nodes

Dong Han , Hlaing Minn This is my paper

Pith reviewed 2026-05-24 22:41 UTC · model grok-4.3

classification 💻 cs.IT cs.NImath.IT
keywords ambient backscatter communicationcoverage probabilityPoisson point processPoisson cluster processstochastic geometrySINR analysisinterference modeling
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The pith

Poisson point process models for primary transmitters and Poisson cluster process for backscatter transmitters yield coverage probabilities that support adding large numbers of ambient backscatter nodes to existing networks.

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

The paper models a setup in which primary transmitter-receiver pairs share spectrum with randomly placed ambient backscatter nodes that reflect primary signals to enable secondary links. Primary transmitters follow a Poisson point process while backscatter transmitters follow a Poisson cluster process. Coverage probabilities are derived at a typical primary receiver using both SINR and SIR, with backscatter signals counted either as decodable information or as interference depending on the scenario. Numerical evaluation of the resulting expressions indicates that substantial densities of such nodes remain compatible with primary link performance. Readers would care because the work explores whether passive reflection can increase overall network density without new spectrum or active transmitters.

Core claim

Under the assumption that primary transmitter locations form a Poisson point process and backscatter transmitter locations form a Poisson cluster process, the SINR and SIR based coverage probabilities are derived for two network configuration scenarios. Numerical results on the coverage probabilities indicate the possibility to involve a large amount of AmBC nodes in existing wireless networks.

What carries the argument

Stochastic geometry analysis that places primary transmitters according to a Poisson point process and backscatter transmitters according to a Poisson cluster process, then computes coverage probabilities while modeling backscatter signals at the primary receiver as either decodable signals or interference.

If this is right

  • Closed-form or numerically tractable expressions exist for coverage probability under both the SINR and SIR treatments in each of the two network configurations.
  • The impact of clustered backscatter nodes on primary coverage can be quantified directly from the point-process parameters.
  • Primary networks can accommodate secondary backscatter activity at densities shown feasible by the numerical results without dedicated spectrum allocation.

Where Pith is reading between the lines

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

  • The same point-process framework could be reused to optimize cluster size or density parameters that maximize secondary throughput while holding primary coverage above a chosen threshold.
  • Direct comparison of the predicted probabilities against drive-test data in environments containing clustered low-power devices would test whether the Poisson cluster assumption matches real deployments.
  • Treating backscatter reflections as either signal or interference opens the possibility of adaptive decoding rules at primary receivers that switch based on instantaneous channel conditions.

Load-bearing premise

The locations of primary transmitters form a Poisson point process and the locations of backscatter transmitters form a Poisson cluster process, with backscatter signals treated as either decodable or interference at the primary receiver.

What would settle it

Field measurements in which measured coverage probability falls more than a fixed margin below the numerically computed values as backscatter node density rises would falsify the feasibility indication.

Figures

Figures reproduced from arXiv: 1907.05469 by Dong Han, Hlaing Minn.

Figure 1
Figure 1. Figure 1: Ambient backscatter scheme a portion of the CWs and 2) modulate its information bits with the other portion of the CWs by backscattering the CWs with different antenna impedances. Then, the backscatter receiver (BR) receives the backscattered (modulated) signals from the BT and detect the ‘0’ or ‘1’ information based on the average symbol energy level. AmBC was proposed to enable devices to communicate by … view at source ↗
Figure 2
Figure 2. Figure 2: Topology of the considered system (scenario-1) [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Coverage probability versus TSRNR deducting the ab [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Coverage probability versus useful signal power ratio [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Coverage probability versus mean fading power gain. [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗
Figure 7
Figure 7. Figure 7: Coverage probability versus SIR threshold [PITH_FULL_IMAGE:figures/full_fig_p006_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Integration area in computing β S (i) BT, i = 1, 2 is the aggregated power of signals from a relatively large number of BTs, β can be written approximately as the ratio between the two expected signal powers β = S (1) BT SBT ≈ E[S (1) BT] E[SBT] . (27) Next, to compute E[S (1) BT], we assume a typical PT is located at the origin, the offspring BTs are located in the circle B(0, ρ), and the typical PR is lo… view at source ↗
Figure 9
Figure 9. Figure 9: β versus ρ and r0 (α = 3.5, ∆B = 100MHz ) Therefore, (27), (30) and (31) yield β ≈ R θ0 0 R ρ 0 P L(r, θ)rdrdθ + R π θ0 R l(1− 2) 1− cos θ 0 PL(r, θ)rdrdθ R π 0 R ρ 0 P L(r, θ)rdrdθ . (32) Numerical results for β versus ρ and r0 are shown in Fig. 9a and Fig. 9b respectively, where the settings are listed in the titles. These two figures show that fraction β decreases with the growth of the radius ρ and t… view at source ↗
read the original abstract

In this paper, we consider a new large-scale communication scheme where randomly distributed AmBC nodes are involved as secondary users to primary transmitter (PT) and primary receiver (PR) pairs. The secondary communication between a backscatter transmitter (BT) and a backscatter receiver (BR) is conducted by the BT's reflecting its corresponding PT's signal with different antenna impedances, which introduces additional double fading channels and potential inter-symbol-interference to the primary communications. Thus, at a typical PR, the backscatter signals are regarded as either decodable signals or interference. Assuming the locations of PTs form a Poisson point process and the locations of BTs form a Poisson cluster process, we derive the SINR and SIR based coverage probabilities for two network configuration scenarios. Numerical results on the coverage probabilities indicate the possibility to involve a large amount of AmBC nodes in existing wireless networks.

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

1 major / 1 minor

Summary. The manuscript analyzes coverage probabilities in a wireless network incorporating clustered ambient backscatter communication nodes. Primary transmitters are distributed according to a Poisson point process, while backscatter transmitters follow a Poisson cluster process. Backscatter signals are modeled as either decodable signals or interference at the primary receiver. The authors derive SINR and SIR based coverage probabilities for two network configuration scenarios and present numerical results suggesting that a large number of AmBC nodes can be integrated into existing wireless networks.

Significance. Should the analytical expressions hold under the stated assumptions, the paper offers a stochastic geometry framework for evaluating the feasibility of dense AmBC deployments in primary networks, which could have implications for spectrum sharing and IoT applications. The choice of PCP for BT locations is a strength for modeling realistic clustering.

major comments (1)
  1. [Abstract and System Model] The binary classification of backscatter signals as strictly decodable or interference (as described in the abstract) is load-bearing for the coverage probability results and the central claim about large node counts. Under the Poisson cluster process for BT locations, intra-cluster nodes share the same PT and experience correlated double-fading plus ISI; this modeling choice may not capture partial correlation or residual interference accurately, potentially rendering the computed coverage probabilities optimistic in the high-density regime.
minor comments (1)
  1. [Abstract] The abstract states that SINR and SIR coverage probabilities are derived but provides no derivation steps, error analysis, or validation details; including these (or references to specific equations) would improve verifiability.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We are grateful to the referee for the thorough review and valuable feedback. Below, we provide a point-by-point response to the major comment.

read point-by-point responses

  1. Referee: The binary classification of backscatter signals as strictly decodable or interference (as described in the abstract) is load-bearing for the coverage probability results and the central claim about large node counts. Under the Poisson cluster process for BT locations, intra-cluster nodes share the same PT and experience correlated double-fading plus ISI; this modeling choice may not capture partial correlation or residual interference accurately, potentially rendering the computed coverage probabilities optimistic in the high-density regime.

    Authors: We appreciate this insightful comment. The binary classification is indeed a key modeling assumption that allows for the derivation of closed-form expressions for the coverage probabilities using tools from stochastic geometry. Specifically, backscatter signals are classified based on whether they contribute to the desired signal or act as interference at the primary receiver, with the Poisson cluster process capturing the spatial correlation among backscatter transmitters. The correlated double-fading and inter-symbol interference are incorporated into the signal-to-interference-plus-noise ratio expressions through the use of the probability generating functional for the clustered point process. While we acknowledge that this may represent an approximation that does not fully capture all partial correlations in extremely dense scenarios, our numerical results, which include comparisons with simulations, indicate that the model provides a reasonable estimate. The central claim is that a large number of AmBC nodes can be integrated without severely degrading primary network performance, which holds under the stated assumptions. We will revise the manuscript to include additional discussion on this modeling choice and its potential limitations in the high-density regime. revision: partial

Circularity Check

0 steps flagged

No significant circularity in coverage probability derivations

full rationale

The paper explicitly assumes PT locations as a Poisson point process and BT locations as a Poisson cluster process, models backscatter signals as either decodable or interference at the PR, and derives SINR/SIR-based coverage probability expressions for two scenarios. Numerical results are presented as direct consequences of these closed-form or integral expressions under the stated point processes and fading models. No parameters are described as fitted to data subsets and then relabeled as predictions; no load-bearing self-citations or uniqueness theorems from prior author work are invoked to force the modeling choices; and the binary signal treatment is stated as an assumption rather than derived from the target coverage metric. The derivation chain is therefore self-contained against the modeling assumptions and does not reduce to its inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 3 axioms · 0 invented entities

The central claim rests on standard stochastic-geometry modeling assumptions stated in the abstract; no free parameters or invented entities are mentioned.

axioms (3)
  • domain assumption Locations of PTs form a Poisson point process
    Explicitly stated in abstract as the model for primary transmitters.
  • domain assumption Locations of BTs form a Poisson cluster process
    Explicitly stated in abstract as the model for backscatter transmitters.
  • domain assumption Backscatter signals are regarded as either decodable signals or interference at a typical PR
    Stated in abstract as the treatment of secondary signals at primary receivers.

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Reference graph

Works this paper leans on

23 extracted references · 23 canonical work pages · 1 internal anchor

  1. [1]

    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 Commun. Surveys Tuts., vol. 20, no. 4, pp. 2889–2922, 2018

    work page 2018

  2. [2]

    Backscatter communication and RFID: Coding, energy, and MIMO analysis,

    C. Boyer and S. Roy, “Backscatter communication and RFID: Coding, energy, and MIMO analysis,” IEEE Trans. Commun., vol. 62, no. 3, pp. 770–785, 2014

    work page 2014

  3. [3]

    Communications and signals design for wireless power transmission,

    Y . Zeng, B. Clerckx, and R. Zhang, “Communications and signals design for wireless power transmission,” IEEE Trans. Commun., vol. 65, no. 5, pp. 2264–2290, 2017

    work page 2017

  4. [4]

    Transmission capacity of wireless Ad hoc networks with successive interference cancellation,

    S. P. Weber, J. G. Andrews, X. Yang, and G. De Veciana, “Transmission capacity of wireless Ad hoc networks with successive interference cancellation,” IEEE Trans. Inf. Theory , vol. 53, no. 8, pp. 2799–2814, 2007

    work page 2007

  5. [5]

    On the performance of non-orthogonal multiple access in 5G systems with randomly deployed users,

    Z. Ding, Z. Yang, P. Fan, and H. V . Poor, “On the performance of non-orthogonal multiple access in 5G systems with randomly deployed users,” IEEE Signal Process. Lett., vol. 21, no. 12, pp. 1501–1505, 2014

    work page 2014

  6. [6]

    Successive interference cancellation in heterogeneous networks,

    M. Wildemeersch, T. Q. Quek, M. Kountouris, A. Rabbachin, and C. H. Slump, “Successive interference cancellation in heterogeneous networks,” IEEE Trans. Commun., vol. 62, no. 12, pp. 4440–4453, 2014

    work page 2014

  7. [7]

    Wirelessly powered backscat- ter communications: Waveform design and SNR-energy tradeoff,

    B. Clerckx, Z. B. Zawawi, and K. Huang, “Wirelessly powered backscat- ter communications: Waveform design and SNR-energy tradeoff,” IEEE Commun. Lett., vol. 21, no. 10, pp. 2234–2237, 2017

    work page 2017

  8. [8]

    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, 2017

    work page 2017

  9. [9]

    Ambient backscatter: wireless communication out of thin air,

    V . Liu, A. Parks, V . Talla, S. Gollakota, D. Wetherall, and J. R. Smith, “Ambient backscatter: wireless communication out of thin air,” in ACM SIGCOMM Computer Communication Review. ACM, 2013, pp. 39–50

    work page 2013

  10. [10]

    Cooperative ambient backscatter communications for green internet-of-things,

    G. Yang, Q. Zhang, and Y .-C. Liang, “Cooperative ambient backscatter communications for green internet-of-things,” IEEE Internet of Things Journal, vol. 5, no. 2, pp. 1116–1130, 2018

    work page 2018

  11. [11]

    Ambient backscatter communication systems: Detection and performance analysis,

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

    work page 2016

  12. [12]

    Noncoherent detec- tions for ambient backscatter system,

    J. Qian, F. Gao, G. Wang, S. Jin, and H. Zhu, “Noncoherent detec- tions for ambient backscatter system,” IEEE Trans. Wireless Commun. , vol. 16, no. 3, pp. 1412–1422, 2017

    work page 2017

  13. [13]

    Stochastic geometry for modeling, analysis, and design of multi-tier and cognitive cellular wire- less networks: A survey,

    H. ElSawy, E. Hossain, and M. Haenggi, “Stochastic geometry for modeling, analysis, and design of multi-tier and cognitive cellular wire- less networks: A survey,” IEEE Communications Surveys & Tutorials , vol. 15, no. 3, pp. 996–1019, 2013

    work page 2013

  14. [14]

    A tractable approach to coverage and rate in cellular networks,

    J. G. Andrews, F. Baccelli, and R. K. Ganti, “A tractable approach to coverage and rate in cellular networks,” IEEE Transactions on communications, vol. 59, no. 11, pp. 3122–3134, 2011

    work page 2011

  15. [15]

    3GPP-inspired HetNet model using Poisson cluster process: Sum-product functionals and downlink coverage,

    C. Saha, M. Afshang, and H. S. Dhillon, “3GPP-inspired HetNet model using Poisson cluster process: Sum-product functionals and downlink coverage,” IEEE Transactions on Communications , vol. 66, no. 5, pp. 2219–2234, 2018

    work page 2018

  16. [16]

    Nearest-neighbor and contact distance distributions for Mat ´ern cluster process,

    M. Afshang, C. Saha, and H. S. Dhillon, “Nearest-neighbor and contact distance distributions for Mat ´ern cluster process,” IEEE Commun. Lett. , vol. 21, no. 12, pp. 2686–2689, 2017

    work page 2017

  17. [17]

    Nearest-neighbor and contact distance distributions for Thomas cluster process,

    ——, “Nearest-neighbor and contact distance distributions for Thomas cluster process,” IEEE Wireless Communications Letters , vol. 6, no. 1, pp. 130–133, 2017

    work page 2017

  18. [18]

    Coverage and interference in d2d networks with poisson cluster process,

    S. Joshi and R. K. Mallik, “Coverage and interference in d2d networks with poisson cluster process,” IEEE Commun. Lett. , vol. 22, no. 5, pp. 1098–1101, 2018

    work page 2018

  19. [19]

    Backscatter multiplicative multiple-access systems: Fundamental limits and practical design,

    W. Liu, Y .-C. Liang, Y . Li, and B. Vucetic, “Backscatter multiplicative multiple-access systems: Fundamental limits and practical design,” IEEE Transactions on Wireless Communications , vol. 17, no. 9, pp. 5713– 5728, 2018

    work page 2018

  20. [20]

    Ambient backscatter assisted wireless powered communications,

    X. Lu, D. Niyato, H. Jiang, D. I. Kim, Y . Xiao, and Z. Han, “Ambient backscatter assisted wireless powered communications,” IEEE Wireless Communications, 2018

    work page 2018

  21. [21]

    Throughput Maximization for Ambient Backscatter Communication: A Reinforcement Learning Approach

    X. Wen, S. Bi, X. Lin, L. Yuan, and J. Wang, “Throughput maximiza- tion for ambient backscatter communication: A reinforcement learning approach,” arXiv preprint arXiv:1901.00608 , 2019

    work page internal anchor Pith review Pith/arXiv arXiv 1901

  22. [22]

    Does ambient backscatter communication need additional regulations?

    K. Ruttik, R. Duan, R. J ¨antti, and Z. Han, “Does ambient backscatter communication need additional regulations?” in IEEE International Symposium on Dynamic Spectrum Access Networks , 2018, pp. 1–6

    work page 2018

  23. [23]

    Haenggi and R

    M. Haenggi and R. K. Ganti, Interference in large wireless networks . Bostan, NY , USA: Now Publishers, 2009

    work page 2009