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Poisson Hole Process: Theory and Applications to Wireless Networks
Information Theory · Submitted 6 Jan 2016
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Numerical comparisons reveal that the new bounds outperform all known bounds and approximations, and are remarkably tight in all operational regimes of interest.
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The abstract, sentence by sentence
Interference field in wireless networks is often modeled by a homogeneous Poisson Point Process (PPP). While it is realistic in modeling the inherent node irregularity and provides meaningful first-order results, it falls short in modeling the effect of interference management techniques, which typically introduce some form of spatial interaction among active transmitters. In some applications, such as cognitive radio and device-to-device networks, this interaction may result in the formation of holes in an otherwise homogeneous interference field. The resulting interference field can be accurately modeled as a Poisson Hole Process (PHP). Despite the importance of PHP in many applications, the exact characterization of interference experienced by a typical node in a PHP is not known. In this paper, we derive several tight upper and lower bounds on the Laplace transform of this interference. Numerical comparisons reveal that the new bounds outperform all known bounds and approximations, and are remarkably tight in all operational regimes of interest. The key in deriving these tight and yet simple bounds is to capture the local neighborhood around the typical point accurately while simplifying the far field to attain tractability. Ideas for tightening these bounds further by incorporating the effect of overlaps in the holes are also discussed. These results immediately lead to an accurate characterization of the coverage probability of the typical node in a PHP under Rayleigh fading.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Interference field in wireless networks is often modeled by a homogeneous Poisson Point Process (PPP). | background 1.00 | 0.04 | 0.02 | asserted 0.93 |
| s1 | While it is realistic in modeling the inherent node irregularity and provides meaningful first-order results, it falls short in modeling the effect of interference management techniques, which typically introduce some form of spatial interaction among active transmitters. | background 0.81 | 0.11 | 0.02 | asserted 1.00 |
| s2 | In some applications, such as cognitive radio and device-to-device networks, this interaction may result in the formation of holes in an otherwise homogeneous interference field. | background 1.00 | 0.07 | 0.02 | hedged possibility 1.00 |
| s3 | The resulting interference field can be accurately modeled as a Poisson Hole Process (PHP). | background 0.94 | 0.08 | 0.06 | asserted 0.98 |
| s4 | Despite the importance of PHP in many applications, the exact characterization of interference experienced by a typical node in a PHP is not known. | gap 1.00 | 0.06 | 0.03 | asserted 1.00 |
| s5 | In this paper, we derive several tight upper and lower bounds on the Laplace transform of this interference. | contribution 0.97 | 0.97 | 0.38 | asserted 1.00 |
| s6 | Numerical comparisons reveal that the new bounds outperform all known bounds and approximations, and are remarkably tight in all operational regimes of interest. | result 0.95 | 0.94 | 0.40 | asserted 1.00 |
| s7 | The key in deriving these tight and yet simple bounds is to capture the local neighborhood around the typical point accurately while simplifying the far field to attain tractability. | method 0.98 | 0.91 | 0.08 | asserted 1.00 |
| s8 | Ideas for tightening these bounds further by incorporating the effect of overlaps in the holes are also discussed. | future work 0.99 | 0.68 | 0.03 | hedged possibility 0.67 |
| s9 | These results immediately lead to an accurate characterization of the coverage probability of the typical node in a PHP under Rayleigh fading. | result 0.68 | 0.91 | 0.27 | asserted 1.00 |
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The paper
Original abstract
Interference field in wireless networks is often modeled by a homogeneous Poisson Point Process (PPP). While it is realistic in modeling the inherent node irregularity and provides meaningful first-order results, it falls short in modeling the effect of interference management techniques, which typically introduce some form of spatial interaction among active transmitters. In some applications, such as cognitive radio and device-to-device networks, this interaction may result in the formation of holes in an otherwise homogeneous interference field. The resulting interference field can be accurately modeled as a Poisson Hole Process (PHP). Despite the importance of PHP in many applications, the exact characterization of interference experienced by a typical node in a PHP is not known. In this paper, we derive several tight upper and lower bounds on the Laplace transform of this interference. Numerical comparisons reveal that the new bounds outperform all known bounds and approximations, and are remarkably tight in all operational regimes of interest. The key in deriving these tight and yet simple bounds is to capture the local neighborhood around the typical point accurately while simplifying the far field to attain tractability. Ideas for tightening these bounds further by incorporating the effect of overlaps in the holes are also discussed. These results immediately lead to an accurate characterization of the coverage probability of the typical node in a PHP under Rayleigh fading.
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References
How the literature uses it
3 arXiv papers cite this in 10 sentences
Papers citing it · 4 sentences without a confident label
Uses its method or tool 2 papers
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The proposed approach is based on the tools developed by the authors for the analysis of PHPs in [ref] .
Serving Distance and Coverage in a Closed Access PHP-Based Heterogeneous Cellular Network · Conclusion · 0.98
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Recent results on Poisson Hole Process [ref] can be used to calculate interference and coverage probability in guard-zone based two-tier networks.
Decentralized Opportunistic Access for D2D Underlaid Cellular Networks · Related Work · 0.84
Cites it as background 1 paper
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Please refer to [ref] for a more detailed discussion about PHP.
Serving Distance and Coverage in a Closed Access PHP-Based Heterogeneous Cellular Network · System model · 0.98
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