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August 2018 When do wireless network signals appear Poisson?
H. Paul Keeler, Nathan Ross, Aihua Xia
Bernoulli 24(3): 1973-1994 (August 2018). DOI: 10.3150/16-BEJ917

Abstract

We consider the point process of signal strengths from transmitters in a wireless network observed from a fixed position under models with general signal path loss and random propagation effects. We show via coupling arguments that under general conditions this point process of signal strengths can be well-approximated by an inhomogeneous Poisson or a Cox point processes on the positive real line. We also provide some bounds on the total variation distance between the laws of these point processes and both Poisson and Cox point processes. Under appropriate conditions, these results support the use of a spatial Poisson point process for the underlying positioning of transmitters in models of wireless networks, even if in reality the positioning does not appear Poisson. We apply the results to a number of models with popular choices for positioning of transmitters, path loss functions, and distributions of propagation effects.

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H. Paul Keeler. Nathan Ross. Aihua Xia. "When do wireless network signals appear Poisson?." Bernoulli 24 (3) 1973 - 1994, August 2018. https://doi.org/10.3150/16-BEJ917

Information

Received: 1 September 2015; Revised: 1 August 2016; Published: August 2018
First available in Project Euclid: 2 February 2018

zbMATH: 06839257
MathSciNet: MR3757520
Digital Object Identifier: 10.3150/16-BEJ917

Keywords: propagation loss , rate of convergence , signal strengths , total variation distance , weak convergence

Rights: Copyright © 2018 Bernoulli Society for Mathematical Statistics and Probability

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Vol.24 • No. 3 • August 2018
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