## Bernoulli

• Bernoulli
• Volume 24, Number 3 (2018), 1973-1994.

### When do wireless network signals appear Poisson?

#### 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.

#### Article information

Source
Bernoulli, Volume 24, Number 3 (2018), 1973-1994.

Dates
Revised: August 2016
First available in Project Euclid: 2 February 2018

https://projecteuclid.org/euclid.bj/1517540465

Digital Object Identifier
doi:10.3150/16-BEJ917

Mathematical Reviews number (MathSciNet)
MR3757520

Zentralblatt MATH identifier
06839257

#### Citation

Keeler, H. Paul; Ross, Nathan; Xia, Aihua. When do wireless network signals appear Poisson?. Bernoulli 24 (2018), no. 3, 1973--1994. doi:10.3150/16-BEJ917. https://projecteuclid.org/euclid.bj/1517540465

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