Large-deviation principles for connectable receivers in wireless networks

TL;DR

This paper establishes large-deviation principles for connectable receivers in wireless networks modeled by Poisson point processes, providing theoretical insights and practical algorithms for rare event probability estimation.

Contribution

It introduces large-deviation principles for connectable receivers in wireless networks and develops importance-sampling algorithms to efficiently estimate rare connection failure events.

Findings

Large-deviation principle for empirical measure of connectable receivers.

Large-deviation principle for the process of connectable receivers as threshold tends to zero.

Development of importance-sampling algorithms reducing variance in rare event estimation.

Abstract

We study large-deviation principles for a model of wireless networks consisting of Poisson point processes of transmitters and receivers, respectively. To each transmitter we associate a family of connectable receivers whose signal-to-interference-and-noise ratio is larger than a certain connectivity threshold. First, we show a large-deviation principle for the empirical measure of connectable receivers associated with transmitters in large boxes. Second, making use of the observation that the receivers connectable to the origin form a Cox point process, we derive a large-deviation principle for the rescaled process of these receivers as the connection threshold tends to zero. Finally, we show how these results can be used to develop importance-sampling algorithms that substantially reduce the variance for the estimation of probabilities of certain rare events such as users being unable to connect