WIAS Preprint No. 2116, (2015)

Large-deviation principles for connectable receivers in wireless networks



Authors

  • Hirsch, Christian
  • Jahnel, Benedikt
    ORCID: 0000-0002-4212-0065
  • Keeler, Paul
    ORCID: 0000-0002-2063-1075
  • Patterson, Robert I. A.
    ORCID: 0000-0002-3583-2857

2010 Mathematics Subject Classification

  • 60F10 60K35

Keywords

  • wireless network, signal-to-interference-and-noise ratio, large-deviation principle, importance sampling

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.

Appeared in

  • Adv. Appl. Probab., 48 (2016) pp. 1061--1094.

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