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The Problem of Localization in Networks of Randomly Deployed Nodes: Asymptotic and Finite Analysis, and Thresholds

F. Daneshgaran,Massimiliano Laddomada,M. Mondin

Published 2007 in arXiv.org

ABSTRACT

We derive the probability that a randomly chosen NL-node over $S$ gets localized as a function of a variety of parameters. Then, we derive the probability that the whole network of NL-nodes over $S$ gets localized. In connection with the asymptotic thresholds, we show the presence of asymptotic thresholds on the network localization probability in two different scenarios. The first refers to dense networks, which arise when the domain $S$ is bounded and the densities of the two kinds of nodes tend to grow unboundedly. The second kind of thresholds manifest themselves when the considered domain increases but the number of nodes grow in such a way that the L-node density remains constant throughout the investigated domain. In this scenario, what matters is the minimum value of the maximum transmission range averaged over the fading process, denoted as $d_{max}$, above which the network of NL-nodes almost surely gets asymptotically localized.

PUBLICATION RECORD

  • Publication year

    2007

  • Venue

    arXiv.org

  • Publication date

    2007-10-02

  • Fields of study

    Mathematics, Computer Science

  • Identifiers
    arXiv 0710.0531
  • External record

    Open on Semantic Scholar

  • Source metadata

    Semantic Scholar

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