Asymptotic critical transmission radius for κ-connectivity in wireless ad hoc networks

Peng Jun Wan*, Tsi-Ui Ik, Lixin Wang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

26 Scopus citations

Abstract

A range assignment to the nodes in a wireless ad hoc network induces a topology in which there is an edge between two nodes if and only if both of them are within each other's transmission range. The critical transmission radius for κ-connectivity is the smallest r such that if all nodes have the transmission radius r, the induced topology is κ-connected. In this paper, we study the asymptotic critical transmission radius for κ -connectivity in a wireless ad hoc network whose nodes are uniformly and independently distributed in a unit-area square or disk. We provide a precise asymptotic distribution of the critical transmission radius for κ-connectivity. In addition, the critical neighbor number for κ-connectivity is the smallest integer l such that if every node sets its transmission radius equal to the distance between itself and its l-th nearest neighbor, the induced (symmetric) topology is κ-connected. Applying the critical transmission radius for κ-connectivity, we can obtain an asymptotic almost sure upper bound on the critical neighbor number for κ-connectivity.

Original languageEnglish
Article number2046254
Pages (from-to)2867-2874
Number of pages8
JournalIEEE Transactions on Information Theory
Volume56
Issue number6
DOIs
StatePublished - 1 Jun 2010

Keywords

  • Asymptotic distribution
  • Critical neighbor number
  • Critical transmission radius
  • Random geometric graph

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