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

Authors:
Peng-Jun Wan;Chih-Wei Yi;Lixin Wang
Affiliations:
Department of Computer Science, Illinois Institute of Technology, Chicago, IL;Department of Computer Science, National Chiao Tung University, Hsinchu City, Taiwan, R.O.C.;Department of Computer Science, Illinois Institute of Technology, Chicago, IL
Venue:
IEEE Transactions on Information Theory
Year:
2010

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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 k-connectivity is the smallest r such that if all nodes have the transmission radius r, the induced topology is k-connected. In this paper, we study the asymptotic critical transmission radius for k-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 k-connectivity. In addition, the critical neighbor number for k-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 k-connected. Applying the critical transmission radius for k-connectivity, we can obtain an asymptotic almost sure upper bound on the critical neighbor number for k-connectivity.