On the connectivity of wireless multi-hop networks with arbitrary wireless channel models

Abstract

Considering a wireless multi-hop network where a total of n nodes are randomly, independently and uniformly distributed in a unit square in R2 and each node has a uniform transmission power, a fundamental problem is to investigate the connectivity of such networks. In this letter, we prove that the probability of having a connected network and the probability of having no isolated node asymptotically converges to the same value as n goes to infinity for an arbitrary wireless channel model satisfying certain intuitively reasonable conditions.