Connectivity of wireless multihop networks in a shadow fading environment

Abstract

This paper investigates the connectivity of wireless multihop networks in a log--normal shadow fading environment. Assuming a spatial Poisson distribution of the network nodes, we derive (a) a closed--form expression for the probability that a node is isolated and (b) a tight bound for the minimum node density that is needed to obtain an almost surely connected subnetwork on a given area. Both results find application in the design and simulation of wireless sensor and ad hoc networks.