Connectivity in wireless ad-hoc networks with a log-normal radio model

In this paper we study connectivity in wireless ad-hoc networks by modeling the network as an undirected geometric random graph. The novel aspect in our study is that for finding the link probability between nodes we use a radio model that takes into account statistical variations of the radio signal power around its mean value. We show that these variations, that are unavoidably caused by the obstructions and irregularities in the surroundings of the transmitting and the receiving antennas, have two distinct effects on the network. Firstly, they reduce the amount of correlation between links causing the geometric random graph tend to behave like a random graph with uncorrelated links. Secondly, these variations increase the probability of long links, which enhances the probability of connectivity for the network. Another new result in our paper is an equation found for the calculation of the giant component size in wireless ad-hoc networks, that takes into account the level of radio signal power variations. With simulations we show that for the planning and design of wireless ad-hoc networks or sensor networks the giant component size is a good measure for "connectivity".