In this paper we study connectivity in wireless ad-hoc networks by modelingthe network as an undirected geometric random graph. The novel aspect in our study is that for finding the link probability bwtween nodes we use in 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 uvoidably caused by the obstructions and irregularities in the surroundings of the trransmitting 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 tend to behave like a random graph with uncorrelated links. Secondly, these variations increase the probability of long links, which enhances the probability of connectivitiy 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 planning and design of wireless ad-hoc networks or sensor networks in gigant component size is a good measure for 'connectivityu".
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