On the Connected Nodes Position Distribution in Ad Hoc Wireless Networks with Statistical Channel Models

In this paper the problem of evaluating the statistics of the connected nodes position in a multi-hop wireless random ad hoc network is addressed. In particular, an analytical model and closed-form expressions for the distribution of the connected nodes position distribution and the probability of coverage, given a maximum number of tolerable hops, are derived. The presence of randomness in the propagation, such as shadowing effects, is accounted for in a general way. The validity of the model is confirmed by simulation results. The impact of the channel randomness on the position distribution as well as on the coverage characteristics is investigated in the numerical results.