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In this paper, we first present an analytical procedure for the computation of the node isolation probability and coverage in an ad hoc network in the presence of channel randomness, with applications to shadowing and fading phenomena. These results are used to obtain an estimate of the connectivity features for very dense networks. Stochastic orderings are used to show the beneficial impact of lognormal shadowing and the negative impact of Rayleigh fading. The impact of SIMO/MISO and MIMO schemes is also addressed, showing how channel diversity can be exploited to enhance network coverage and connectivity.