Abstract-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.

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We consider extended wireless networks characterized by a random topology of access points (APs) contending for medium access over the same wireless channel. Recently, stochastic geometry has emerged as a powerful tool to analyze random networks adopting MAC protocols such as ALOHA and CSMA. The main strength of this methodology lies in its ability to account for the randomness in the nodes' location jointly with an accurate description at the physical layer, based on the SINR, that allows considering also random fading on each link. In this paper we extend previous stochastic geometry models of CSMA networks, developing computationally efficient techniques to obtain throughput distributions, in addition to spatial averages, which permit us to get interesting insights into the impact of protocol parameters and channel variability on the spatial fairness among the nodes. Moreover we extend the analysis to a significant class of topologies in which APs are not placed according to a Poisson process.

We consider static ad hoc wireless networks comprising significant inhomogeneities in the node spatial distribution over the area, and analyze the scaling laws of their transport capacity as the number of nodes increases. In particular, we consider nodes placed according to a shot-noise Cox process, which allows to model the clustering behavior usually recognized in large-scale systems. For this class of networks, we propose novel scheduling and routing schemes which approach previously computed upper bounds to the per-flow throughput as the number of nodes tends to infinity.