Title: Coverage Analysis of a Vehicular Network Modeled as Cox Process Driven by Poisson Line Process,
Abstract: In this paper, we consider a vehicular network in which the wireless nodes
are located on a system of roads. We model the roadways, which are
predominantly straight and randomly oriented, by a Poisson line process (PLP)
and the locations of nodes on each road as a homogeneous 1D Poisson point
process (PPP). Assuming that each node transmits independently, the locations
of transmitting and receiving nodes are given by two Cox processes driven by
the same PLP. For this setup, we derive the coverage probability of a typical
receiver, which is an arbitrarily chosen receiving node, assuming independent
Nakagami-$m$ fading over all wireless channels. Assuming that the typical
receiver connects to its closest transmitting node in the network, we first
derive the distribution of the distance between the typical receiver and the
serving node to characterize the desired signal power. We then characterize
coverage probability for this setup, which involves two key technical
challenges. First, we need to handle several cases as the serving node can
possibly be located on any line in the network and the corresponding
interference experienced at the typical receiver is different in each case.
Second, conditioning on the serving node imposes constraints on the spatial
configuration of lines, which require careful analysis of the conditional
distribution of the lines. We address these challenges in order to accurately
characterize the interference experienced at the typical receiver. We then
derive an exact expression for coverage probability in terms of the derivative
of Laplace transform of interference power distribution. We analyze the trends
in coverage probability as a function of the network parameters: line density
and node density. We also study the asymptotic behavior of this model and
compare the coverage performance with that of a homogeneous 2D PPP model with
the same node density.