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. 2 Stochastic geometry, Cox process, Poisson line process, coverage probability, vehicular network, road systems, Nakagami-m fading.

Coverage and Rate Analysis of Downlink Cellular Vehicle-to-Everything (C-V2X) Communication

“…In order to determine the coverage probability, we need to compute the conditional Laplace transform of the interference power distribution. Recall that the aggregate interference at the typical receiver can be decomposed into three independent components I 1 , I 20 , and L 0 , respectively, as given in (5) and (6). However, upon applying this technique to the Cox process of tier 2 nodes excluding the nodes on the typical line Φ 2 = Φ 2 \ Ξ L 0 , the collinearity of the locations of the nodes is disrupted in the resulting point process Φ x, x ∈ Φ 2 } due to the random displacement of each point on a line.…”

“…For this purpose, tools from stochastic geometry are of particular interest, where the idea is to endow appropriate distributions to the locations of different network entities and then use properties of these distributions to characterize network performance. From the perspective of vehicular networks, the spatial model that is gaining popularity is the so-called Cox process, where the spatial layout of roads is modeled by a Poisson line process (PLP) and the locations of vehicular nodes and road side units (RSUs) on each line (road) are modeled by a 1D Poisson point process (PPP) [6], [7]. While this spatial model has been employed in a few works in the literature, the effect of shadowing on the performance of the vehicular network has not been considered.…”

Outage in Motorway Multi-Lane VANETs With Hardcore Headway Distance Using Synthetic Traces

“…Despite their impressive accuracy, these models seem quite complex to incorporate into the performance evaluation of Vehicular ad hoc networks (VANETs). In order to balance between accuracy and analytical tractability, the Poisson line process can be used to model roads with random orientation, coupled with one-dimensional (1D) Poisson Point Processs (PPPs) for the locations of vehicles along each road [12], [13]. Under these assumptions, the distribution of vehicles becomes a Cox process in the plane, and the coverage probability of a typical vehicle is available in [12,Theorem 1].…”

“…In order to balance between accuracy and analytical tractability, the Poisson line process can be used to model roads with random orientation, coupled with one-dimensional (1D) Poisson Point Processs (PPPs) for the locations of vehicles along each road [12], [13]. Under these assumptions, the distribution of vehicles becomes a Cox process in the plane, and the coverage probability of a typical vehicle is available in [12,Theorem 1]. The conflicting effect of road intensity (higher intensity increases the interference level) and vehicle intensity (higher intensity increases the average link gain) has also been investigated.…”

The Meta Distribution of the SIR in Linear Motorway VANETs

“…The resulting point process is commonly referred to as a Cox process in the plane. The study in [12] shows that the distribution of interference level is discontinuous at the intersections, the study in [13] brings up the trade-off between the intensities of streets and vehicles in the coverage probability (or probability of successful reception) of the typical receiver, and the study in [14] enhances the model of [13] assuming both vehicular and macro-base stations. Simpler models for the road network, e.g., two orthogonal streets in [15] and a grid of roads in [16], highlight the fact that the coverage probability of the typical receiver becomes lower near intersections, because there, the generated interference from both horizontal and vertical streets is significant.…”