Performance of a Link in a Field of Vehicular Interferers With Hardcore Headway Distance

Stochastic Geometry Analysis of Spatial-Temporal Performance in Wireless Networks: A Tutorial

“…Step 0-From the contact distribution function of the homogeneous PPP, the PDF of the contact distance at time t 1 follows as (18). Moreover, due to the symmetry, we can assume φ is uniformly distributed in [0, π].…”

“…3) Moments of the CSP Φ in Downlink Cellular Networks: With Rayleigh fading, the exact moments of the CSP given Φ M and Φ G β can be obtained using the following steps: • deriving the CSP Φ by averaging over the randomness of the channel gains of the contact link and interfering links based on the PDF of the exponential distribution due to Rayleigh fading; • deriving the moments of the CSP Φ by deconditioning on the spatial distributions of the interferers in the different random fields and contact distance. Specifically, the spatial randomness of the interferers in Matérn cluster and Poisson downlink networks is averaged out based on the reduced PGFL of MCP and PPP, respectively, given in (35) and (23), and that in Ginibre downlink networks is averaged out based on the PDF of the distances of the interfering links given in (40); based on the nearest-BS associated rule, the contact distances in Matérn cluster, Poisson, and Ginibre downlink networks are averaged out based on their PDFs given in ( 32), (18), and (40), respectively. For non-Poisson networks, since deriving the exact downlink success probability is tedious (if not impossible) and the resulting expressions are cumbersome, we use an approximation method, referred to as Approximate SIR analysis based on the PPP (ASAPPP) method [39], [94], [97], to simplify the evaluation of the SIR distribution.…”

“…Hence, developing tractable approaches for modeling large-scale wireless systems and analyzing their statistical performance taking into account the randomness (due to the above-mentioned factors) have become compelling. In this context, stochastic geometry [3] (also referred to as geometric probability), a probabilistic analytical approach to study (random) point configurations, has become a necessary theoretical tool for the analysis and characterization of large-scale wireless systems including heterogeneous cellular networks [4]- [6], dynamic spectrum access systems [7], [8], wireless ad hoc networks [9]- [12], drone networks [13]- [15], vehicular networks [16]- [18], and low earth orbit satellite networks [19], [20]. Spatio-temporal aspects of mobile communications, including the spatial distribution of network nodes, wireless channels and traffic patterns have to be considered for system development, resource allocation, performance evaluation and optimization.…”

The Transdimensional Poisson Process for Vehicular Network Analysis

“…Ideally, the transmitting vehicles should be distributed such that no other transmitting vehicle is in its vicinity, mimicking a hard-core point process. However, the analysis of hard-core models is less tractable [9]. In this work, we assume that the vehicles transmit with a certain probability in each slot following slotted ALOHA, i.e., the transmitting vehicles on each street form independently thinned 1D PPPs.…”

“…and(9), the conditional success probability can be expressed asP PLP−PPP m (θ) = P(g > θD α I | I, V) = E I [exp(−θD α I) | V] s z −α + 1 − p b ,(30)where s = θD α , and (a) is obtained by averaging over ALOHA and fading. ThenM PLP−PPP b,m = E[P m (θ) b ]where (b) follows from the independence of the 1D PPPs.…”