Cell-Vertex UAV Networks: Stochastic Geometry Modeling and Coverage Analysis

This paper investigates the coverage performance of unmanned aerial vehicle (UAV) networks when serving cellcorner users that experience link outages from terrestrial base stations (BSs). We consider a Poisson cellular network in which the BSs are modeled as a homogeneous Poisson point process (PPP), thereby tessellating the ground plane into Poisson-Voronoi (PV) cells. Concentrating on the worst-case scenario in which cellcorner users are clustered at PV vertices (i.e., the intersections of cell edges), we propose deploying UAVs that act as aerial BSs directly above these vertices to provide dedicated coverage for such users. Unfortunately, the intricate spatial distribution of PV vertices severely complicates system-level performance analysis because no tractable mathematical tools are available. To bridge this gap, we introduce a novel approximation based on a thinned uniform pair-cluster process (UPCP) and its statistical resemblance to PV vertices is justified through the asymptotic behaviors of pair correlation function (PCF). Leveraging the probability generating functional (PGFL) of UPCP, we derive the nearest distance distribution and Laplace transform of interference from UAVs. Subsequently, we obtain the coverage probability of the resulting cell-vertex UAV network. Extensive Monte-Carlo simulations validate our theoretical results and demonstrate that the proposed UPCP approximation yields substantially more accurate analytical results than the conventional PPP approximation.