Downlink Coverage and Rate Analysis of an Aerial User in Vertical Heterogeneous Networks (VHetNets).

In this paper, we analyze the downlink coverage probability and rate of an aerial user in vertical HetNets (VHetNets) comprising aerial base stations (aerial-BSs) and terrestrial-BSs. The locations of terrestrial-BSs are modeled as an infinite 2-D Poisson Point Process (PPP), while the locations of aerial-BSs are modeled as a finite 2-D Binomial Point Process (BPP). Our cellular-to-air (C2A) channel model incorporates line-of-sight (LoS) and non-LoS transmissions between terrestrial-BSs and a typical aerial user, while we assume LoS transmissions for all aerial links. We assume that the aerial user is associated with an aerial-BS or terrestrial-BS that provides the strongest average received power. Using stochastic geometry, we derive exact and approximate expressions of the coverage probability and rate in terms of interference power's Laplace transform. The expressions are simplified assuming only LoS transmissions for the C2A channels. This enables easy-to-compute equations with good accuracy at elevated aerial user heights. We find that aerial users hovering at low altitudes tend to connect to aerial-BSs in denser terrestrial environments. Employing directive beamforming at aerial-BSs guarantees an acceptable performance at the aerial user by reducing interference signals received from the aerial-BSs. In denser terrestrial networks, the performance at the aerial user degrades substantially despite beamforming.