  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.
