  In this paper, we characterize the performance of a three-dimensional (3D)
two-hop cellular network in which terrestrial base stations (BSs) coexist with
unmanned aerial vehicles (UAVs) to serve a set of ground user equipment (UE).
In particular, a UE connects either directly to its serving terrestrial BS by
an access link or connects first to its serving UAV which is then wirelessly
backhauled to a terrestrial BS (joint access and backhaul). We consider
realistic antenna radiation patterns for both BSs and UAVs using practical
models developed by the third generation partnership project (3GPP). We assume
a probabilistic channel model for the air-to-ground transmission, which
incorporates both line-of-sight (LoS) and non-line-of-sight (NLoS) links.
Assuming the max-power association policy, we study the performance of the
network in both amplify-and-forward (AF) and decode-and-forward (DF) relaying
protocols. Using tools from stochastic geometry, we analyze the joint
distribution of distance and zenith angle of the closest (and serving) UAV to
the origin in a 3D setting. Further, we identify and extensively study key
mathematical constructs as the building blocks of characterizing the received
signal-to-interference-plus-noise ratio (SINR) distribution. Using these
results, we obtain exact mathematical expressions for the coverage probability
in both AF and DF relaying protocols. Furthermore, considering the fact that
backhaul links could be quite weak because of the downtilted antennas at the
BSs, we propose and analyze the addition of a directional uptilted antenna at
the BS that is solely used for backhaul purposes. The superiority of having
directional antennas with wirelessly backhauled UAVs is further demonstrated
via simulation.
