Fundamentals of 3D Two-Hop Cellular Networks Analysis with Wireless Backhauled UAVs

This paper provides the performance characterization of a three-dimensional (3D) two-hop decode-and-forward (DF) aerial-terrestrial communication network, where unmanned aerial vehicles (UAVs) coexist with terrestrial base stations (BSs) to serve a set of user equipment (UE) on the ground. We assume that each UE connects either to a BS via access link or through a UAV to a BS via joint access and backhaul links, where the link from the UE to the UAV is an access link and from the UAV to the BS is a backhaul link. To capture the impact of directionality in practical antennas, we use a model developed by the third generation partnership project (3GPP) for the antenna radiation pattern of both BSs and UAVs. Following the nearest neighbor association policy, we obtain the joint distance and angle distribution of the serving UAV to the origin in a 3D setting using tools from stochastic geometry. Furthermore, we identify and analyze key mathematical constructs as the building blocks of characterizing the received signal-to-interference-plus-noise ratio (SINR) distribution at the typical UE for the DF relaying protocol. Using these intermediate results, we derive an exact mathematical expression for the coverage probability in UAV-assisted two-hop DF cellular networks. One key takeaway from our analysis is the existence of a mean UAV height and a 3D density of UAVs that optimize the network coverage performance.