Downlink Coverage and Rate Analysis of an Aerial User in Integrated Aerial and Terrestrial Networks

In this paper, the downlink coverage probability and average achievable rate of an aerial user in a vertical HetNet (VHetNet) comprising aerial base stations (aerial-BSs) and terrestrial-BSs are analyzed. 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 3-D Binomial point process (BPP) deployed at a particular height. We adopt cellular-to-air (C2A) channel model that incorporates LoS and NLoS transmissions between the terrestrial-BSs and the typical aerial user while we assume LoS transmissions for the air-toair (A2A) channels separating the aerial user and aerial-BSs. For tractability reasons, we simplify the expression of the LoS probability provided by the International Telecommunications Union using curve fitting. We assume that the aerial user is associated with the BS (either an aerial-BS or terrestrial-BS) that provides the strongest average received power. Using tools from stochastic geometry, we derive analytical expressions of the coverage probability and achievable rate in terms of the Laplace transform of interference power. To simplify the derived analytical expressions, we assume that the C2A links are in LoS conditions. Although this approximation gives pessimistic results compared to the exact performance, the analytical approximations are easier to evaluate and quantify well the performance at high heights of the aerial user. Our findings reveal that using directive beamforming for the aerial-BSs improves the downlink performance substantially since it alleviates the strong interference signals received from the aerial-BSs.