Downlink Coverage Analysis of An Aerial User in Vertical Heterogeneous Networks

Ubiquitous wireless connectivity is critical for the operation of aerial users. In this paper, we investigate the downlink coverage probability of a typical aerial user served by a network of terrestrial-BSs and aerial-BSs, which we refer to as the vertical HetNet (VHetNet). We model the terrestrial-BSs as an infinite 2-D Poisson point process (PPP) and aerial-BSs as a finite 2-D Binomial point process (BPP). A typical aerial user is assumed to be associated with the BS that provides the strongest biased average received signal power. Closed-form expressions for the association probabilities to a terrestrial-BS and an aerial-BS are derived. Under the assumption of an interference-limited network, we derive an expression for the coverage probability in terms of the Laplace transform of the aggregate interference power. Several design insights are presented, showing that the coverage probability does not have a steady behavior with the aerial user height; and a denser aerial-BS network improves the overall coverage probability. Moreover, the results reveal that the coverage probability under unbiased aerial user association always outperforms its biased counterpart.