Coverage and Rate Analysis for Vertical Heterogeneous Networks (VHetNets)

In this paper, we leverage concepts from stochastic geometry to investigate the downlink performance of a vertical heterogeneous network (VHetNet) comprising aerial base stations (ABSs) and terrestrial base stations (TBSs). We model the ABSs as a 2D Poisson point process (PPP) deployed at a particular altitude while the TBSs are modelled as a 2D PPP deployed on the ground. The proposed analytical framework adopts an appropriate air-to-ground (A2G) channel model that incorporates line-of-sight (LoS) and non-line-of-sight (NLoS) transmissions. We begin the main technical part of the analysis by deriving analytical expressions for the distribution of the distances between a typical user and the closest LoS ABS, NLoS ABS, and TBS. After that, we derive expressions for the probabilities that a typical user is associated with a NLoS ABS, LoS ABS, or TBS. Under the assumption that A2G and terrestrial channels experience Nakagami-<inline-formula> <tex-math notation="LaTeX">$m$ </tex-math></inline-formula> fading with different <inline-formula> <tex-math notation="LaTeX">$m$ </tex-math></inline-formula> parameters, we derive an expression for the Laplace transform of interference power. Furthermore, we derive exact and approximate analytical expressions for the coverage probability and achievable rate. We show that these approximations match the simulations with negligible errors for small <italic>SINR</italic> thresholds and <inline-formula> <tex-math notation="LaTeX">$m$ </tex-math></inline-formula> parameters of Nakagami-<inline-formula> <tex-math notation="LaTeX">$m$ </tex-math></inline-formula> fading.