Modeling and Performance Analysis of Vertical Heterogeneous Networks under 3D Blockage Effects and Multiuser MIMO Systems

In dense cities, vertical heterogeneous networks (VHetNets) operating in the millimeter wave (mmWave) bands can deliver massive data rates and bridge coverage gaps, but are prone to 3D blockages and suffer from high penetration loss. Drawing on stochastic geometry theory, this paper studies the downlink performance in a mmWave network of Ground Bases Stations (GBSs) assisted by a finite number of Unmanned Aerial Vehicle (UAV)-Base Stations (UBSs) under 3D blockage effects of buildings. The UBSs are distributed according to Binomial Point Process within a bounded circular area. To mitigate the significant propagation loss, we deploy multiuser multiple-input-multiple-output (MU-MIMO) at the UBS. The buildings are modeled by a Boolean scheme of rectangles with a height following exponential distribution. To depict a hotspot scenario, the users (UEs) distribution is modeled as a Thomas Cluster Process and gathered around the GBSs. Then, we have developed formulas for LoS/NLoS probabilities, that take into account the density, height, and area of blockages. Assuming shadowing, Nakagami- m fading channels, and using the gamma approximation, we evaluate the coverage probability and area spectral efficiency (ASE). In addition, a 3D beamforming analysis is performed. The analytical results are validated through Monte Carlo simulations. The findings reveal that in dense areas, UBSs can improve performance with an optimal number, altitude, and tilt angle, that depend on the target area and the city's blockage density index. Furthermore, MU-MIMO transmission enhances the ASE.