Coverage and network spectral efficiency analysis for UAV swarm under 3D beamforming in isolated regions

Fifth-generation networks are facing coverage problems due to the vulnerability of millimeter-wave bands caused by blockage and penetration loss phenomena, resulting in shadow zones commonly called isolated regions (IRs). Unmanned aerial vehicles (UAVs) acting as aerial base stations, can be rapidly applied to provide communications coverage in IR. Existing research mainly adopts UAVs with conventional beamforming, but this scheme simply neglects the array gain in the vertical plane, and interference coordination becomes complicated. Considering a 3D beamforming approach that adjusts the tilt angle, this paper explores the coverage and network spectral efficiency (NSE) analysis using stochastic geometry, where UAVs are distributed as a binomial point process within a bounded circular area over the IR. Specifically, the association probability of an arbitrarily-located typical user in the finite region is computed based on the strongest averaged received power in line-of-sight/non-line-of-sight propagation. Furthermore, the signal-to-interference-plus-noise ratio coverage probability and NSE expressions are obtained under the hypothesis of Nakagami-m fading. Monte Carlo simulations are performed to illustrate the effectiveness of the proposed analysis method. Through the results we show the impact of antenna elevation on the coverage, the optimal tilt angle and the optimal number of simultaneously active UAVs to maximize performance.