An Analytical Framework for HAPS Downlink Coverage Based on Stochastic Geometry

The high-altitude platform station (HAPS), which is anticipated to play a key role in future networks, has drawn increasing attention in both industry and academia. In this paper, a realistic downlink communication scenario is introduced in which an aerodynamic HAPS flies along a circular trajectory and serves handheld users in an urban environment. Stochastic geometry-based analysis is conducted, along with the assimilation of approximations using simulation data to incorporate the circular aperture antenna model of the HAPS. Analytical expressions are derived for the coverage probability and the ergodic capacity, and the validity of these expressions is demonstrated through extensive Monte Carlo simulations. Although there are slight gaps in the performance analysis, the general tendencies between the analysis and simulation results show a close match. The impact of aerodynamic parameters such as flight radius and altitude on the coverage probability is demonstrated to be relatively marginal to that of communication system parameters such as the number of simultaneous service users and the total transmission power. In terms of ergodic capacity, both aerodynamic parameters show improved performance as their values decrease, with the altitude being more dominant. Although smaller flight radii are favorable for improving network performance, such configurations impose additional constraints on aircraft design, highlighting the need to carefully consider the limitations of size, weight, and power (SWaP). A discussion on real-world HAPS design is supplemented in order to offer practical guidelines for balancing communication performances with the SWaP constraints of the HAPS.