🤖 AI Summary
This study addresses the joint optimization of coverage performance and energy efficiency for high-altitude platforms (HAPs) performing circular patrol missions. For the first time, a stochastic geometry framework based on small-circle Cox processes is developed under a spherical Earth model, yielding Poisson and binomial patrol trajectory models. By integrating communication interference analysis with a circular flight energy consumption model, closed-form expressions are derived for the nearest-neighbor distance distribution, coverage probability, and coverage energy efficiency. The work reveals fundamental differences between intensity-driven deployment and finite-formation strategies and provides a closed-form condition for the energy-optimal patrol radius, demonstrating that efficient operation requires joint optimization of patrol geometry, platform density, and cruising speed.
📝 Abstract
This paper develops a stochastic-geometry framework for high-altitude platform station (HAPs) networks in which platforms execute cyclic patrol trajectories anchored to designated service regions. We introduce two small-circle ring Cox process models on the spherical Earth. In the small-circle ring Poisson Cox process (SCR-PCP), platforms form one-dimensional Poisson point processes on localized patrol rings, whereas in the small-circle ring binomial Cox process (SCR-BCP), each ring contains a fixed number of uniformly distributed platforms. We establish the isotropy of both models and derive spatial statistics, including the distributions of the nearest-anchor, nearest-ring, and nearest-HAPs distances, together with the joint serving distance and serving ring angle distribution required for SCR-BCP analysis. Building on these results, we derive coverage probability expressions under nearest-HAPs association by decomposing aggregate interference into same-ring and other-ring components and characterizing their conditional Laplace transforms. To account for the flight dynamics of patrol-based HAPs, we integrate a steady circular flight propulsion model with the communication analysis and introduce a coverage energy efficiency (CEE) metric. This yields an analytical condition for the energy-optimal patrol radius that balances coverage performance against the propulsion cost of circular flight. Numerical results reveal fundamental differences between intensity-driven (SCR-PCP) and finite-fleet (SCR-BCP) deployments and demonstrate that patrol geometry, platform density, and cruising velocity should be jointly optimized to achieve energy-efficient HAPs operation.