Overview
This paper presents a stochastic geometry framework designed for high-altitude platform station (HAPS) networks. The framework specifically addresses HAPS systems where platforms execute cyclic patrol trajectories over designated service regions. It analyzes both network coverage and energy efficiency for these configurations.
Research Context
The study focuses on HAPS networks, a type of communication infrastructure characterized by platforms operating at high altitudes. A key element of the HAPS networks under consideration is the platforms' adherence to cyclic patrol trajectories. These trajectories are anchored to specific service regions, implying a degree of spatial localization and structured movement for the platforms.
Approach
The core of the methodology involves developing a stochastic-geometry framework. This framework introduces two distinct small-circle ring Cox process models applicable to the spherical Earth:
- Small-Circle Ring Poisson Cox Process (SCR-PCP): In this model, platforms are represented as one-dimensional Poisson point processes. These processes are situated on localized patrol rings.
- Small-Circle Ring Binomial Cox Process (SCR-BCP): This model posits that each patrol ring contains a fixed number of platforms, which are uniformly distributed along the ring.
The framework establishes the isotropy of both the SCR-PCP and SCR-BCP models. Subsequently, it derives several spatial statistics, which include:
- Distributions of the nearest-anchor distance.
- Distributions of the nearest-ring distance.
- Distributions of the nearest-HAPs distance.
For the SCR-BCP model, the framework additionally derives the joint serving distance and serving ring angle distribution. These distributions are critical for the subsequent analytical steps.
Building upon these spatial statistics, the research derives expressions for coverage probability under a nearest-HAPs association scheme. This derivation involves a decomposition of the aggregate interference into two components: same-ring interference and other-ring interference. The conditional Laplace transforms of these interference components are then characterized.
To incorporate the operational dynamics of patrol-based HAPs, the framework integrates a steady circular flight propulsion model directly into the communication analysis. This integration allows for the examination of energy expenditure associated with platform movement.
A new metric, Coverage Energy Efficiency (CEE), is introduced. This metric quantifies the balance between coverage performance and the propulsion cost of circular flight. The analytical framework then yields a condition for determining the energy-optimal patrol radius, specifically designed to achieve this balance.
Findings
- The derived spatial statistics, including nearest-anchor, nearest-ring, and nearest-HAPs distances, provide foundational insights into the spatial organization of patrol-based HAP networks under both SCR-PCP and SCR-BCP models.
- Coverage probability expressions were established by decomposing aggregate interference into same-ring and other-ring components and characterizing their conditional Laplace transforms.
- An analytical condition for the energy-optimal patrol radius was identified, aiming to balance coverage performance with the propulsion cost of circular flight.
- Numerical results indicate fundamental differences between intensity-driven deployments (SCR-PCP) and finite-fleet deployments (SCR-BCP) in HAPS networks.
- The study suggests that patrol geometry, platform density, and cruising velocity necessitate joint optimization to achieve energy-efficient HAPs operation.
Why This Matters
The research provides an analytical framework for understanding and optimizing the performance of HAPS networks that utilize patrolling strategies. The integration of flight dynamics with communication analysis and the introduction of a Coverage Energy Efficiency metric offer a comprehensive approach to designing more efficient HAPS deployments. The findings highlight the importance of jointly considering patrol geometry, platform density, and cruising velocity for energy-efficient operation.