Two-Tier High Altitude Platform Stations (HAPS) for Exploring Wireless Energy Harvesting

1. Problem Statement

The deployment of aerial platforms like High-Altitude Platform Stations (HAPS) and Uncrewed Aerial Vehicles (UAVs) in 6G networks is limited by energy scarcity, which restricts mission duration and operational continuity. While existing solutions include solar energy harvesting (limited by weather/day-night cycles) and harvesting from ground-based stations (vulnerable to line-of-sight blockages or disasters), there is a lack of research on inter-platform wireless energy harvesting.

The core problem addressed is how to extend the flight time and energy efficiency of HAPS systems by utilizing the ubiquitous electromagnetic waves generated by other aerial platforms during transmission, specifically within a two-tier HAPS architecture, while optimizing the trade-off between energy harvesting time and data transmission time.

2. System Architecture and Methodology

System Architecture

The authors propose a novel Two-Tier HAPS-Super Macro Base Station (HAPS-SMBS) architecture:

• Mother HAPS-SMBS: A high-altitude node (approx. 20 km) acting as a central manager and energy source. It coordinates backhaul links and transmits energy signals but does not serve ground users directly.
• Regular HAPS-SMBS: Lower-altitude nodes (approx. 18 km) that act as base stations for ground users. They harvest energy from the Mother HAPS-SMBS and use it to transmit data.
• Mechanism: The system operates in time-slots. A fraction of time ($\tau$) is dedicated to Wireless Energy Harvesting (EH) from the Mother node, and the remaining time ($1-\tau$) is used for Information Transmission.

Modeling

• Energy Harvesting Models: The paper analyzes both Linear and Non-Linear EH models.
  • Linear: Assumes a constant conversion efficiency.
  • Non-Linear: Uses a logistic function to model the saturation effects and non-linear input-output characteristics of practical EH circuits.
• Propagation Model: The system accounts for path loss in the stratospheric channel, considering distances between the Mother and Regular HAPS ($d_1$) and between the Regular HAPS and ground users ($d_2$).

Optimization Approaches

The paper formulates a joint non-convex optimization problem to maximize the system data rate by optimizing two variables:

1. Horizontal Positioning ($d_A$): The distance between the Mother and Regular HAPS.
2. EH Factor ($\tau$): The time allocation for harvesting vs. transmission.

To solve this, two methods are proposed and compared:

1. Iterative Distance and EH Factor Algorithm (IDFA): A coordinate descent approach that splits the problem into two sub-problems (optimizing $d_A$ while fixing $\tau$, and vice versa) to find a sub-optimal solution.
2. Q-Learning: A Reinforcement Learning (RL) approach where the Regular HAPS acts as an agent. It learns the optimal policy for $d_A$ and $\tau$ jointly by interacting with the environment to maximize the reward (data rate), without splitting the problem.

Flight Mission Optimization

A secondary optimization addresses scenarios where harvested energy is insufficient. The system minimizes the draw from the onboard battery inventory by borrowing only the necessary energy to meet the minimum transmit power requirement ($P_{Req}$).

3. Key Contributions

• Novel Paradigm: First proposal of a two-tier HAPS architecture where aerial platforms harvest energy from other aerial platforms rather than just ground stations or solar sources.
• Theoretical Derivation: Derivation of closed-form solutions for the optimal horizontal positioning ($d_A$) for both linear and non-linear EH models to maximize data rate.
• Algorithmic Innovation: Development of the IDFA for efficient sub-optimal solving and the application of Q-Learning to verify results and handle the joint optimization problem without decomposition.
• Energy Management Strategy: A convex optimization framework to minimize battery consumption when harvested energy is insufficient, ensuring continuous operation.

4. Key Results

Numerical simulations (using parameters like 2.45 GHz frequency, 20km altitude) yielded the following insights:

• Performance Gains:
  • Optimal Positioning: Using Theorems 1 and 2 improved data rates by 0.8–3.6% (Linear) and 0.25–0.4% (Non-Linear) compared to non-optimized positioning.
  • Joint Optimization: Q-Learning and IDFA significantly outperformed random selection. Q-Learning provided 7–11% improvement in Linear EH scenarios and 0.8–1.8% in Non-Linear scenarios compared to baseline.
  • Q-Learning vs. IDFA: In linear models with intensive training, Q-Learning outperformed IDFA, achieving 1.5–4% higher data rates, demonstrating its ability to approximate global optima more closely in complex non-convex landscapes.
• Non-Linearity Impact: Non-linear EH models showed saturation at higher transmit powers, confirming that linear assumptions often overestimate performance in real-world circuits.
• Parameter Sensitivity:
  • Frequency: Higher frequencies reduce harvested energy due to increased attenuation.
  • Distance: Increasing the distance between HAPS nodes drastically reduces harvested energy.
  • Antenna Gain: Higher receiver antenna gains significantly boost harvested energy and data rates.
• Battery Conservation: The proposed power maximization strategy effectively minimizes the use of stored onboard energy, allowing the system to rely primarily on harvested energy when available.

5. Significance and Future Outlook

This research is significant for the evolution of 6G Non-Terrestrial Networks (NTN). By enabling HAPS to recharge from each other, the system offers a robust solution for maintaining connectivity in disaster zones or areas where ground infrastructure is compromised.

• Sustainability: It reduces reliance on finite onboard batteries and variable solar power, potentially extending flight missions from days to months.
• Resilience: The architecture ensures service continuity even if ground-based energy sources are unavailable.
• Future Work: The authors suggest integrating Reconfigurable Intelligent Surfaces (RIS), Free-Space Optics (FSO), and advanced Massive MIMO to further enhance energy transfer efficiency and mitigate the limitations of non-linear EH circuits.

In conclusion, the paper demonstrates that intelligent positioning and joint optimization of time allocation and platform location can significantly enhance the energy efficiency and data throughput of aerial networks, with Q-Learning emerging as a powerful tool for solving complex, non-convex resource allocation problems in 6G.