Optimal Transport Theory for Power-Efficient Deployment of Unmanned Aerial Vehicles (1602.01532v1)

Abstract: In this paper, the optimal deployment of multiple unmanned aerial vehicles (UAVs) acting as flying base stations is investigated. Considering the downlink scenario, the goal is to minimize the total required transmit power of UAVs while satisfying the users' rate requirements. To this end, the optimal locations of UAVs as well as the cell boundaries of their coverage areas are determined. To find those optimal parameters, the problem is divided into two sub-problems that are solved iteratively. In the first sub-problem, given the cell boundaries corresponding to each UAV, the optimal locations of the UAVs are derived using the facility location framework. In the second sub-problem, the locations of UAVs are assumed to be fixed, and the optimal cell boundaries are obtained using tools from optimal transport theory. The analytical results show that the total required transmit power is significantly reduced by determining the optimal coverage areas for UAVs. These results also show that, moving the UAVs based on users' distribution, and adjusting their altitudes can lead to a minimum power consumption. Finally, it is shown that the proposed deployment approach, can improve the system's power efficiency by a factor of 20 compared to the classical Voronoi cell association technique with fixed UAVs locations.

• The paper proposes an iterative two-step method that decomposes UAV deployment into facility location and optimal transport subproblems.
• The approach optimally adjusts UAV positions and altitudes, reducing transmit power by up to 20 times compared to traditional methods.
• Numerical results demonstrate that dynamic user distributions can be managed effectively, enhancing coverage and service quality.

Optimal Transport Theory for Power-Efficient Deployment of Unmanned Aerial Vehicles

This paper explores the deployment of unmanned aerial vehicles (UAVs) as flying base stations, with a focus on minimizing the total transmit power required to meet user rate demands. This problem is approached in the context of a downlink communication scenario, where multiple UAVs are tasked with providing wireless service. The proposed solution involves an iterative approach that separates the problem into two subproblems, each focusing on different aspects of the deployment challenge.

Methodological Approach

1. Problem Decomposition: The major optimization problem is divided into two subproblems to efficiently tackle the deployment challenge. First, given fixed cell boundaries, the optimal location for each UAV is determined using a facility location framework. Second, with fixed UAV locations, optimal cell boundaries are deduced using optimal transport theory.
2. Facility Location Framework: For a preset coverage area, the optimal placement of UAVs is determined by considering users as clients and UAVs as facilities. The algorithm seeks to minimize the transmit power, treated as the transportation cost.
3. Optimal Transport Theory: This mathematical framework is utilized to define cell boundaries that account for user distribution. By drawing parallels to resource transport methodologies, an optimal model for UAV service areas is computed, ensuring efficient power distribution across users.
4. Altitudinal Adjustments: The analysis also investigates how varying the altitude of UAVs affects power efficiency, suggesting that specific altitudes optimize LOS links while minimizing path loss.

Numerical Results and Implications

The results demonstrate that the proposed deployment strategy can significantly enhance power efficiency. The system can lower required transmit power by a factor of 20 compared to the traditional Voronoi cell association method. Furthermore, adjusting the UAV locations and altitudes in response to user distribution not only reduces transmit power but also enhances service quality.

Practical and Theoretical Implications

• Efficiency Gains in Dynamic Environments: The approach provides a powerful mechanism for the efficient deployment of UAVs in dynamic urban environments where user density can vary significantly. This deployment model is particularly useful for temporary events or areas where rapid deployment is necessary.
• Influence of User Distribution: Understanding how user distribution impacts power requirements allows for a more nuanced deployment strategy, where UAVs can dynamically adjust coverage boundaries.
• Future Research Directions: This paper opens avenues for exploring multiple UAV scenarios with diverse user density profiles and the integration of advanced control methods for real-time UAV positioning and altitude adjustments. There is also potential for extending these strategies to incorporate renewable energy sources and energy harvesting methods to further improve the sustainability of UAV-based communication networks.

In conclusion, this paper presents a rigorous examination of power-efficient UAV deployment through the integration of advanced mathematical frameworks. The findings provide a foundation for improving wireless communication networks by deploying UAVs in a manner that is both power-efficient and responsive to user demands. Future advancements in this area could transform how temporary and dynamic wireless services are provisioned, highlighting the importance of interdisciplinary methodologies in tackling complex deployment challenges.