Wireless Communication using Unmanned Aerial Vehicles (UAVs): Optimal Transport Theory for Hover Time Optimization (1704.04813v1)

Abstract: In this paper, the effective use of flight-time constrained unmanned aerial vehicles (UAVs) as flying base stations that can provide wireless service to ground users is investigated. In particular, a novel framework for optimizing the performance of such UAV-based wireless systems in terms of the average number of bits (data service) transmitted to users as well as UAVs' hover duration (i.e. flight time) is proposed. In the considered model, UAVs hover over a given geographical area to serve ground users that are distributed within the area based on an arbitrary spatial distribution function. In this case, two practical scenarios are considered. In the first scenario, based on the maximum possible hover times of UAVs, the average data service delivered to the users under a fair resource allocation scheme is maximized by finding the optimal cell partitions associated to the UAVs. Using the mathematical framework of optimal transport theory, a gradient-based algorithm is proposed for optimally partitioning the geographical area based on the users' distribution, hover times, and locations of the UAVs. In the second scenario, given the load requirements of ground users, the minimum average hover time that the UAVs need for completely servicing their ground users is derived. To this end, first, an optimal bandwidth allocation scheme for serving the users is proposed. Then, given this optimal bandwidth allocation, the optimal cell partitions associated with the UAVs are derived by exploiting the optimal transport theory. Results show that our proposed cell partitioning approach leads to a significantly higher fairness among the users compared to the classical weighted Voronoi diagram. In addition, our results reveal an inherent tradeoff between the hover time of UAVs and bandwidth efficiency while serving the ground users.

• The paper introduces optimal transport theory to optimize UAV cell partitioning for enhanced service fairness and resource allocation.
• It employs convex optimization and gradient-based algorithms to reduce UAV hover time by up to 64% compared to classical methods.
• The study demonstrates practical UAV deployment strategies that balance bandwidth efficiency, energy consumption, and user data service requirements.

Overview of UAV-based Wireless Communication through Optimal Transport Theory

The paper investigates the use of Unmanned Aerial Vehicles (UAVs) as mobile base stations to enhance wireless communication services. It proposes a framework to optimize wireless network performance considering UAVs with flight-time constraints. This paper explores two key scenarios: maximizing average data service under preset constraints on UAV hover time, and minimizing hover time while fulfilling user load requirements. The theoretical foundation is rooted in optimal transport theory, transforming complex partitioning and resource allocation problems into more tractable forms using convex optimization techniques.

The authors introduce a novel application of optimal transport theory to tackle the problem of cell partitioning in UAV-enabled networks, where UAVs must effectively allocate resources and service time to ground users distributed across a geographic area. Two scenarios are considered:

1. Scenario 1: Here, the authors address UAV operations under fixed hover time constraints. The objective is optimizing the average data service delivered to users. Leveraging optimal transport theory, the cell partitioning challenge becomes a convex optimization problem. The solution involves deriving optimal geographical partitions based on user distribution and UAV parameters through a gradient-based algorithm.
2. Scenario 2: This scenario minimizes the UAV hover times needed to meet the data demands of ground users. Here, the paper focuses on allocating bandwidth optimally and determining UAV cell partitions to minimize hover time. Again, optimal transport theory facilitates finding the ideal solutions.

The results indicate that their proposed method for Scenario 1, compared to classical Voronoi-based partitioning, ensures fairness in user service, achieving up to 64% reduction in UAV hover time by adopting optimal bandwidth and area partitioning strategies. This efficiency gain highlights the balancing act between UAV hover time and bandwidth efficiency.

Numerical Results and Analysis

Simulation results underscore the superiority of the proposed framework over classical methods. The paper demonstrates that employing the optimal transport-based approach significantly enhances fairness across users in terms of service level, leading to a fairer distribution of resources. Additionally, simulations reveal how strategic deployment and optimized resource allocation dramatically reduce necessary hover time, thus conserving UAV energy and extending operational periods.

Numerical simulation outcomes demonstrate that these improvements are not marginal. In highly congested areas (non-uniform distributions), the fairness index improves substantively over weighted Voronoi diagrams. The reduction in hover time (up to 64%) highlights the advantages of the proposed method, notably in ensuring realistic, practical deployment scenarios where battery life and regulatory constraints are critical.

Implications and Future Perspectives

The implications of these results are twofold. Practically, they offer wireless service providers strategies to manage UAV network deployments effectively, particularly in urban environments with heterogeneous user distributions. Theoretically, the framework advances the application of optimal transport theory in telecommunications, presenting an efficient, mathematically robust approach to addressing multi-UAV resource distribution challenges.

Looking ahead, the integration of advanced signal processing techniques and machine learning models into this framework could further optimize UAV path planning and user association in real-time, adapting dynamically to changing environmental and user demand conditions. Additionally, extending this approach to consider 3D user distributions and dynamic environments represents a potential avenue for future research, enhancing the system's adaptability and efficiency.

In conclusion, the paper contributes an innovative, theoretically grounded methodology with significant potential for practical implementation in UAV-based wireless communication systems. It lays a solid foundation for future exploration into more complex multi-agent scenarios, where UAVs, equipped with robust optimization strategies, can deliver enhanced and fair wireless services across diverse and challenging environments.