Optimal Transport Theory for Power-Efficient Deployment of Unmanned   Aerial Vehicles
  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. 
Mohammad Mozaffari, Walid Saad, Mehdi Bennis, and Merouane Debbah
cs.IT math.IT