  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.
