  Unmanned aerial vehicles (UAVs) can enhance the performance of cellular
networks, due to their high mobility and efficient deployment. In this paper,
we present a first study on how the user mobility affects the UAVs'
trajectories of a multiple-UAV assisted wireless communication system.
Specifically, we consider the UAVs are deployed as aerial base stations to
serve ground users who move between different regions. We maximize the
throughput of ground users in the downlink communication by optimizing the
UAVs' trajectories, while taking into account the impact of the user mobility,
propulsion energy consumption, and UAVs' mutual interference. We formulate the
problem as a route selection problem in an acyclic directed graph. Each vertex
represents a task associated with a reward on the average user throughput in a
region-time point, while each edge is associated with a cost on the energy
propulsion consumption during flying and hovering. For the centralized
trajectory design, we first propose the shortest path scheme that determines
the optimal trajectory for the single UAV case. We also propose the centralized
route selection (CRS) scheme to systematically compute the optimal trajectories
for the more general multiple-UAV case. Due to the NP-hardness of the
centralized problem, we consider the distributed trajectory design that each
UAV selects its trajectory autonomously and propose the distributed route
selection (DRS) scheme, which will converge to a pure strategy Nash equilibrium
within a finite number of iterations.
