  In this paper, considering an interference limited inband downlink cellular
network, we study the effects of scheduling criteria, mobility constraints,
path loss models, backhaul constraints, and 3D antenna radiation pattern on
trajectory optimization problem of an unmanned aerial vehicle (UAV). In
particular, we consider a UAV that is tasked to travel between two locations
within a given amount of time (e.g., for delivery or surveillance purposes),
and we consider that such a UAV can be used to improve cellular connectivity of
mobile users by serving as a relay for the terrestrial network. As the
optimization problem is hard to solve numerically, we explore the dynamic
programming (DP) technique for finding the optimum UAV trajectory. We utilize
capacity and coverage performance of the terrestrial network while studying all
the effects of different techniques and phenomenon. Extensive simulations show
that the maximum sum-rate trajectory provides the best per user capacity
whereas, the optimal proportional fair (PF) rate trajectory provides higher
coverage probability than the other two. Since, the generated trajectories are
infeasible for the UAV to follow exactly as it can not take sharp turns due to
kinematic constraints, we generate smooth trajectory using Bezier curves. Our
results show that the cellular capacity using the Bezier curves is close to the
capacity observed when using the optimal trajectories.
