  In this paper we study the impact of unmanned aerial vehicles (UAVs)
trajectories on terrestrial users' spectral efficiency (SE). Assuming a strong
line of sight path to the users, the distance from all users to all UAVs
influence the outcome of an online trajectory optimization. The trajectory
should be designed in a way that the fairness rate is maximized over time. That
means, the UAVs travel in the directions that maximize the minimum of the
users' SE. From the free-space path-loss channel model, a data-rate gradient is
calculated and used to direct the UAVs in a long-term perspective towards the
local optimal solution on the two-dimensional spatial grid. Therefore, a
control system implementation is designed. Thereby, the UAVs follow the
data-rate gradient direction while having a more smooth trajectory compared
with a gradient method. The system can react to changes of the user locations
online; this system design captures the interaction between multiple UAV
trajectories by joint processing at the central unit, e.g., a ground base
station. Because of the wide spread of user locations, the UAVs end up in
optimal locations widely apart from each other. Besides, the SE expectancy is
enhancing continuously while moving along this trajectory.
