  Over-the-air computation (AirComp) provides a promising way to support
ultrafast aggregation of distributed data. However, its performance cannot be
guaranteed in long-distance transmission due to the distortion induced by the
channel fading and noise. To unleash the full potential of AirComp, this paper
proposes to use a low-cost unmanned aerial vehicle (UAV) acting as a mobile
base station to assist AirComp systems. Specifically, due to its controllable
high-mobility and high-altitude, the UAV can move sufficiently close to the
sensors to enable line-of-sight transmission and adaptively adjust all the
links' distances, thereby enhancing the signal magnitude alignment and noise
suppression. Our goal is to minimize the time-averaging mean-square error for
AirComp by jointly optimizing the UAV trajectory, the scaling factor at the
UAV, and the transmit power at the sensors, under constraints on the UAV's
predetermined locations and flying speed, sensors' average and peak power
limits. However, due to the highly coupled optimization variables and
time-dependent constraints, the resulting problem is non-convex and
challenging. We thus propose an efficient iterative algorithm by applying the
block coordinate descent and successive convex optimization techniques.
Simulation results verify the convergence of the proposed algorithm and
demonstrate the performance gains and robustness of the proposed design
compared with benchmarks.
