Optimized UAV Trajectory and Transceiver Design for Over-the-Air Computation Systems

This article investigates a multi-slot unmanned aerial vehicle (UAV) assisted over-the-air computation (AirComp) system, where the UAV is deployed as a flying base station to compute functional values of data distributed at multiple ground sensors via AirComp. Subject to the power constraints of the UAV and ground sensors, we minimize the computational mean-squared error (MSE) of AirComp, by optimizing UAV's trajectory, the ground sensors' transmit coefficients, and the de-noising factors within multiple slots. As a low-complexity design solution, we decompose the formulated non-convex multi-slot UAV-assisted AirComp design problem into two low-dimensional sub-problems, one for optimizing the sensor groups and the energy-minimal UAV trajectory design, and the other for jointly optimizing the ground sensors' transmit coefficients and the UAV's receive de-noising factors for AirComp. First, we use the K-means algorithm to cluster the ground sensors, and then optimize the energy-minimal UAV trajectory for visiting the sensor groups. Next, based on the Lagrange duality method, we obtain the optimal AirComp transceiver design solution in a closed form. Numerical results show that the proposed design solution achieves a significant computational MSE performance gain compared with the existing benchmark schemes.