Performance Analysis of UAV-Enabled Over-the-Air Computation Under Imperfect Channel Estimation

Over-the-air computation (AirComp) is a powerful technique to combine data collected from an enormous number of nodes with limited bandwidth availability. When unmanned aerial vehicles are involved in AirComp as flying fusion centers (FFCs), ultrafast data aggregation can be achieved for ubiquitous sensing and environmental surveillance applications. However, one of the main challenges in AirComp is channel estimation. Whereas most of existing studies assume perfect channel estimation, in this paper, considering the common channel estimation approach using reference signals sent by the FFC, we investigate how imperfect channel state information (CSI) impacts the mean square error (MSE) performance of AirComp. We derive a closed-form expression of MSE, in which the degradation due to the amplitude and phase errors can be identified. Both analytical and simulation results show that the MSE floors are incurred by the imperfect CSI even in the high SNR regime. We observe that the average MSE becomes about 100 times worse compared to that with perfect CSI, which exhibits the significance of accurate channel estimation.