Modeling and Performance Analysis of Over-the-Air Computing in Cellular IoT Networks

Ultra-fast wireless data aggregation (WDA) of distributed sensor data has emerged as a critical design challenge in the ultra-densely-deployed cellular Internet of Things networks (CITN) due to limited spectral resources. Over-the-air computing (AirComp) has been proposed as an effective solution for ultra-fast WDA by exploiting the signal-superposition property of wireless channels. However, how the random spatial locations of AirComp devices and the access radius (AR) to allow these devices to operate AirComp in the access point (AP) affect AirComp performance has not been investigated yet. In this letter, we derive the analytical result of average mean square error (MSE) in an AirComp AP with a given AR, where the AirComp devices are modelled following the Poisson point process. Based on the analytical average MSE result, we investigate the effect of AR on the AirComp performance numerically. The results show that there exists an optimal AR for AirComp, which is approximately 50 m, and the average MSE can be decreased by up to 71% under our simulation environment.