  Ultra-fast wireless data aggregation (WDA) of distributed data has emerged as
a critical design challenge in the ultra-densely deployed cellular internet of
things network (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 superposition property of wireless channels. However, the effect
of access radius of access point (AP) on the AirComp performance has not been
investigated yet. Therefore, in this work, the mean square error (MSE)
performance of AirComp in the ultra-densely deployed CITN is analyzed with the
AP access radius. By modelling the spatial locations of internet of things
devices as a Poisson point process, the expression of MSE is derived in an
analytical form, which is validated by Monte Carlo simulations. Based on the
analytical MSE, we investigate the effect of AP access radius on the MSE of
AirComp numerically. The results show that there exists an optimal AP access
radius for AirComp, which can decrease the MSE by up to 12.7%. It indicates
that the AP access radius should be carefully chosen to improve the AirComp
performance in the ultra-densely deployed CITN.
