Performance Comparison Between Coherent and Non-Coherent Approaches for Over-the-Air Computation

Over-the-air computation (OAC) can effectively support rapid data aggregation from a plethora of devices, exploiting the inherent superposition property of wireless multiple access channels. The key challenge in OAC is the synchronization of multiple devices, which are handled through either the coherent approach using the beacon transmissions by the fusion center or the non-coherent approach based on random sequences. Motivated by the lack of a fair comparison in prior arts, we derive the closed-form expressions of their mean squared errors (MSEs), which provides an explicit guideline on which approach to use and how we improve one compared to the other by adjusting their key design factors. Thus, this paper provides design insights into the OAC synchronization method depending on the system requirements in terms of MSE.