  Over-the-air computation (AirComp)-based federated learning (FL) enables
low-latency uploads and the aggregation of machine learning models by
exploiting simultaneous co-channel transmission and the resultant waveform
superposition. This study aims at realizing secure AirComp-based FL against
various privacy attacks where malicious central servers infer clients' private
data from aggregated global models. To this end, a differentially private
AirComp-based FL is designed in this study, where the key idea is to harness
receiver noise perturbation injected to aggregated global models inherently,
thereby preventing the inference of clients' private data. However, the
variance of the inherent receiver noise is often uncontrollable, which renders
the process of injecting an appropriate noise perturbation to achieve a desired
privacy level quite challenging. Hence, this study designs transmit power
control across clients, wherein the received signal level is adjusted
intentionally to control the noise perturbation levels effectively, thereby
achieving the desired privacy level. It is observed that a higher privacy level
requires lower transmit power, which indicates the tradeoff between the privacy
level and signal-to-noise ratio (SNR). To understand this tradeoff more fully,
the closed-form expressions of SNR (with respect to the privacy level) are
derived, and the tradeoff is analytically demonstrated. The analytical results
also demonstrate that among the configurable parameters, the number of
participating clients is a key parameter that enhances the received SNR under
the aforementioned tradeoff. The analytical results are validated through
numerical evaluations.
