On Signal Peak Power Constraint of Over-the-Air Federated Learning

Federated learning (FL) has been considered a promising privacy preserving distributed edge learning framework. Over-the-air computation (AirComp) technique leveraging analog transmission enables the aggregation of local updates directly over-the-air by exploiting the superposition properties of wireless multiple-access channel, thereby drastically reducing the communication bottleneck issues of FL compared with digital transmission schemes. This work points out that existing AirComp-FL overlooks a key practical constraint, the instantaneous peak-power constraints imposed by the non-linearity of radiofrequency power amplifiers. We present and analyze the effect of the classic method to deal with this issue, amplitude clipping combined with filtering. We investigate the effect of instantaneous peak-power constraints in AirComp-FL for both single-carrier and multi-carrier orthogonal frequency-division multiplexing (OFDM) systems. We highlight the specificity of AirComp-FL: the samples depend on the gradient value distribution, leading to a higher peak-to-average power ratio (PAPR) than that observed for uniformly distributed signals. Simulation results demonstrate that, in practical settings, the instantaneous transmit power regularly exceeds the power-amplifier limit; however, by applying clipping and filtering, the FL performance can be degraded. The degradation becomes pronounced especially in multi-carrier OFDM systems due to the in-band distortions caused by clipping and filtering.