Error Analysis for Over-the-Air Federated Learning under Misaligned and Time-Varying Channels

This paper investigates an OFDM-based over-the-air federated learning (OTA-FL) system, where multiple mobile devices, e.g., unmanned aerial vehicles (UAVs), transmit local machine learning (ML) models to a central parameter server (PS) for global model aggregation. The high mobility of local devices results in imperfect channel estimation, leading to a misalignment problem, i.e., the model parameters transmitted from different local devices do not arrive at the central PS simultaneously. Moreover, the mobility introduces time-varying uploading channels, which further complicates the aggregation process. All these factors collectively cause distortions in the OTA-FL training process which are underexplored. To quantify these effects, we first derive a closed-form expression for a single-round global model update in terms of these channel imperfections. We then extend our analysis to capture multiple rounds of global updates, yielding a bound on the accumulated error in OTA-FL. We validate our theoretical results via extensive numerical simulations, which corroborate our derived analysis.