Robust Over-the-Air Federated Learning Under Imperfect CSI

Interest continues to grow in utilizing federated learning (FL) for various signal processing and communications applications. Over-the-air (OTA) computation has been proposed to improve FL efficiency in bandwidth-limited environments by leveraging the superposition characteristic of a wireless multiple-access channel (MAC). However, OTA FL faces inherent challenges due to channel noise and fading in any wireless MAC scenario, which can degrade optimization and significantly reduce model accuracy. This paper aims to design a robust OTA FL system to counteract the effects of noise and fading over time-varying channels. We propose a novel approach employing a Kalman filter (KF)-based OTA FL algorithm under imperfect channel state information (CSI). We conduct a convergence analysis of our OTA FL scheme, which motivates our development of a complementary hierarchical optimization methodology to minimize the impact of bias and noise terms. Numerical results confirm that our methodology has superior performance to conventional OTA FL, and approaches the performance obtained by the upper limit of perfect CSI in low-SNR scenarios.