CHARLES: Channel-Quality-Adaptive Over-the-Air Federated Learning over Wireless Networks

Over-the-air federated learning (OTA-FL) has emerged as an efficient mechanism that exploits the superposition property of the wireless medium and performs model aggregation for federated learning in the air. OTA-FL is naturally sensitive to wireless channel fading, which could significantly diminish its learning accuracy. To address this challenge, in this paper, we propose an OTA-FL algorithm called CHARLES (channel- quality-aware over-the-air local estimating and scaling). Our CHARLES algorithm performs channel state information (CSI) estimation and adaptive scaling to mitigate the impacts of wireless channel fading. We establish the theoretical convergence rate performance of CHARLES and analyze the impacts of CSI error on the convergence of CHARLES. We show that the adaptive channel inversion scaling scheme in CHARLES is robust under imperfect CSI scenarios. We also demonstrate through numerical results that CHARLES outperforms existing OTA-FL algorithms with heterogeneous data under imperfect CSI.