Over-the-Air Federated Edge Learning with Error-Feedback One-Bit Quantization and Power Control

Over-the-air federated edge learning (Air-FEEL) is a communication-efficient framework for distributed machine learning using training data distributed at edge devices. This framework enables all edge devices to transmit model updates simultaneously over the entire available bandwidth, allowing for over-the-air aggregation. The existing one-bit digital over-the-air aggregation scheme features one-bit gradient quantization at edge devices and majority voting-based decoding at edge server, and therefore offers enhanced communication efficiency. However, the low-resolution one-bit gradient quantization slows down the model convergence and leads to performance degradation, while the aggregation errors caused by channel fading in Air-FEEL further impair the performance. To address these issues, we propose the error-feedback one-bit broadband digital aggregation (EFOBDA) with an optimized power control policy. To this end, we first derive the impact of aggregation errors on the convergence of FEEL with EFOBDA. Then, we further introduce a power control policy by maximizing the convergence rate under instantaneous power constraints. The analytical results and optimized power control policy are validated by the experiments, which show that the proposed scheme achieves significantly faster convergence and higher test accuracy in image classification tasks compared with the vanilla one-bit quantization scheme without error feedback or optimized power control policy.