降低无线联邦学习通信开销，用标量传输和异步机制提升效率

Federated Learning (FL) is an emerging learning framework that enables edge devices to collaboratively train ML models without sharing their local data. FL faces, however, a significant challenge due to the high amount of information that must be exchanged between the devices and the aggregator in the training phase, which can exceed the limited capacity of wireless systems. In this paper, two communication-efficient FL methods are considered where communication overhead is reduced by communicating scalar values instead of long vectors and by allowing high number of users to send information simultaneously. The first approach employs a zero-order optimization technique with two-point gradient estimator, while the second involves a first-order gradient computation strategy. The novelty lies in leveraging channel information in the learning algorithms, eliminating hence the need for additional resources to acquire channel state information (CSI) and to remove its impact, as well as in considering asynchronous devices. We provide a rigorous analytical framework for the two methods, deriving convergence guarantees and establishing appropriate performance bounds.