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. A one-bit digital over-the-air aggregation (OBDA) scheme has been recently proposed, featuring one-bit gradient quantization at edge devices and majority-voting based decoding at the edge server. However, the low-resolution one-bit gradient quantization slows down the model convergence and leads to performance degradation. On the other hand, the aggregation errors caused by fading channels in Air-FEEL is still remained to be solved. To address these issues, we propose the error-feedback one-bit broadband digital aggregation (EFOBDA) and an optimized power control policy. To this end, we first provide a theoretical analysis to evaluate the impact of error feedback on the convergence of FL with EFOBDA. The analytical results show that, by setting an appropriate feedback strength, EFOBDA is comparable to the Air-FEEL without quantization, thus enhancing the performance of OBDA. Then, we further introduce a power control policy by maximizing the convergence rate under instantaneous power constraints. The convergence analysis and optimized power control policy are verified by the experiments, which show that the proposed scheme achieves significantly faster convergence and higher test accuracy in image classification tasks compared with the one-bit quantization scheme without error feedback or optimized power control policy.

翻译：空中联邦边缘学习是一种利用边缘设备分布式训练数据的通信高效框架，用于分布式机器学习。该框架使所有边缘设备能够同时在整个可用带宽上传输模型更新，从而实现空中聚合。最近提出了一种一位数字空中聚合方案，该方案在边缘设备上采用了一位梯度量化，并在边缘服务器上基于多数投票解码。然而，低分辨率的一位梯度量化会减缓模型收敛速度，并导致性能下降。另一方面，空中联邦边缘学习中由衰落信道引起的聚合误差仍有待解决。为解决这些问题，我们提出了基于误差反馈的一位宽带数字聚合方法和优化的功率控制策略。为此，我们首先进行了理论分析，评估误差反馈对采用该方法的联邦学习收敛性的影响。分析结果表明，通过设置适当的反馈强度，该方法可与无量化的空中联邦边缘学习相媲美，从而提升一位数字空中聚合方案的性能。接着，我们进一步引入了一种功率控制策略，该策略通过最大化瞬时功率约束下的收敛速率来实现。收敛性分析和优化的功率控制策略通过实验得到验证，实验表明，与未采用误差反馈或优化功率控制策略的一位量化方案相比，所提出的方法在图像分类任务中实现了显著更快的收敛速度和更高的测试准确率。