Addressing the communication bottleneck inherent in federated learning (FL), over-the-air FL (AirFL) has emerged as a promising solution, which is, however, hampered by deep fading conditions. In this paper, we propose AirFL-Mem, a novel scheme designed to mitigate the impact of deep fading by implementing a \emph{long-term} memory mechanism. Convergence bounds are provided that account for long-term memory, as well as for existing AirFL variants with short-term memory, for general non-convex objectives. The theory demonstrates that AirFL-Mem exhibits the same convergence rate of federated averaging (FedAvg) with ideal communication, while the performance of existing schemes is generally limited by error floors. The theoretical results are also leveraged to propose a novel convex optimization strategy for the truncation threshold used for power control in the presence of Rayleigh fading channels. Experimental results validate the analysis, confirming the advantages of a long-term memory mechanism for the mitigation of deep fading.

翻译：针对联邦学习中固有的通信瓶颈，空中联邦学习（AirFL）作为有前景的解决方案应运而生，但深度衰落条件制约了其性能。本文提出AirFL-Mem——一种通过引入长时记忆机制来缓解深度衰落影响的新型方案。我们为一般非凸目标函数提供了考虑长时记忆以及现有短时记忆AirFL变体的收敛界。理论表明，AirFL-Mem在理想通信条件下具有与联邦平均算法相同的收敛速率，而现有方案的性能通常受误差平台限制。基于理论结果，我们进一步提出了一种针对瑞利衰落信道中功率控制截断阈值的新型凸优化策略。实验验证了理论分析，证实了长时记忆机制在缓解深度衰落方面的优势。