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（FL）固有的通信瓶颈，空中联邦学习（AirFL）作为一种有前景的解决方案应运而生，然而其性能受到深度衰落条件的严重制约。本文提出AirFL-Mem——一种通过实现长期记忆机制来缓解深度衰落影响的新型方案。我们推导了考虑长期记忆及现有短期记忆AirFL变体的收敛界，适用于一般非凸目标函数。理论表明，AirFL-Mem在理想通信条件下具有与联邦平均算法（FedAvg）相同的收敛速率，而现有方案的性能普遍受限于误差下限。基于理论结果，我们进一步提出一种新颖的凸优化策略，用于瑞利衰落信道中功率控制的截断阈值选取。实验结果验证了理论分析，证实了长期记忆机制在缓解深度衰落方面的优势。