大规模联邦学习用无线信号传输参数，反而提升隐私与收敛速度。

Federated learning facilitates collaborative model training across multiple clients while preserving data privacy. However, its performance is often constrained by limited communication resources, particularly in systems supporting a large number of clients. To address this challenge, integrating over-the-air computations into the training process has emerged as a promising solution to alleviate communication bottlenecks. The system significantly increases the number of clients it can support in each communication round by transmitting intermediate parameters via analog signals rather than digital ones. This improvement, however, comes at the cost of channel-induced distortions, such as fading and noise, which affect the aggregated global parameters. To elucidate these effects, this paper develops a theoretical framework to analyze the performance of over-the-air federated learning in large-scale client scenarios. Our analysis reveals three key advantages of scaling up the number of participating clients: (1) Enhanced Privacy: The mutual information between a client's local gradient and the server's aggregated gradient diminishes, effectively reducing privacy leakage. (2) Mitigation of Channel Fading: The channel hardening effect eliminates the impact of small-scale fading in the noisy global gradient. (3) Improved Convergence: Reduced thermal noise and gradient estimation errors benefit the convergence rate. These findings solidify over-the-air model training as a viable approach for federated learning in networks with a large number of clients. The theoretical insights are further substantiated through extensive experimental evaluations.