When implementing hierarchical federated learning over wireless networks, scalability assurance and the ability to handle both interference and device data heterogeneity are crucial. This work introduces a learning method designed to address these challenges, along with a scalable transmission scheme that efficiently uses a single wireless resource through over-the-air computation. To provide resistance against data heterogeneity, we employ gradient aggregations. Meanwhile, the impact of interference is minimized through optimized receiver normalizing factors. For this, we model a multi-cluster wireless network using stochastic geometry, and characterize the mean squared error of the aggregation estimations as a function of the network parameters. We show that despite the interference and the data heterogeneity, the proposed scheme achieves high learning accuracy and can significantly outperform the conventional hierarchical algorithm.

翻译：在无线网络中实现分层联邦学习时，可扩展性保证以及处理干扰与设备数据异构性的能力至关重要。本文提出一种旨在应对这些挑战的学习方法，同时设计了一种可扩展的传输方案，通过空中计算高效利用单一无线资源。为抵抗数据异构性，我们采用梯度聚合技术。同时，通过优化接收端归一化因子，将干扰影响降至最低。为此，我们利用随机几何对多簇无线网络进行建模，并刻画了聚合估计均方误差随网络参数变化的函数关系。研究表明，尽管存在干扰和数据异构性，所提方案仍能实现高学习精度，并显著优于传统分层算法。