  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.
