In this work, we propose a communication-efficient hierarchical federated learning algorithm for distributed setups including core servers and multiple edge servers with clusters of devices. Assuming different learning tasks, clusters with a same task collaborate. To implement the algorithm over wireless links, we propose a scalable clustered over-the-air aggregation scheme for the uplink with a bandwidth-limited broadcast scheme for the downlink that requires only a single resource block for each algorithm iteration, independent of the number of edge servers and devices. This setup is faced with interference of devices in the uplink and interference of edge servers in the downlink that are to be modeled rigorously. We first develop a spatial model for the setup by modeling devices as a Poisson cluster process over the edge servers and quantify uplink and downlink error terms due to the interference. Accordingly, we present a comprehensive mathematical approach to derive the convergence bound for the proposed algorithm including any number of collaborating clusters and provide special cases and design remarks. Finally, we show that despite the interference and data heterogeneity, the proposed algorithm not only achieves high learning accuracy for a variety of parameters but also significantly outperforms the conventional hierarchical learning algorithm.

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