Optimizing Power for Interference-Resilient Hierarchical Over-the-Air Federated Learning

In this paper, we investigate a large-scale Hierarchical over-the-air federated learning (Hierarchical-Air-FL) network comprising a fusion center (FC) and multiple clusters, where each cluster includes a base station (BS) and several edge devices. During the model training process, we leverage over-the-air computation (AirComp) for gradient aggregation to facilitate simultaneous transmission from devices to their respective BSs and from the BSs to the FC. To enhance communication efficiency and reduce transmission overhead, we employ a two-stage amplify-and-forward (AF) relaying mechanism. A significant challenge in such systems is inter-cluster interference due to shared wireless resources among clusters. To address this, we first conduct a comprehensive convergence analysis focusing on the optimality gap. Building upon this analysis, we propose an optimized power allocation strategy to minimize the optimality gap. Simulation results demonstrate that the proposed method exhibits significant advantages over baseline schemes.