  Federated learning (FL) has been recognized as a promising distributed
learning paradigm to support intelligent applications at the wireless edge,
where a global model is trained iteratively through the collaboration of the
edge devices without sharing their data. However, due to the relatively large
communication cost between the devices and parameter server (PS), direct
computing based on the information from the devices may not be resource
efficient. This paper studies the joint communication and learning design for
the over-the-air computation (AirComp)-based two-tier wireless FL scheme, where
the lead devices first collect the local gradients from their nearby
subordinate devices, and then send the merged results to the PS for the second
round of aggregation. We establish a convergence result for the proposed scheme
and derive the upper bound on the optimality gap between the expected and
optimal global loss values. Next, based on the device distance and data
importance, we propose a hierarchical clustering method to build the two-tier
structure. Then, with only the instantaneous channel state information (CSI),
we formulate the optimality gap minimization problem and solve it by using an
efficient alternating minimization method. Numerical results show that the
proposed scheme outperforms the baseline ones.
