  Federated learning (FL) leverages data distributed at the edge of the network
to enable intelligent applications. The efficiency of FL can be improved by
using over-the-air computation (AirComp) technology in the process of gradient
aggregation. In this paper, we propose a relay-assisted large-scale FL
framework, and investigate the device scheduling problem in relay-assisted FL
systems under the constraints of power consumption and mean squared error
(MSE). we formulate a joint device scheduling, and power allocation problem to
maximize the number of scheduled devices. We solve the resultant non-convex
optimization problem by transforming the optimization problem into multiple
sparse optimization problems. By the proposed device scheduling algorithm,
these sparse sub-problems are solved and the maximum number of federated
learning edge devices is obtained. The simulation results demonstrate the
effectiveness of the proposed scheme as compared with other benchmark schemes.
