  This paper studies the joint device selection and power control scheme for
wireless federated learning (FL), considering both the downlink and uplink
communications between the parameter server (PS) and the terminal devices. In
each round of model training, the PS first broadcasts the global model to the
terminal devices in an analog fashion, and then the terminal devices perform
local training and upload the updated model parameters to the PS via
over-the-air computation (AirComp). First, we propose an AirComp-based adaptive
reweighing scheme for the aggregation of local updated models, where the model
aggregation weights are directly determined by the uplink transmit power values
of the selected devices and which enables the joint learning and communication
optimization simply by the device selection and power control. Furthermore, we
provide a convergence analysis for the proposed wireless FL algorithm and the
upper bound on the expected optimality gap between the expected and optimal
global loss values is derived. With instantaneous channel state information
(CSI), we formulate the optimality gap minimization problems under both the
individual and sum uplink transmit power constraints, respectively, which are
shown to be solved by the semidefinite programming (SDR) technique. Numerical
results reveal that our proposed wireless FL algorithm achieves close to the
best performance by using the ideal FedAvg scheme with error-free model
exchange and full device participation.
