  Over-the-air computation (AirComp) has emerged as a new analog power-domain
non-orthogonal multiple access (NOMA) technique for low-latency
model/gradient-updates aggregation in federated edge learning (FEEL). By
integrating communication and computation into a joint design, AirComp can
significantly enhance the communication efficiency, but at the cost of
aggregation errors caused by channel fading and noise. This paper studies a
particular type of FEEL with federated averaging (FedAvg) and AirComp-based
model-update aggregation, namely over-the-air FedAvg (Air-FedAvg). We
investigate the transmission power control to combat against the AirComp
aggregation errors for enhancing the training accuracy and accelerating the
training speed of Air-FedAvg. Towards this end, we first analyze the
convergence behavior (in terms of the optimality gap) of Air-FedAvg with
aggregation errors at different outer iterations. Then, to enhance the training
accuracy, we minimize the optimality gap by jointly optimizing the transmission
power control at edge devices and the denoising factors at edge server, subject
to a series of power constraints at individual edge devices. Furthermore, to
accelerate the training speed, we also minimize the training latency of
Air-FedAvg with a given targeted optimality gap, in which learning
hyper-parameters including the numbers of outer iterations and local training
epochs are jointly optimized with the power control. Finally, numerical results
show that the proposed transmission power control policy achieves significantly
faster convergence for Air-FedAvg, as compared with benchmark policies with
fixed power transmission or per-iteration mean squared error (MSE)
minimization. It is also shown that the Air-FedAvg achieves an
order-of-magnitude shorter training latency than the conventional FedAvg with
digital orthogonal multiple access (OMA-FedAvg).
