  In this work, we investigate federated edge learning over a fading multiple
access channel. To alleviate the communication burden between the edge devices
and the access point, we introduce a pioneering digital over-the-air
computation strategy employing q-ary quadrature amplitude modulation,
culminating in a low latency communication scheme. Indeed, we propose a new
federated edge learning framework in which edge devices use digital modulation
for over-the-air uplink transmission to the edge server while they have no
access to the channel state information. Furthermore, we incorporate multiple
antennas at the edge server to overcome the fading inherent in wireless
communication. We analyze the number of antennas required to mitigate the
fading impact effectively. We prove a non-asymptotic upper bound for the mean
squared error for the proposed federated learning with digital over-the-air
uplink transmissions under both noisy and fading conditions. Leveraging the
derived upper bound, we characterize the convergence rate of the learning
process of a non-convex loss function in terms of the mean square error of
gradients due to the fading channel. Furthermore, we substantiate the
theoretical assurances through numerical experiments concerning mean square
error and the convergence efficacy of the digital federated edge learning
framework. Notably, the results demonstrate that augmenting the number of
antennas at the edge server and adopting higher-order modulations improve the
model accuracy up to 60\%.
