  In this paper, we investigate the communication designs of over-the-air
computation (AirComp) empowered federated learning (FL) systems considering
uplink model aggregation and downlink model dissemination jointly. We first
derive an upper bound on the expected difference between the training loss and
the optimal loss, which reveals that optimizing the FL performance is
equivalent to minimizing the distortion in the received global gradient vector
at each edge node. As such, we jointly optimize each edge node transmit and
receive equalization coefficients along with the edge server forwarding matrix
to minimize the maximum gradient distortion across all edge nodes. We further
utilize the MNIST dataset to evaluate the performance of the considered FL
system in the context of the handwritten digit recognition task. Experiment
results show that deploying multiple antennas at the edge server significantly
reduces the distortion in the received global gradient vector, leading to a
notable improvement in recognition accuracy compared to the single antenna
case.
