  We study federated learning (FL), where power-limited wireless devices
utilize their local datasets to collaboratively train a global model with the
help of a remote parameter server (PS). The PS has access to the global model
and shares it with the devices for local training, and the devices return the
result of their local updates to the PS to update the global model. This
framework requires downlink transmission from the PS to the devices and uplink
transmission from the devices to the PS. The goal of this study is to
investigate the impact of the bandwidth-limited shared wireless medium in both
the downlink and uplink on the performance of FL with a focus on the downlink.
To this end, the downlink and uplink channels are modeled as fading broadcast
and multiple access channels, respectively, both with limited bandwidth. For
downlink transmission, we first introduce a digital approach, where a
quantization technique is employed at the PS to broadcast the global model
update at a common rate such that all the devices can decode it. Next, we
propose analog downlink transmission, where the global model is broadcast by
the PS in an uncoded manner. We consider analog transmission over the uplink in
both cases. We further analyze the convergence behavior of the proposed analog
approach assuming that the uplink transmission is error-free. Numerical
experiments show that the analog downlink approach provides significant
improvement over the digital one, despite a significantly lower transmit power
at the PS. The experimental results corroborate the convergence results, and
show that a smaller number of local iterations should be used when the data
distribution is more biased, and also when the devices have a better estimate
of the global model in the analog downlink approach.
