  We study federated learning (FL) at the wireless edge, where power-limited
devices with local datasets collaboratively train a joint model with the help
of a remote parameter server (PS). We assume that the devices are connected to
the PS through a bandwidth-limited shared wireless channel. At each iteration
of FL, a subset of the devices are scheduled to transmit their local model
updates to the PS over orthogonal channel resources, while each participating
device must compress its model update to accommodate to its link capacity. We
design novel scheduling and resource allocation policies that decide on the
subset of the devices to transmit at each round, and how the resources should
be allocated among the participating devices, not only based on their channel
conditions, but also on the significance of their local model updates. We then
establish convergence of a wireless FL algorithm with device scheduling, where
devices have limited capacity to convey their messages. The results of
numerical experiments show that the proposed scheduling policy, based on both
the channel conditions and the significance of the local model updates,
provides a better long-term performance than scheduling policies based only on
either of the two metrics individually. Furthermore, we observe that when the
data is independent and identically distributed (i.i.d.) across devices,
selecting a single device at each round provides the best performance, while
when the data distribution is non-i.i.d., scheduling multiple devices at each
round improves the performance. This observation is verified by the convergence
result, which shows that the number of scheduled devices should increase for a
less diverse and more biased data distribution.
