  This paper investigates federated learning in a wireless communication
system, where random device selection is employed with non-independent and
identically distributed (non-IID) data. The analysis indicates that while
training deep learning networks using federated stochastic gradient descent
(FedSGD) on non-IID datasets, device selection can generate gradient errors
that accumulate, leading to potential weight divergence. To mitigate training
divergence, we design an age-weighted FedSGD to scale local gradients according
to the previous state of devices. To further improve learning performance by
increasing device participation under the maximum time consumption constraint,
we formulate an energy consumption minimization problem by including resource
allocation and sub-channel assignment. By transforming the resource allocation
problem into convex and utilizing KKT conditions, we derived the optimal
resource allocation solution. Moreover, this paper develops a matching based
algorithm to generate the enhanced sub-channel assignment. Simulation results
indicate that i) age-weighted FedSGD is able to outperform conventional FedSGD
in terms of convergence rate and achievable accuracy, and ii) the proposed
resource allocation and sub-channel assignment strategies can significantly
reduce energy consumption and improve learning performance by increasing the
number of selected devices.
