  Due to its communication efficiency and privacy-preserving capability,
federated learning (FL) has emerged as a promising framework for machine
learning in 5G-and-beyond wireless networks. Of great interest is the design
and optimization of new wireless network structures that support the stable and
fast operation of FL. Cell-free massive multiple-input multiple-output
(CFmMIMO) turns out to be a suitable candidate, which allows each communication
round in the iterative FL process to be stably executed within a large-scale
coherence time. Aiming to reduce the total execution time of the FL process in
CFmMIMO, this paper proposes choosing only a subset of available users to
participate in FL. An optimal selection of users with favorable link conditions
would minimize the execution time of each communication round, while limiting
the total number of communication rounds required. Toward this end, we
formulate a joint optimization problem of user selection, transmit power, and
processing frequency, subject to a predefined minimum number of participating
users to guarantee the quality of learning. We then develop a new algorithm
that is proven to converge to the neighbourhood of the stationary points of the
formulated problem. Numerical results confirm that our proposed approach
significantly reduces the FL total execution time over baseline schemes. The
time reduction is more pronounced when the density of access point deployments
is moderately low.
