  Cell-free massive MIMO is emerging as a promising technology for future
wireless communication systems, which is expected to offer uniform coverage and
high spectral efficiency compared to classical cellular systems. We study in
this paper how cell-free massive MIMO can support federated edge learning.
Taking advantage of the additive nature of the wireless multiple access
channel, over-the-air computation is exploited, where the clients send their
local updates simultaneously over the same communication resource. This
approach, known as over-the-air federated learning (OTA-FL), is proven to
alleviate the communication overhead of federated learning over wireless
networks. Considering channel correlation and only imperfect channel state
information available at the central server, we propose a practical
implementation of OTA-FL over cell-free massive MIMO. The convergence of the
proposed implementation is studied analytically and experimentally, confirming
the benefits of cell-free massive MIMO for OTA-FL.
