  This paper considers a downlink cell-free multiple-input multiple-output
(MIMO) network in which multiple multi-antenna base stations (BSs) serve
multiple users via coherent joint transmission. In order to reduce the energy
consumption by radio frequency components, each BS selects a subset of antennas
for downlink data transmission after estimating the channel state information
(CSI). We aim to maximize the sum spectral efficiency by jointly optimizing the
antenna selection and precoding design. To alleviate the fronthaul overhead and
enable real-time network operation, we propose a distributed scalable machine
learning algorithm. In particular, at each BS, we deploy a convolutional neural
network (CNN) for antenna selection and a graph neural network (GNN) for
precoding design. Different from conventional centralized solutions that
require a large amount of CSI and signaling exchange among the BSs, the
proposed distributed machine learning algorithm takes only locally estimated
CSI as input. With well-trained learning models, it is shown that the proposed
algorithm significantly outperforms the distributed baseline schemes and
achieves a sum spectral efficiency comparable to its centralized counterpart.
