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.

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