<p>Cell-free massive MIMO systems
consist of many distributed access points with simple components that jointly
serve the users. In millimeter wave bands, only a limited set of predetermined
beams can be supported. In a network that
consolidates these technologies, downlink analog beam selection stands as a challenging task for the network sum-rate maximization. Low-cost digital filters
can improve the network sum-rate
further. In this work, we propose low-cost joint designs of analog beam selection and digital filters. The pro-posed
joint designs achieve significantly higher sum-rates than the disjoint design benchmark.
Supervised machine learning (ML)
algorithms can efficiently approximate the input-output mapping functions of the beam selection decisions of the joint designs with low computational
complexities. Since the training
of ML algorithms is performed off-line, we pro-pose a well-constructed joint
design that combines multiple initializations,
iterations, and selection features, as well as beam conflict control, i.e., the same beam cannot be used for multiple users. The numerical
results indicate that ML algorithms
can retain 99-100% of the original sum-rate results achieved by the proposed
well-constructed designs.</p>