  Cell-free massive multiple-input multiple-output (CF mMIMO) systems serve the
user equipments (UEs) by geographically distributed access points (APs) by
means of joint transmission and reception. To limit the power consumption due
to fronthaul signaling and processing, each UE should only be served by a
subset of the APs, but it is hard to identify that subset. Previous works have
tackled this combinatorial problem heuristically. In this paper, we propose a
sparse distributed processing design for CF mMIMO, where the AP-UE association
and long-term signal processing coefficients are jointly optimized. We
formulate two sparsity-inducing mean-squared error (MSE) minimization problems
and solve them by using efficient proximal approaches with block-coordinate
descent. For the downlink, more specifically, we develop a virtually optimized
large-scale fading precoding (V-LSFP) scheme using uplink-downlink duality. The
numerical results show that the proposed sparse processing schemes work well in
both uplink and downlink. In particular, they achieve almost the same spectral
efficiency as if all APs would serve all UEs, while the energy efficiency is
2-4 times higher thanks to the reduced processing and signaling.
