  We consider fairness scheduling in a user-centric cell-free massive MIMO
network, where $L$ remote radio units, each with $M$ antennas, serve $K_{\rm
tot} \approx LM$ user equipments (UEs). Recent results show that the maximum
network sum throughput is achieved where $K_{\rm act} \approx \frac{LM}{2}$ UEs
are simultaneously active in any given time-frequency slots. However, the
number of users $K_{\rm tot}$ in the network is usually much larger. This
requires that users are scheduled over the time-frequency resource and achieve
a certain throughput rate as an average over the slots. We impose throughput
fairness among UEs with a scheduling approach aiming to maximize a concave
component-wise non-decreasing network utility function of the per-user
throughput rates. In cell-free user-centric networks, the pilot and cluster
assignment is usually done for a given set of active users. Combined with
fairness scheduling, this requires pilot and cluster reassignment at each
scheduling slot, involving an enormous overhead of control signaling exchange
between network entities. We propose a fixed pilot and cluster assignment
scheme (independent of the scheduling decisions), which outperforms the
baseline method in terms of UE throughput, while requiring much less control
information exchange between network entities.
