  This letter focuses on the pilot contamination problem in the uplink and
downlink of cell-free massive multiple-input multiple-output networks with
different degrees of cooperation between access points. The optimum minimum
mean square error processing can take advantage of large-scale fading
coefficients for canceling the interference of pilot-sharing user-equipments
and thus achieves asymptotically unbounded capacity. However, it is
computationally demanding and can only be implemented in a fully centralized
network. Here, sub-optimal schemes are derived that provide unbounded capacity
with linear-growing complexity and using only local channel estimates but
global channel statistics. This makes them suited for both centralized and
distributed networks. In this latter case, the best performance is achieved
with a generalized maximum ratio combiner that maximizes a capacity bound based
on channel statistics only.
