  We consider a cell-free wireless system operated in Time Division Duplex
(TDD) mode with user-centric clusters of remote radio units (RUs). Since the
uplink pilot dimensions per channel coherence slot is limited, co-pilot users
might incur mutual pilot contamination. In the current literature, it is
assumed that the long-term statistical knowledge of all user channels is
available. This enables Minimum Mean-Square Error channel estimation or
simplified dominant subspace projection, which achieves significant pilot
decontamination under certain assumptions on the channel covariance matrices.
However, estimating the channel covariance matrix or even just its dominant
subspace at all RUs forming a user cluster is not an easy task. In fact, if not
properly designed, a piloting scheme for such long-term statistics estimation
will also be subject to the contamination problem. In this paper, we propose a
new channel subspace estimation scheme explicitly designed for cell-free
wireless networks. Our scheme is based on 1) a sounding reference signal (SRS)
using latin squares wideband frequency hopping, and 2) a subspace estimation
method based on robust Principal Component Analysis (R-PCA). The SRS hopping
scheme ensures that for any user and any RU participating in its cluster, only
a few pilot measurements will contain strong co-pilot interference. These few
heavily contaminated measurements are (implicitly) eliminated by R-PCA, which
is designed to regularize the estimation and discount the ``outlier''
measurements. Our simulation results show that the proposed scheme achieves
almost perfect subspace knowledge, which in turns yields system performance
very close to that with ideal channel state information, thus essentially
solving the problem of pilot contamination in cell-free user-centric TDD
wireless networks.
