  Massive multiple-input multiple-output (MIMO) systems use antenna arrays with
a large number of antenna elements to serve many different users
simultaneously. The large number of antennas in the system makes, however, the
channel state information (CSI) acquisition strategy design critical and
particularly challenging. Interestingly, in the context of massive MIMO
systems, channels exhibit a large degree of spatial correlation which results
in strongly rank-deficient spatial covariance matrices at the base station
(BS). With the final objective of analyzing the benefits of covariance-aided
uplink multi-user CSI acquisition in massive MIMO systems, here we compare the
channel estimation mean-square error (MSE) for (i) conventional CSI
acquisition, which does not assume any knowledge on the user spatial covariance
matrices and uses orthogonal pilot sequences; and (ii) covariance-aided CSI
acquisition, which exploits the individual covariance matrices for channel
estimation and enables the use of non-orthogonal pilot sequences. We apply a
large-system analysis to the latter case, for which new asymptotic MSE
expressions are established under various assumptions on the distributions of
the pilot sequences and on the covariance matrices. We link these expressions
to those describing the estimation MSE of conventional CSI acquisition with
orthogonal pilot sequences of some equivalent length. This analysis provides
insights on how much training overhead can be reduced with respect to the
conventional strategy when a covariance-aided approach is adopted.
