  Although the benefits of precoding and combining of data signals are widely
recognized, the potential of these techniques for pilot transmission is not
fully understood. This is particularly relevant for multiuser multiple-input
multiple-output (MU-MIMO) cellular systems using millimeter-wave (mmWave)
communications, where multiple antennas will have to be used both at the
transmitter and the receiver to overcome the severe path loss. In this paper,
we characterize the gains of pilot precoding and combining in terms of channel
estimation quality and achievable data rate. Specifically, we consider three
uplink pilot transmission scenarios in a mmWave MU-MIMO cellular system: 1)
non-precoded and uncombined, 2) precoded but uncombined, and 3) precoded and
combined. We show that a simple precoder that utilizes only the second-order
statistics of the channel reduces the variance of the channel estimation error
by a factor that is proportional to the number of user equipment (UE) antennas.
We also show that using a linear combiner designed based on the second-order
statistics of the channel significantly reduces multiuser interference and
provides the possibility of reusing some pilots. Specifically, in the large
antenna regime, pilot precoding and combining help to accommodate a large
number of UEs in one cell, significantly improve channel estimation quality,
boost the signal-to-noise ratio of the UEs located close to the cell edges,
alleviate pilot contamination, and address the imbalanced coverage of pilot and
data signals.
