  In this work, we study the asymptotic behavior of the zero-forcing precoder
based on the least squares (LS) and the linear minimum mean-square error
(LMMSE) channel estimates for the downlink (DL) of a frequency-division-duplex
(FDD) massive multiple-input-single-output (MISO) system. We show analytically
the rather surprising result that zero-forcing precoding based on the LS
estimate leads asymptotically to an interference-free transmission, even if the
number of pilots used for DL channel training is less than the number of
antennas available at the base station (BS). Although the LMMSE channel
estimate exhibits a better quality in terms of the MSE due to the exploitation
of the channel statistics, we show that in the case of contaminated channel
observations, zero-forcing based on the LMMSE is unable to eliminate the
inter-user interference in the asymptotic limit of high DL transmit powers. In
order for the results to hold, mild conditions on the channel probing phase are
assumed. The validity of our analytical results is demonstrated through
numerical simulations for different scenarios.
