  In this letter, we present a widely-linear minimum mean square error
(WL-MMSE) precoding scheme employing real-valued transmit symbols for downlink
large-scale multi-user multiple-input single-output (MU-MISO) systems. In
contrast to the existing WL-MMSE transceivers for single-user multiple-input
multiple-output (SU-MIMO) systems, which use both WL precoders and WL
detectors, the proposed scheme uses WL precoding only and simple conventional
detection at the user terminals (UTs). Moreover, to avoid the computational
complexity associated with inversion of large matrices, we modify the WL-MMSE
precoder using polynomial expansion (PE). Our simulation results show that in
overloaded systems, where the number of UTs is larger than the number of base
station antennas, the proposed PE WL-MMSE precoder with only a few terms in the
matrix polynomial achieves a substantially higher sum rate than systems
employing conventional MMSE precoding. Hence, more UTs sharing the same
time/frequency resources can be served in a cell. We validate our simulation
results with an analytical expression for the asymptotic sum rate which is
obtained by using results from random matrix theory.
