Low-Complexity Widely-Linear Precoding for Downlink Large-Scale MU-MISO Systems

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.