  By processing in the frequency domain (FD), massive MIMO systems can approach
the theoretical per-user capacity using a single carrier modulation (SCM)
waveform with a cyclic prefix. Minimum mean squared error (MMSE) detection and
zero forcing (ZF) precoding have been shown to effectively cancel multi-user
interference while compensating for inter-symbol interference. In this paper,
we present a modified downlink precoding approach in the FD based on
regularized zero forcing (RZF), which reuses the matrix inverses calculated as
part of the FD MMSE uplink detection. By reusing these calculations, the
computational complexity of the RZF precoder is drastically lowered, compared
to the ZF precoder. Introduction of the regularization in RZF leads to a bias
in the detected data symbols at the user terminals. We show this bias can be
removed by incorporating a scaling factor at the receiver. Furthermore, it is
noted that user powers have to be optimized to strike a balance between noise
and interference seen at each user terminal. The resulting performance of the
RZF precoder exceeds that of the ZF precoder for low and moderate input
signal-to-noise ratio (SNR) conditions, and performance is equal for high input
SNR. These results are established and confirmed by analysis and simulation.
