  In this paper, we consider the precoder design for an under-loaded or
critically loaded downlink multi-user multiple-input multiple-output (MU-MIMO)
communication system. We propose novel precoding and decoding schemes which
enhance system performance based on rate splitting at the transmitter and
single-stage successive interference cancellation at the receivers. The
proposed successive null-space (SNS) precoding scheme utilizes linear
combinations of the null-space basis vectors of the successively augmented MIMO
channel matrices of the users as precoding vectors to adjust the
inter-user-interference experienced by the receivers. We formulate a non-convex
weighted sum rate (WSR) optimization problem, and solve it via successive
convex approximation to obtain a suboptimal solution for the precoding vectors
and the associated power allocation. Our simulation results reveal that the
proposed SNS precoders outperform block diagonalization based linear and rate
splitting designs, and in many cases, have a relatively small gap to the
maximum sum rate achieved by dirty paper coding.
