Robust THP Transceiver Designs for Multiuser MIMO Downlink

In this paper, we present two robust nonlinear transceiver designs for multiuser multi-input multi-output (MIMO) downlink in the presence of imperfections in the channel state information at the transmitter (CSIT). Both the base station (BS) as well as the users are equipped with multiple antennas. The BS employs Tomlinson-Harashima precoding (THP) for inter-user interference pre-cancellation at the transmitter. First, we consider the case where the CSIT error is Gaussian-distributed. In this case, the robust transceiver design seeks to minimize a stochastic function of the sum mean square error (SMSE) under a constraint on the total BS transmit power. We propose an iterative algorithm to solve this problem. Each iteration involves the solution of a second order cone program (SOCP). Next, we consider the case where the CSIT error can be specified by an uncertainty set. In this case, we consider a minimax design for the robust transceiver, where the worst-case SMSE is minimized under a constraint on the total BS transmit power. We show that this design problem can be solved by an iterative algorithm, wherein each iteration involves a pair of semi-definite programs (SDP). Further, we consider an extension of the proposed algorithm to the case with per-antenna power constraints. We illustrate the robustness of the proposed algorithms to imperfections in CSIT through simulations.