  In this paper, we present robust joint non-linear transceiver designs for
multiuser multiple-input multiple-output (MIMO) downlink in the presence of
imperfections in the channel state information at the transmitter (CSIT). The
base station (BS) is equipped with multiple transmit antennas, and each user
terminal is equipped with one or more receive antennas. The BS employs
Tomlinson-Harashima precoding (THP) for inter-user interference
pre-cancellation at the transmitter. We consider robust transceiver designs
that jointly optimize the transmit THP filters and receive filter for two
models of CSIT errors. The first model is a stochastic error (SE) model, where
the CSIT error is Gaussian-distributed. This model is applicable when the CSIT
error is dominated by channel estimation error. In this case, the proposed
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. The other model we
consider is a norm-bounded error (NBE) model, where the CSIT error can be
specified by an uncertainty set. This model is applicable when the CSIT error
is dominated by quantization errors. In this case, we consider a worst-case
design. For this model, we consider robust i) minimum SMSE, ii)
MSE-constrained, and iii) MSE-balancing transceiver designs. We propose
iterative algorithms to solve these problems, 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.
