  This paper considers the implementation of Tomlinson-Harashima (TH) precoding
for multiuser MIMO systems based on quantized channel state information (CSI)
at the transmitter side. Compared with the results in [1], our scheme applies
to more general system setting where the number of users in the system can be
less than or equal to the number of transmit antennas. We also study the
achievable average sum rate of the proposed quantized CSI-based TH precoding
scheme. The expressions of the upper bounds on both the average sum rate of the
systems with quantized CSI and the mean loss in average sum rate due to CSI
quantization are derived. We also present some numerical results. The results
show that the nonlinear TH precoding can achieve much better performance than
that of linear zero-forcing precoding for both perfect CSI and quantized CSI
cases. In addition, our derived upper bound on the mean rate loss for TH
precoding converges to the true rate loss faster than that of zeroforcing
precoding obtained in [2] as the number of feedback bits becomes large. Both
the analytical and numerical results show that nonlinear precoding suffers from
imperfect CSI more than linear precoding does.
