  This paper studies the sum rate performance of a low complexity quantized
CSI-based Tomlinson-Harashima (TH) precoding scheme for downlink multiuser MIMO
tansmission, employing greedy user selection. The asymptotic distribution of
the output signal to interference plus noise ratio of each selected user and
the asymptotic sum rate as the number of users K grows large are derived by
using extreme value theory. For fixed finite signal to noise ratios and a
finite number of transmit antennas $n_T$, we prove that as K grows large, the
proposed approach can achieve the optimal sum rate scaling of the MIMO
broadcast channel. We also prove that, if we ignore the precoding loss, the
average sum rate of this approach converges to the average sum capacity of the
MIMO broadcast channel. Our results provide insights into the effect of
multiuser interference caused by quantized CSI on the multiuser diversity gain.
