  We consider the Multiple Input Single Output (MISO) Gaussian Broadcast
channel with $N_t$ antennas at the base station (BS) and $N_u$ single-antenna
users in the downlink. We propose a novel user grouping precoder which improves
the sum rate performance of the Zero-Forcing (ZF) precoder specially when the
channel is ill-conditioned. The proposed precoder partitions all the users into
small groups of equal size. Downlink beamforming is then done in such a way
that, at each user's receiver the interference from the signal intended for
users not in its group is nulled out. Intra-group interference still remains,
and is cancelled through successive interference pre-subtraction at the BS
using Dirty Paper Coding (DPC). The proposed user grouping method is different
from user selection, since it is a method for precoding of information to the
selected (scheduled) users, and not for selecting which users are to be
scheduled. Through analysis and simulations, the proposed user grouping based
precoder is shown to achieve significant improvement in the achievable sum rate
when compared to the ZF precoder. When users are paired (i.e., each group has
two users), the complexity of the proposed precoder is $O(N_u^3) + O(N_u^2
N_t)$ which is the same as that of the ZF precoder.
