  The 3-user multiple-input single-output (MISO) broadcast channel (BC) with
hybrid channel state information at the transmitter (CSIT) is considered. In
this framework, there is perfect and instantaneous CSIT from a subset of users
and delayed CSIT from the remaining users. We present new results on the
degrees of freedom (DoF) of the 3-user MISO BC with hybrid CSIT. In particular,
for the case of 2 transmit antennas, we show that with perfect CSIT from one
user and delayed CSIT from the remaining two users, the optimal DoF is 5/3. For
the case of 3 transmit antennas and the same hybrid CSIT setting, it is shown
that a higher DoF of 9/5 is achievable and this result improves upon the best
known bound. Furthermore, with 3 transmit antennas, and the hybrid CSIT setting
in which there is perfect CSIT from two users and delayed CSIT from the third
one, a novel scheme is presented which achieves 9/4 DoF. Our results also
reveal new insights on how to utilize hybrid channel knowledge for multi-user
scenarios.
