On the Degrees-of-freedom of the 3-user MISO Broadcast Channel with   Hybrid CSIT
  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. 
SaiDhiraj Amuru, Ravi Tandon, Shlomo Shamai (Shitz)
cs.IT math.IT