Optimal DoF Region of the K -User MISO BC with Partial CSIT

We consider the K -user multiple-input-single-output broadcast channel, where the transmitter, equipped with M antennas, serves K users, with K \leq M. The transmitter has access to a partial channel state information of the users. This is modeled by letting the variance of the channel state information at the transmitter error of user i scale as O(P^{-\alpha {i}} ) for the signal-to-noise ratio P and some constant \alpha {i} \geq 0. In this letter, we derive the optimal degrees-of-freedom region in such setting, and we show that rate-splitting is the key scheme to achieve such a region.