  We consider a $K$-user multiple-input single-output (MISO) broadcast channel
(BC) where the channel state information (CSI) of user $i(i=1,2,\ldots,K)$ may
be instantaneously perfect (P), delayed (D) or not known (N) at the transmitter
with probabilities $\lambda_P^i$, $\lambda_D^i$ and $\lambda_N^i$,
respectively. In this setting, according to the three possible CSIT for each
user, knowledge of the joint CSIT of the $K$ users could have at most $3^K$
states. In this paper, given the marginal probabilities of CSIT (i.e.,
$\lambda_P^i$, $\lambda_D^i$ and $\lambda_N^i$), we derive an outer bound for
the DoF region of the $K$-user MISO BC. Subsequently, we tighten this outer
bound by taking into account a set of inequalities that capture some of the
$3^K$ states of the joint CSIT. One of the consequences of this set of
inequalities is that for $K\geq3$, it is shown that the DoF region is not
completely characterized by the marginal probabilities in contrast to the
two-user case. Afterwards, the tightness of these bounds are investigated
through the discussion on the achievability. Finally, a two user MIMO BC having
CSIT among P and N is considered in which an outer bound for the DoF region is
provided and it is shown that in some scenarios it is tight.
