DoF Analysis of the MIMO Broadcast Channel with Alternating/Hybrid CSIT
  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. 
Borzoo Rassouli, Chenxi Hao and Bruno Clerckx
cs.IT math.IT