DoF Analysis of the K-user MISO Broadcast Channel with Alternating CSIT

Abstract

We consider a $K$-user multiple-input single-output (MISO) broadcast channel (BC) where the channel state information (CSI) of user $i(i=1,2,\dots ,K)$ may be either 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 channel, according to the three possible CSIT for each user, joint CSIT of the $K$ users could have at most $3^K$ realizations. Although the results by Tandon et al. show that the Degrees of Freedom (DoF) region for the two user MISO BC with symmetric marginal probabilities (i.e., ${\lambda }_Q^i={\lambda }_Q\forall i\in \{1,2,\dots ,K\},Q\in \{P,D,N\}$) depends only on the marginal probabilities, we show that this interesting result does not hold in general when the number of users is more than two. In other words, the DoF region is a function of the \textit{CSIT pattern}, or equivalently, all the joint probabilities. In this paper, given the marginal probabilities of CSIT, we derive an outer bound for the DoF region of the $K$-user MISO BC. Subsequently, the achievability of these outer bounds are considered in certain scenarios. Finally, we show the dependence of the DoF region on the joint probabilities.

24 pages, submitted to IEEE Trans. on Information Theory

References in corpus (4)

• Degrees-of-Freedom Region of the MISO Broadcast Channel with General Mixed-CSIT
• On the Degrees of Freedom of the K-User Time Correlated Broadcast Channel with Delayed CSIT
• Imperfect and Unmatched CSIT is Still Useful for the Frequency Correlated MISO Broadcast Channel
• Toward the Performance vs. Feedback Tradeoff for the Two-User MISO Broadcast Channel

Cited by in corpus (1)

• On the DoF Region of the K-user MISO Broadcast Channel with Hybrid CSIT