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

TL;DR

This paper analyzes the degrees of freedom in a K-user MISO broadcast channel with hybrid CSIT, revealing that the DoF region depends on joint CSIT probabilities, not just marginal ones, and provides bounds and scenarios for achievability.

Contribution

It extends DoF analysis to K-user MISO BC with hybrid CSIT, showing the importance of joint probabilities and deriving bounds for the DoF region.

Findings

DoF region depends on joint CSIT probabilities for K≥3

Outer bounds for the DoF region are derived based on marginal probabilities

Achievability of bounds is explored in specific scenarios

Abstract

We consider a $K$-user multiple-input single-output (MISO) broadcast channel (BC) where the channel state information (CSI) of user $i(i=1,2,\ldots,K)$ may be either 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. Although the results by Tandon et al. show that for the symmetric two user MISO BC (i.e., $\lambda_Q^i=\lambda_Q,\ \forall i\in \{1,2\}, Q\in \{P,D,N\}$), the Degrees of Freedom (DoF) region depends only on the marginal probabilities, we show that this interesting result does not hold in general when $K\geq3$. In other words, the DoF region is a function of 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, we investigate the achievability of the outer bound in some scenarios. Finally, we show the dependence of the DoF region on the joint probabilities.