DoF Analysis of the MIMO Broadcast Channel with Alternating/Hybrid CSIT

TL;DR

This paper derives bounds on the degrees of freedom (DoF) for a K-user MISO broadcast channel with mixed instantaneous, delayed, or unavailable channel state information (CSI), revealing complexities beyond the two-user case.

Contribution

It introduces an outer bound for the DoF region based on marginal CSIT probabilities and refines it considering joint CSIT states, highlighting differences from the two-user scenario.

Findings

Outer bound for K-user MISO BC DoF region derived

Joint CSIT state inequalities tighten the bounds

For K≥3, DoF region not fully characterized by marginal probabilities

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 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.