DoF Upper Bound on Three-User MISO Broadcast Channel with Two Antennas and Mixed CSIT

TL;DR

This paper derives an upper bound on the sum degrees-of-freedom for a three-user MISO broadcast channel with two antennas and mixed CSIT, filling a gap in the understanding of such systems.

Contribution

It provides the first sum-DoF upper bound for the three-user MISO broadcast channel with two antennas and mixed CSIT, using genie-aided signaling and extremal inequalities.

Findings

The sum-DoF upper bound is (1-α)3/2 + 9α/4.

The bound is at most 12.5% larger than the expected sum-DoF.

The result suggests potential for tighter bounds with improved techniques.

Abstract

With delayed and imperfect current channel state information at the transmitter (CSIT), namely mixed CSIT, the sum degrees-of-freedom (sum-DoF) in the two-user multiple-input multiple-output (MIMO) broadcast channel and the $K$-user multiple-input single-output (MISO) broadcast channel with not-less-than-$K$ transmit antennas have been obtained. However, the case of the three-user broadcast channel with two transmit antennas and mixed CSIT is still unexplored. In this paper, we investigate the sum-DoF upper bound of three-user MISO broadcast channel with two transmit antennas and mixed CSIT. By exploiting genie-aided signaling and extremal inequalities, we derive the sum-DoF upper bound as $(1-\alpha)3/2 + 9\alpha/4$, which is at most $12.5\%$ larger than the expected sum-DoF, given by $(1-\alpha)3/2 + 2\alpha$. This indicates that the gap may mitigate by better bounding the imperfect current CSIT counterpart.