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

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 - 0:)3/2+ 90:/4, which is at most 12.5% larger than the expected sum-DoF, given by (1 - 0:) 3/2 + 20:. This indicates that the gap may mitigate by better bounding the imperfect current CSIT counterpart.