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.

翻译：在发射端具有延迟与非完美当前信道状态信息（CSIT）即混合CSIT的条件下，两用户多输入多输出广播信道以及发射天线数不少于$K$的$K$用户多输入单输出广播信道的总自由度已获知。然而，两根发射天线与混合CSIT下三用户广播信道的情况仍有待探索。本文研究两根天线与混合CSIT下三用户MISO广播信道的总自由度上界。通过利用辅助信号与极值不等式，我们推导出总自由度上界为$(1-\alpha)3/2 + 9\alpha/4$，该值比预期总自由度$(1-\alpha)3/2 + 2\alpha$最多高出$12.5\%$，表明通过更精确地界定非完美当前CSIT部分可缩小该差距。