In this paper, we propose a rate-splitting design and characterize the sum-degrees-of-freedom (DoF) for the $K$-user multiple-input-single-output (MISO) broadcast channel with mixed channel state information at the transmitter (CSIT) and order-$(K-1)$ messages, where mixed CSIT refers to the delayed and imperfect-current CSIT, and order-$(K-1)$ message refers to the message desired by $K-1$ users simultaneously. In particular, for the sum-DoF lower bound, we propose a rate-splitting scheme embedding with retrospective interference alignment. In addition, we propose a matching sum-DoF upper bound via genie signalings and extremal inequality. Opposed to existing works for $K=2$, our results show that the sum-DoF is saturated with CSIT quality when CSIT quality thresholds are satisfied for $K>2$.

翻译：本文针对具有混合信道状态信息（CSIT）和阶-(K-1)消息的$K$用户多输入单输出（MISO）广播信道，提出了一种速率分裂设计并刻画了和自由度（DoF）特性。其中，混合CSIT指延迟CSIT与非完美当前CSIT并存的情形，阶-(K-1)消息指同时被$K-1$个用户需要的消息。具体而言，在和自由度下界方面，我们提出了一种嵌入回顾式干扰对齐的速率分裂方案；此外，通过精灵信号和极值不等式推导了匹配的和自由度上界。与现有$K=2$的研究结果不同，我们的结果表明：当$K>2$且CSIT质量达到阈值时，和自由度将随着CSIT质量提高而饱和。