Most of the existing research on degrees-of-freedom (DoF) with imperfect channel state information at the transmitter (CSIT) assume the messages are private, which may not reflect reality as the two receivers can request the same content. To overcome this limitation, we therefore consider the hybrid unicast and multicast messages. In particular, we characterize the optimal DoF region for the two-user multiple-input multiple-output (MIMO) broadcast channel (BC) with imperfect CSIT and hybrid messages. For the converse, we establish a three-step procedure to exploit the utmost possible relaxation. For the achievability, since the DoF region is with specific three-dimensional structure regarding antenna configurations and CSIT qualities, we verify the existence or non-existence of corner point candidates via the feature of antenna configurations and CSIT qualities categorization and provide a hybrid message-aware rate-splitting scheme. Besides, we show that to achieve the strictly positive corner points, it is unnecessary to split the unicast messages into private and common parts. This implies adding a multicast message may mitigate the rate-splitting complexity.

翻译：现有关于发射机端信道状态信息（CSIT）不完全的自由度（DoF）研究大多假设消息为私有消息，但这一假设可能无法反映现实情况——因为两个接收端可能请求相同内容。为突破这一局限，我们因此考虑混合单播与多播消息。具体而言，我们刻画了具有不完全CSIT与混合消息的两用户多输入多输出（MIMO）广播信道（BC）的最优自由度域。在对偶证明中，我们建立了三步流程以充分利用最大可能的松弛空间。在可达性证明中，鉴于自由度域在天线配置与CSIT质量方面具有特定三维结构，我们通过天线配置特征与CSIT质量分类验证角点候选点的存在性，并提出一种混合消息感知的速率分割方案。此外，我们证明要实现严格正的角点，无需将单播消息分割为私有与公共部分，这意味着添加多播消息可降低速率分割的复杂度。