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, implying that adding a multicast message may mitigate the rate-splitting complexity.

翻译：现有关于非理想发射端信道状态信息（CSIT）下自由度（DoF）的大多数研究均假设消息为私有消息，这一假设无法反映两接收端可能请求相同内容的现实情况。为突破此局限，本文考虑混合单播与组播消息。具体而言，我们刻画了非理想CSIT与混合消息下两用户多输入多输出（MIMO）广播信道（BC）的最优DoF区域。在逆定理方面，我们建立了一个三步流程以探索最大可能的松弛边界。在可达性方面，由于DoF区域在天线配置与CSIT质量维度上具有特定的三维结构，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，并提出了一种混合消息感知的速率分裂方案。此外，研究表明：为实现严格正角点，无需将单播消息分裂为私有部分与公共部分，这意味着添加组播消息可降低速率分裂的复杂度。