Rate-Splitting with Hybrid Messages: DoF Analysis of the Two-User MIMO Broadcast Channel with Imperfect CSIT

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.