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 consider hybrid private and common messages. We characterize the optimal DoF region for the two-user multiple-input multiple-output (MIMO) broadcast channel (BC) with hybrid messages and imperfect CSIT. We establish a three-step procedure for the converse to exploit the utmost possible relaxation. For the achievability, since the DoF region is with three-dimensional structure regarding antenna configurations and CSIT qualities, we verify the existence or nonexistence of corner point candidates by the feature of antenna configurations and CSIT qualities categorization, and give a hybrid message-aware rate-splitting scheme with specific power allocation. Besides, we show that to achieve the strictly positive corner points, it is unnecessary to split the private messages into unicast and multicast parts. This implies that adding a common message can mitigate the rate-splitting complexity.