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 with hybrid messages and imperfect CSIT. We establish a three-step procedure for the DoF converse to exploit the utmost possible relaxation. For the DoF achievability, since the DoF region has a specific three-dimensional structure w.r.t. antenna configurations and CSIT qualities, by dividing CSIT qualities into cases, we check the existence of corner point solutions, and then design a hybrid messages-aware rate-splitting scheme to achieve them. Besides, we show that to achieve the strictly positive corner points, it is unnecessary to split the private messages into unicast and multicast parts because the allocated power for the multicast part should be zero. This implies that adding a common message can mitigate the rate-splitting complexity of private messages.