Optimal DoF Region of MIMO Y Channel with Hybrid Data Exchanges

We study the optimal degrees of freedom (DoF) region of three-user asymmetric multiple-input multiple- output (MIMO) Y channel by considering a hybrid data exchange model. In the hybrid data exchange, we consider both the pairwise data exchange and full data exchange. To derive the optimal DoF region, we analyze the DoF region from both the converse and the achievability aspects. For the converse part, the tight DoF region outer bound is derived using cut-set theorem and genie aided approach. Further, a novel and systematic approach is proposed to analyze the achievability of DoF region. In proving the optimality of achievability, we propose to design distinct patterns to pack the overall transmit data over the channel. We find that the obtained achievable DoF coincides with derived DoF region outer bound.