On the degrees of freedom of asymmetric MIMO interference broadcast channels

In this paper, we study the degrees of freedom (DoF) of the asymmetric multi-input-multi-output interference broadcast channel (MIMO-IBC). By introducing a notion of connection pattern chain, we generalize the genie chain proposed in [10] to derive and prove the necessary condition of IA feasibility for the asymmetric MIMO-IBC, which is denoted as irreducible condition. It is necessary for both linear interference alignment (IA) and asymptotic IA feasibility in MIMO-IBC with arbitrary configurations. In a special class of the asymmetric two-cell MIMO-IBC, the irreducible condition is proved to be the sufficient and necessary condition for asymptotic IA feasibility, while the combination of proper condition and irreducible condition is proved to the sufficient and necessary condition for linear IA feasibility. From these conditions, we derive the information theoretic maximal DoF and the maximal DoF achieved by linear IA. The derived maximal DoF per user for the asymmetric two-cell MIMO-IBC are also the upper-bounds of DoF per user for the asymmetric G-cell MIMO-IBC.