A general outer bound for MISO broadcast channel with heterogeneous CSIT

We study the impact of heterogeneity of channel-state-information available at the transmitters (CSIT) on the capacity of broadcast channels with a multiple-antenna transmitter and k single-antenna receivers (MISO BC). In particular, we consider the k-user MISO BC, where the CSIT with respect to each receiver can be either instantaneous/perfect (P), delayed (D), or not available (N); and we study the impact of this heterogeneity of CSIT on the degrees-of-freedom (DoF) of such network. We develop a general outer bound on the DoF region of k-user MISO BC for all possible heterogeneous CSIT configurations, assuming linear encoding strategies at the transmitter. The outer bound leads to an approximate linear sum-DoF characterization to within 0.5 for a broad range of CSIT configurations. It also leads to an exact characterization of linear sum-DoF for some specific CSIT configurations. Our proof of the outer bound relies on the development of a novel lemma, called Interference Decomposition Bound, which lower bounds the interference dimension at a receiver which supplies delayed CSIT based on the average dimension of constituents of that interference, thereby decomposing it into its components.