Optimal Sum-DoF of the K-user MISO BC with Current and Delayed Feedback

This work identifies the optimal sum degrees-of-freedom (DoF) of the K-user MISO Broadcast Channel (BC), in the presence of delayed channel-state information at the transmitter (CSIT) and additional current CSIT of imperfect precision. In a setting where the current channel estimation error scales — in the high SNR regime — as SNR−α for α ∈ [0, 1], the optimal sum-DoF takes the simple form (1 − α)K/( ∑K k=1 1 k ) + αK, and is the result of a novel scheme which deviates from existing efforts as it i) digitally combines interference, ii) uses MAT-type alignment where all symbols are decoded irrespective of order, and iii) utilizes a hierarchical quantizer whose output is distributed across rounds in a way that minimizes unwanted interference. These jointly deliver, for the first time, the elusive simultaneous scaling of both MAT-type delayed-CSI gains as well as ZF-type imperfect-CSI gains.