Optimally bridging the gap from delayed to perfect CSIT in the K-user MISO BC

This work1 derives the optimal Degrees-of-Freedom (DoF) of the K-User MISO Broadcast Channel (BC) with delayed Channel-State Information at the Transmitter (CSIT) and with additional current noisy CSIT where the channel estimation error scales in P−α for α ∈ [0, 1]. The optimal sum DoF takes the simple form (1 − α)K/HK + αK where HK≜ Σk=1K1/k. This optimal performance is the result of a novel scheme which deviates from existing efforts as it digitally combines interference, decodes symbols of any order in the MAT alignment [1], and 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 DoF-optimal combining of MAT and ZF.