Optimal DoF of the K-User Broadcast Channel with Delayed and Imperfect Current CSIT

This work studies 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 current channel estimation error scales in~$P^{-\alpha}$ for $\alpha\in[0,1]$. This papers establishes for the first time the optimal DoF in this setting thanks to a new transmission scheme which achieves the elusive DoF-optimal combining of the Maddah-Ali and Tse scheme (MAT) introduced in their seminal work in $2010$ with Zero-Forcing (ZF) for an arbitrary number of users. The derived sum DoF takes the surprisingly simple form $(1-\alpha) K/H_K+\alpha K$ where $H_K\triangleq \sum_{k=1}^K \frac{1}{k}$ is the sum-DoF achieved using solely MAT.