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

Paul DeKerret, David Gesbert, Jingjing Zhang, Petros Elia
### Abstract

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 $SNR^{−\alpha}$ for $\alpha \in [0,1]$, the optimal sum-DoF takes the simple form $(1−\alpha)K / (\sum_{k=1}^K \frac{1}{k})+\alpha K$, 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.

Publication

In *arXiv.org*, Computer Science – Information Theory.