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

TL;DR

This paper determines the optimal Degrees-of-Freedom for the K-user MISO broadcast channel with both delayed and noisy current CSIT, combining existing schemes to achieve a new, optimal sum DoF formula.

Contribution

It introduces a novel transmission scheme that combines Maddah-Ali and Tse's method with Zero-Forcing to achieve the first optimal DoF in this setting for any number of users.

Findings

Derived a simple formula for the optimal sum DoF: (1−α)K/H_K + αK.

Achieved the first known optimal DoF for the K-user MISO BC with delayed and imperfect current CSIT.

Unified existing schemes to optimize DoF in a new setting.

Abstract

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.