Degrees-of-Freedom Regions for $K$-User MISO Time-Correlated Broadcast Channel

TL;DR

This paper characterizes the degrees-of-freedom regions for K-user MISO broadcast channels with time-correlated channels, providing new achievable schemes and confirming their optimality against existing bounds.

Contribution

It derives the DoF regions for symmetric and asymmetric cases in time-correlated MISO BCs, introducing novel achievability schemes and establishing their optimality.

Findings

Derived total DoF formulas for symmetric cases.

Proposed achievability schemes match outer bounds.

Confirmed optimality with existing bounds and schemes.

Abstract

In this paper, we study the achievable degrees-of-freedom (DoF) regions of the $K$-user multiple-input-single-output (MISO) time correlated broadcast channel (BC). The time correlation induces knowledge of the current channel state information at transmitter (CSIT) with an estimation error $P^{-\alpha}$, where $P$ is the signal-to-noise ratio (SNR). We consider the following two scenarios: $(i)$ $K$-user with $K$-antenna base station (BS) and $(ii)$ $3$-user with $2$-antenna BS. In case of symmetric DoF tuples, where all the users obtain the same DoF, we derive the total DoF equal to $\frac{K(1-\alpha)}{1+\frac{1}{2}+\cdots+\frac{1}{K}}+K\alpha$ for the first scenario and $\frac{3+\alpha}{2}$ for the second one. In particular, we provide the achievability schemes for these two DoF tuples. Nevertheless, we also consider the asymmetric case where one of the users is guaranteed {\it one} DoF, and provide the achievability scheme. Notably, the consistency of the proposed DoF regions with an already published outer bound , as well as with the Maddah-Ali-Tse (MAT), which assumes only perfect delayed CSIT, and the ZF beamforming schemes (perfect current CSIT) consents to the optimality of the proposed achievability schemes.