Degrees of Freedom of the Two-User MIMO Broadcast Channel with Private and Common Messages Under Hybrid CSIT Models

TL;DR

This paper characterizes the degrees of freedom regions for a two-user MIMO broadcast channel with private and common messages under various hybrid CSIT models, considering arbitrary antenna configurations and linear encoding strategies.

Contribution

It provides the first comprehensive DoF region analysis for the MIMO BC with hybrid CSIT, including new results for cases with partial channel knowledge and the impact of antenna configurations.

Findings

DoF regions are established for five hybrid CSIT models with full channel knowledge or unknown channels.

Linear DoF regions are characterized for four cases with partial channel knowledge, revealing the irrelevance of receiver with more antennas' CSI when the other has none.

The channel state information from the receiver with more antennas does not aid if the other receiver's CSI is unavailable, under linear encoding.

Abstract

We study the degrees of freedom (DoF) regions of the two-user multiple-input multiple-output (MIMO) broadcast channel with a general message set (BC-CM) - that includes private and common messages - under fast fading. Nine different channel state knowledge assumptions -collectively known as hybrid CSIT models - are considered wherein the transmitter has either perfect/instantaneous (P), delayed (D) or no (N) channel state information (CSI) from each of the two receivers. General antenna configurations are addressed wherein the three terminals have arbitrary numbers of antennas. The DoF regions are established for the five hybrid CSIT models in which either both channels are unknown at the transmitter or each of the two channels is known perfectly or with delay. In the four remaining cases in which exactly one of the two channels is unknown at the transmitter, the DoF regions under the restriction of linear encoding strategies - also known as the linear DoF (LDoF) regions- are established. As the key to the converse proofs of the LDoF region of the MIMO BC-CM under such hybrid CSIT assumptions, we show that, when only considering linear encoding strategies, the channel state information from the receiver with more antennas does not help if there is no channel state information available from the receiver with fewer antennas. This result is conjectured to be true even without the restriction on the encoding strategies to be linear. If true, the LDoF regions obtained for the four hybrid CSIT cases herein will also be the DoF regions for those cases.