On X-Channels with Feedback and Delayed CSI

TL;DR

This paper characterizes the sum degrees of freedom in two-user MIMO X-channels with feedback and delayed CSI, showing no performance loss in symmetric cases and providing new bounds for multi-user single-antenna scenarios.

Contribution

It demonstrates that feedback and delayed CSI can achieve optimal sum DoF in MIMO X-channels and establishes improved bounds for single-antenna K-user X-channels.

Findings

Sum DoF equals that of a MIMO broadcast channel in symmetric cases.

Feedback and delayed CSI enable optimal DoF without performance loss.

New lower bounds for sum DoF in single-antenna K-user X-channels.

Abstract

The sum degrees of freedom (DoF) of the two-user MIMO X-channel is characterized in the presence of output feedback and delayed channel state information (CSI). The number of antennas at each transmitters is assumed to be M and the number of antennas at each of the receivers is assumed to be N. It is shown that the sum DoF of the two-user MIMO X-channel is the same as the sum DoF of a two-user MIMO broadcast channel with 2M transmit antennas, and N antennas at each receiver. Hence, for this symmetric antenna configuration, there is no performance loss in the sum degrees of freedom due to the distributed nature of the transmitters. This result highlights the usefulness of feedback and delayed CSI for the MIMO X-channel. The K-user X-channel with single antenna at each transmitter and each receiver is also studied. In this network, each transmitter has a message intended for each receiver. For this network, it is shown that the sum DoF with partial output feedback alone is at least 2K/(K+1). This lower bound is strictly better than the best lower bound known for the case of delayed CSI assumption for all values of K.