The Degrees of Freedom Region and Interference Alignment for the MIMO Interference Channel with Delayed CSI

TL;DR

This paper characterizes the degrees of freedom region for the 2-user MIMO interference channel with delayed CSI, developing interference alignment schemes and comparing with perfect and no CSI scenarios.

Contribution

It provides a complete characterization of the DoF region for all antenna configurations under delayed CSI and introduces interference alignment schemes that achieve these bounds.

Findings

Outer bound on the DoF region derived.

Interference alignment schemes achieve the bounds for all classes.

Comparison with perfect and no CSI cases shows the impact of delayed CSI.

Abstract

The degrees of freedom (DoF) region of the 2-user multiple-antenna or MIMO (multiple-input, multiple-output) interference channel (IC) is studied under fast fading and the assumption of {\em delayed} channel state information (CSI) wherein all terminals know all (or certain) channel matrices perfectly, but with a delay, and each receiver in addition knows its own incoming channels instantaneously. The general MIMO IC is considered with an arbitrary number of antennas at each of the four terminals. Dividing it into several classes depending on the relation between the numbers of antennas at the four terminals, the fundamental DoF regions are characterized under the delayed CSI assumption for {\em all} possible values of number of antennas at the four terminals. In particular, an outer bound on the DoF region of the general MIMO IC is derived. This bound is then shown to be tight for all MIMO ICs by developing interference alignment based achievability schemes for each class. A comparison of these DoF regions under the delayed CSI assumption is made with those of the idealistic `perfect CSI' assumption where perfect and instantaneous CSI is available at all terminals on the one hand and with the DoF regions of the conservative `no CSI' assumption on the other, where CSI is available at the receivers but not at all at the transmitters.