The DoF of the K-user Interference Channel with a Cognitive Relay

TL;DR

This paper investigates the degrees of freedom in the K-user interference channel with a cognitive relay, revealing that the DoF per user varies with the number of users and channel variation, and providing new bounds and characterizations.

Contribution

It extends the understanding of DoF in K-user IC-CR, showing the DoF scaling with K and channel type, and characterizes the DoF region for the 3-user case with constant channels.

Findings

K-user IC-CR has 2K/3 DoF for K>2 with time-varying channels.

The 2-user IC-CR achieves 1 DoF per user with time-varying channels.

The DoF region for the 3-user IC-CR with constant channels is characterized.

Abstract

It was shown recently that the 2-user interference channel with a cognitive relay (IC-CR) has full degrees of freedom (DoF) almost surely, that is, 2 DoF. The purpose of this work is to check whether the DoF of the $K$-user IC-CR, consisting of $K$ user pairs and a cognitive relay, follow as a straight forward extension of the 2-user case. As it turns out, this is not the case. The $K$-user IC-CR is shown to have $2K/3$ DoF if $K>2$ for the when the channel is time varying, achievable using interference alignment. Thus, while the basic $K$-user IC with time varying channel coefficients has 1/2 DoF per user for all $K$, the $K$-user IC-CR with varying channels has 1 DoF per user if K=2 and 2/3 DoF per user if $K>2$. Furthermore, the DoF region of the 3-user IC-CR with constant channels is characterized using interference neutralization, and a new upper bound on the sum-capacity of the 2-user IC-CR is given.