The Degrees of Freedom of the Interference Channel with a Cognitive Relay under Delayed Feedback

TL;DR

This paper investigates the degrees of freedom in a two-user interference channel with a cognitive relay under various delayed feedback scenarios, deriving bounds and proposing schemes that improve DoF performance.

Contribution

It introduces new outer bounds and achievable schemes for the ICCR with delayed feedback, extending the understanding of DoF in such channels.

Findings

Delayed feedback can increase sum-DoF from 1 to 4/3 in SISO case.

Achievable schemes based on retrospective interference alignment meet upper bounds.

DoF regions for MIMO ICCR are characterized with feedback extensions.

Abstract

This paper studies the interference channel with a cognitive relay (ICCR) under delayed feedback. Three types of delayed feedback are studied: delayed channel state information at the transmitter (CSIT), delayed output feedback, and delayed Shannon feedback. Outer bounds are derived for the DoF region of the two-user multiple-input multiple-output (MIMO) ICCR with delayed feedback as well as without feedback. For the single-input single-output (SISO) scenario, optimal schemes are proposed based on retrospective interference alignment. It is shown that while a cognitive relay without feedback cannot extend the sum-DoF beyond $1$ in the two-user SISO interference channel, delayed feedback in the same scenario can extend the sum-DoF to $4/3$. For the MIMO case, achievable schemes are obtained via extensions of retrospective interference alignment, leading to DoF regions that meet the respective upper bounds.