Degrees of Freedom of the Rank-deficient Interference Channel with Feedback

TL;DR

This paper analyzes the degrees of freedom in rank-deficient interference channels with feedback, revealing that feedback can increase DoF in large-antenna scenarios by creating alternative signal paths.

Contribution

It provides new achievable schemes and bounds for the K-user rank-deficient interference channel with feedback, highlighting conditions where feedback enhances DoF.

Findings

Feedback increases DoF when nodes have many antennas and channel ranks are limited.

Achievable schemes using interference alignment are developed for three-user channels.

Upper bounds are derived and shown to be tight for large antenna configurations.

Abstract

We investigate the total degrees of freedom (DoF) of the K-user rank-deficient interference channel with feedback. For the two-user case, we characterize the total DoF by developing an achievable scheme and deriving a matching upper bound. For the three-user case, we develop a new achievable scheme which employs interference alignment to efficiently utilize the dimension of the received signal space. In addition, we derive an upper bound for the general K-user case and show the tightness of the bound when the number of antennas at each node is sufficiently large. As a consequence of these results, we show that feedback can increase the DoF when the number of antennas at each node is large enough as compared to the ranks of channel matrices. This finding is in contrast to the full-rank interference channel where feedback provides no DoF gain. The gain comes from using feedback to provide alternative signal paths, thereby effectively increasing the ranks of desired channel matrices.