Real Interference Alignment and Degrees of Freedom Region of Wireless X Networks

TL;DR

This paper develops a real interference alignment scheme for single-hop wireless X networks with multiple transmitters and receivers, deriving achievable degrees of freedom regions that match known outer bounds in some cases.

Contribution

It introduces a novel interference alignment scheme using real signals and streams, expanding the understanding of DoF regions in wireless X networks.

Findings

Derived several achievable DoF regions for wireless X networks.

In some cases, the achievable region matches the outer bound, confirming optimality.

Recovered previous results on DoF and total DoF for special cases.

Abstract

We consider a single hop wireless X network with $K$ transmitters and $J$ receivers, all with single antenna. Each transmitter conveys for each receiver an independent message. The channel is assumed to have constant coefficients. We develop interference alignment scheme for this setup and derived several achievable degrees of freedom regions. We show that in some cases, the derived region meets a previous outer bound and are hence the DoF region. For our achievability schemes, we divide each message into streams and use real interference alignment on the streams. Several previous results on the DoF region and total DoF for various special cases can be recovered from our result.