Perfect Interference Alignment for an Interference Network with General Message Demands

TL;DR

This paper establishes necessary and sufficient channel conditions for perfect interference alignment in general interference networks with arbitrary message demands, enabling optimal degrees of freedom with limited channel extensions.

Contribution

It extends the channel aided interference alignment scheme to networks with general message demands, providing optimal DoF feasibility conditions based on channel structure.

Findings

Derived channel aiding conditions as optimal DoF feasibility criteria

Proved no user has a unique maximum DoF in optimal assignment

Extended IA feasibility analysis beyond network topology constraints

Abstract

Dimensionality requirement poses a major challenge for Interference alignment (IA) in practical systems. This work evaluates the necessary and sufficient conditions on channel structure of a fully connected general interference network to make perfect IA feasible within limited number of channel extensions. So far, IA feasibility literature have mainly focused on network topology, in contrast, this work makes use of the channel structure to achieve total number of degrees of freedom (DoF) of the considered network by extending the channel aided IA scheme to the case of interference channel with general message demands. We consider a single-hop interference network with $K$ transmitters and $N$ receivers each equipped with a single antenna. Each transmitter emits an independent message and each receiver requests an arbitrary subset of the messages. Obtained channel aiding conditions can be considered as the optimal DoF feasibility conditions on channel structure. As a byproduct, assuming optimal DoF assignment, it is proved that in a general interference network, there is no user with a unique maximum number of DoF.