The Feasibility Conditions for Interference Alignment in MIMO Networks

TL;DR

This paper develops a new mathematical framework to analyze the feasibility of interference alignment in MIMO networks, providing sufficient and necessary conditions that enhance the theoretical understanding of IA's applicability.

Contribution

It introduces a novel approach linking polynomial solvability to linear independence, establishing comprehensive feasibility conditions for IA in general MIMO network configurations.

Findings

Proposed a sufficient condition for IA feasibility in MIMO networks.

Showed the sufficient condition matches necessary conditions in many cases.

Strengthened the theoretical foundation of interference alignment.

Abstract

Interference alignment (IA) has attracted great attention in the last few years for its breakthrough performance in interference networks. However, despite the numerous works dedicated to IA, the feasibility conditions of IA remains unclear for most network topologies. The IA feasibility analysis is challenging as the IA constraints are sets of high-degree polynomials, for which no systematic tool to analyze the solvability conditions exists. In this work, by developing a new mathematical framework that maps the solvability of sets of polynomial equations to the linear independence of their first-order terms, we propose a sufficient condition that applies to MIMO interference networks with general configurations. We have further proved that this sufficient condition matches with the necessary conditions under a wide range of configurations. These results further consolidate the theoretical basis of IA.