Settling the feasibility of interference alignment for the MIMO interference channel: the symmetric square case

TL;DR

This paper establishes the precise conditions under which interference alignment is feasible in symmetric square MIMO interference channels, using algebraic geometry to derive necessary and sufficient criteria.

Contribution

It provides a complete characterization of feasibility conditions for symmetric square MIMO channels, a problem previously unresolved, with a novel algebraic geometry approach.

Findings

Alignment is feasible if and only if N >= d(K+1)/2.

Necessary conditions for arbitrary system parameters are also derived.

Algebraic geometry is used to prove the feasibility criteria.

Abstract

Determining the feasibility conditions for vector space interference alignment in the K-user MIMO interference channel with constant channel coefficients has attracted much recent attention yet remains unsolved. The main result of this paper is restricted to the symmetric square case where all transmitters and receivers have N antennas, and each user desires d transmit dimensions. We prove that alignment is possible if and only if the number of antennas satisfies N>= d(K+1)/2. We also show a necessary condition for feasibility of alignment with arbitrary system parameters. An algebraic geometry approach is central to the results.