Interference alignment for the MIMO interference channel

TL;DR

This paper establishes the fundamental limits and conditions for interference alignment in MIMO interference channels without time or frequency diversity, revealing a maximum of 2 degrees of freedom with spatial diversity alone.

Contribution

It provides necessary and sufficient conditions for interference alignment feasibility in symmetric MIMO channels, and characterizes the maximum degrees of freedom achievable using only spatial diversity.

Findings

Maximum 2 degrees of freedom in spatial-only MIMO interference channels

Feasibility conditions for symmetric three-user channels derived

Use of Schubert calculus to count solutions when finite

Abstract

We study vector space interference alignment for the MIMO interference channel with no time or frequency diversity, and no symbol extensions. We prove both necessary and sufficient conditions for alignment. In particular, we characterize the feasibility of alignment for the symmetric three-user channel where all users transmit along d dimensions, all transmitters have M antennas and all receivers have N antennas, as well as feasibility of alignment for the fully symmetric (M=N) channel with an arbitrary number of users. An implication of our results is that the total degrees of freedom available in a K-user interference channel, using only spatial diversity from the multiple antennas, is at most 2. This is in sharp contrast to the K/2 degrees of freedom shown to be possible by Cadambe and Jafar with arbitrarily large time or frequency diversity. Moving beyond the question of feasibility, we additionally discuss computation of the number of solutions using Schubert calculus in cases where there are a finite number of solutions.