Interference Alignment for the $K$ User MIMO Interference Channel

TL;DR

This paper characterizes the Degrees of Freedom for the K-user MIMO interference channel using interference alignment, providing exact results for large K and introducing a new upper bound.

Contribution

It introduces a new interference alignment technique and derives an exact DoF characterization for large K in MIMO interference channels.

Findings

Achieves $rac{MN}{M+N} K$ degrees of freedom for almost all channel realizations.

Provides a new upper bound on the DoF of the channel.

Exact DoF characterization for K ≥ (M+N)/gcd(M,N).

Abstract

We consider the $K$-user Multiple Input Multiple Output (MIMO) Gaussian interference channel with $M$ antennas at each transmitter and $N$ antennas at each receiver. It is assumed that channel coefficients are constant and are available at all transmitters and at all receivers. The main objective of this paper is to characterize the Degrees of Freedom (DoF) for this channel. Using a new interference alignment technique which has been recently introduced in \cite{abolfazl-final}, we show that $\frac{MN}{M+N} K$ degrees of freedom can be achieved for almost all channel realizations. Also, a new upper-bound on the DoF of this channel is provided. This upper-bound coincides with our achievable DoF for $K\geq K_u\define\frac{M+N}{\gcd(M,N)}$, where $\gcd(M,N)$ denotes the greatest common divisor of $M$ and $N$. This gives an exact characterization of DoF for $M\times N$ MIMO Gaussian interference channel in the case of $K\geq K_u$.