On the Degrees of Freedom Achievable Through Interference Alignment in a MIMO Interference Channel

TL;DR

This paper establishes fundamental limits on the degrees of freedom in MIMO interference channels without channel extension, showing that linear interference alignment cannot achieve linear growth in total DoF as the number of users increases.

Contribution

It provides a general necessary condition for achievable DoF tuples in MIMO interference channels without channel extension, and derives a tight upper bound for symmetric systems.

Findings

Total DoF cannot grow linearly with the number of users without channel extension.

The maximum achievable DoF is bounded by K(M + N)=(K + 1) in symmetric systems.

The derived bound is tight when antennas are divisible by the number of data streams.

Abstract

Consider a K-user flat fading MIMO interference channel where the k-th transmitter (or receiver) is equipped with M_k (respectively N_k) antennas. If a large number of statistically independent channel extensions are allowed either across time or frequency, the recent work [1] suggests that the total achievable degrees of freedom (DoF) can be maximized via interference alignment, resulting in a total DoF that grows linearly with K even if M_k and N_k are bounded. In this work we consider the case where no channel extension is allowed, and establish a general condition that must be satisfied by any degrees of freedom tuple (d_1, d2, ..., d_K) achievable through linear interference alignment. For a symmetric system with M_k = M, N_k = N, d_k = d for all k, this condition implies that the total achievable DoF cannot grow linearly with K, and is in fact no more than K(M + N)=(K + 1). We also show that this bound is tight when the number of antennas at each transceiver is divisible by the number of data streams.