On the Degrees of Freedom Achievable Through Interference Alignment in a MIMO Interference Channel
Abstract
Consider a K-user flat fading MIMO interference channel where the k-th transmitter (or receiver) is equipped with Mk (respectively Nk) 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 Mk and Nk 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 (d1, d2, ..., dK) achievable through linear interference alignment. For a symmetric system with Mk = M, Nk = N, dk = 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.