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

Consider a K-user flat fading MIMO interference channel where the kth transmitter (or receiver) is equipped with M_k (respectively N_k) antennas. If an exponential (in K) number of generic channel extensions are used either across time or frequency, Cadambe and Jafar [1] showed that the total achievable degrees of freedom (DoF) can be maximized via interference alignment, resulting in a total DoF that grows linearly with A 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 (d₁. 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 d, the number of data streams per user.