Interference alignment and spatially-normalized degrees of freedom of cellular networks with two cells and three users per cell

This paper characterizes the spatially-normalized degrees of freedom (DoF) of a 2-cell, 3-user per cell multiple input multiple output (MIMO) cellular networks with M antennas at each user and N antennas at each base station. We show that the spatially-normalized DoF is a piecewise linear function, with either M or N being the bottleneck. Given γ = M / N, we shown that for

there is redundancy in both M and N, i.e., either can be reduced without losing spatially-normalized DoF. On the other hand, for

it is shown that there is no redundancy in either M or N, i.e, neither can be reduced without losing spatially-normalized DoF. Our results also settle the issue of feasibility of linear interference alignment for all values of M and N. Specifically, it is shown that except for

for every other γ, the proper systems are actually not feasible.