Degrees of freedom of MIMO cellular networks with two cells and two users per cell

This paper characterizes the spatially-normalized degrees of freedom of a 2-cell, 2-user/cell MIMO cellular networks with M antennas at each user and N antennas at each base-station. We show that the optimal DoF is a piecewise linear function, with either M or N being the bottleneck. Denoting the ratio M/N as γ, we show that the network has redundant dimensions in both M and N when γ ϵ {1/2,1} and that the network has no redundancy when γ ϵ {1/4, 2/3, 3/2}. We also show that not all proper systems are feasible and that the only set of feasible proper systems that lie on the proper-improper boundary are those with γ ϵ {1/4, 2/3, 3/2}. We make comparisons between the DoF achievable using strategies such as time sharing between users or cells and discuss their implications on user scheduling in such networks.