Degrees of freedom of MIMO cellular networks: Two-cell three-user-per-cell case

In this paper we investigate the spatially-normalized degrees of freedom (sDoF) of 2-cell, multiple-input multiple-output (MIMO) cellular networks with three users per cell having M antennas at each user and N antennas at each base-station. We characterize the optimal sDoF/user for all values of M and N and show that the optimal sDoF is a piecewise linear function, with either M or N being the bottleneck. We assume all channels to be generic, and establish achievability through linear transmit beamforming strategies. We introduce the notion of packing ratio that describes the interference footprint or shadow cast by a set of transmit beamformers. Through this notion, we reinterpret the alternating behavior of the optimal sDoF and attribute it to the availability of sets of transmit beamformers with certain packing ratios. We also derive a new DoF outer bound when 5 over 9 ≤ M over N ≤ 3 over 4.