  This paper investigates the symmetric degrees of freedom (DoF) of MIMO
cellular networks with G cells and K users per cell, having N antennas at each
base station and M antennas at each user. In particular, we investigate
achievability techniques based on either decomposition with asymptotic
interference alignment (IA) or linear beamforming schemes, and show that there
are distinct regimes of (G,K,M,N) where one outperforms the other. We first
note that both one-sided and two-sided decomposition with asymptotic IA achieve
the same degrees of freedom. We then establish specific antenna configurations
under which the DoF achieved using decomposition based schemes is optimal by
deriving a set of outer bounds on the symmetric DoF. For linear beamforming
schemes, we first focus on small networks and propose a structured approach to
linear beamforming based on a notion called packing ratios. Packing ratio
describes the interference footprint or shadow cast by a set of transmit
beamformers and enables us to identify the underlying structures for aligning
interference. Such a structured beamforming design can be shown to achieve the
optimal spatially normalized DoF (sDoF) of two-cell two-user/cell network and
the two-cell three-user/cell network. For larger networks, we develop an
unstructured approach to linear interference alignment, where transmit
beamformers are designed to satisfy conditions for IA without explicitly
identifying the underlying structures for IA. The main numerical insight of
this paper is that such an approach appears to be capable of achieving the
optimal sDoF for MIMO cellular networks in regimes where linear beamforming
dominates asymptotic decomposition, and a significant portion of sDoF
elsewhere. Remarkably, polynomial identity test appears to play a key role in
identifying the boundary of the achievable sDoF region in the former case.
