This paper proposes a linear beamforming strategy for interference alignment in multiple-input multiple-output (MIMO) cellular networks. In particular, we consider a network consisting of G mutually interfering cells with K users/cell, having N antennas at each base station (BS) and M antennas at each user — a (G, K, M, N) network. We develop an unstructured approach to designing linear beamformers for interference alignment where transmit beamformers are designed to satisfy conditions for interference alignment without explicitly identifying the underlying structures for alignment. Specifically, the transmit beamformers in the uplink are required to satisfy a certain number of random linear vector equations in order to constrain the number of dimensions occupied by interference at each BS. The conceptual simplicity and the fact that no customization to a given network is needed makes this method applicable to a broad class of cellular networks. The key observation made in this paper is that such an approach appears to be capable of achieving the optimal DoF for MIMO cellular networks in regimes where linear beamforming dominates asymptotic decomposition-based schemes for interference alignment, and a significant portion of the DoF elsewhere. Remarkably, polynomial identity test plays a key role in identifying the scope and limitations of such a technique.
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