1Subspace Estimation and Decomposition for Large Millimeter-Wave MIMO systems

Abstract—Channel estimation and precoding in hybrid analog-digital millimeter-wave (mmWave) MIMO systems is a funda-mental problem that has yet to be addressed, before any of the promised gains can be harnessed. For that matter, we propose a method (based on the well-known Arnoldi iteration) exploiting channel reciprocity in TDD systems and the sparsity of the channel’s eigenmodes, to estimate the right (resp. left) singular subspaces of the channel, at the BS (resp. MS). We first describe the algorithm in the context of conventional MIMO systems, and derive bounds on the estimation error in the presence of distortions at both BS and MS. We later identify obstacles that hinder the application of such an algorithm to the hybrid analog-digital architecture, and address them individually. In view of fulfilling the constraints imposed by the hybrid analog-digital architecture, we further propose an iterative algorithm for subspace decomposition, whereby the above estimated subspaces, are approximated by a cascade of analog and digital precoder / combiner. Finally, we evaluate the performance of our scheme against the perfect CSI, fully digital case (i.e., an equivalent con-ventional MIMO system), and conclude that similar performance can be achieved, especially at medium-to-high SNR (where the performance gap is less than 5%), however, with a drastically lower number of RF chains ( ∼ 4 to 8 times less). Keywords—Millimeter wave MIMO systems, sparse channel esti-mation, hybrid architecture, hybrid precoding, subspace decompo-sition, Arnoldi iteration, subspace estimation, echo-based channel estimation. I