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In order to cope with the large path-loss exponent of mm-Wave channels, ahigh beamforming gain is needed. This can be achieved with small hardwarecomplexity and high hardware power efficiency by Hybrid Digital-Analog (HDA)beamforming, where a very large number $M\gg 1$ of antenna array elementsrequires only a relatively small $m\ll M$ number of A/D converters andmodulators/demodulators. As such, the estimation of mm-Wave MIMO channels mustdeal with two specific problems: 1) high Doppler, due to the large carrierfrequency; 2) impossibility of observing directly the M-dimensional channelvector at the antenna array elements, due to the mentioned HDA implementation.In this paper, we consider a novel scheme inspired by recent results ongridless multiple measurement vectors problem in compressed sensing, that isable to exploit the inherent mm-Wave channel sparsity in the angular domain inorder to cope with both the above problems simultaneously. Our scheme uses pastpilot-symbol observations in a window of length $T$ in order to estimate alow-dimensional subspace that approximately contains the channel vector at thecurrent time. This subspace information can be used directly, in order toseparate users in the spatial domain, or indirectly, in order to improve theestimate of the user channel vector from the current pilot-symbol observation.

Enhancing the Estimation of mm-Wave Large Array Channels by Exploiting Spatio-Temporal Correlation and Sparse Scattering