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