  In this paper, a data-driven position-aided approach is proposed to reduce
the training overhead in MIMO systems, by leveraging side information and
on-the-field measurements. A data tensor is constructed by collecting
beam-training measurements on a subset of positions and beams, and a hybrid
noisy tensor completion (HNTC) algorithm is proposed to predict the received
power across the coverage area, which exploits both the spatial smoothness and
the low-rank property of MIMO channels. A recommendation algorithm based on the
completed tensor, beam subset selection (BSS), is proposed to achieve fast and
accurate beam-training. Besides, a grouping-based BSS algorithm is proposed to
combat the detrimental effect of noisy positional information. Numerical
results evaluated with the Quadriga channel simulator at 60 GHz millimeter-wave
channels show that the proposed BSS recommendation algorithm in combination
with HNTC achieve accurate received power predictions, enabling beam-alignment
with small overhead: given power measurements on 40% of possible discretized
positions, HNTC-based BSS attains a probability of correct alignment of 91%,
with only 2% of trained beams, as opposed to a state-of-the-art position-aided
beam-alignment scheme which achieves 54% correct alignment in the same
configuration. Finally, an online HNTC method via warm-start is proposed, that
alleviates the computational complexity by 50%, with no degradation in
prediction accuracy.
