  This paper presents a novel radio frequency (RF) beam training algorithm for
sparse multiple input multiple output (MIMO) channels using unitary RF
beamforming codebooks at transmitter (Tx) and receiver (Rx). The algorithm
leverages statistical knowledge from past beam data for expedited beam search
with statistically-minimal training overheads. Beams are tested in the order of
their ranks based on their probabilities for providing a communication link.
For low beam entropy scenarios, statistically-ranked beam search performs
excellent in reducing the average number of beam tests per Tx-Rx beam pair
identification for a communication link. For high beam entropy cases, a hybrid
algorithm involving both memory-assisted statistically-ranked (MarS) beam
search and multi-level (ML) beam search is also proposed. Savings in training
overheads increase with decrease in beam entropy and increase in MIMO channel
dimensions.
