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This paper presents novel radio frequency (RF) beam training algorithms for sparse multiple-input multiple-output (MIMO) channels using unitary RF beamforming codebooks at transmitter (Tx) and receiver (Rx). The algorithms leverage the statistical knowledge from memory-based past beam training data for expedited massive MIMO channel-learning 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 RF beam training 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 relative beam entropy and increase in MIMO channel dimensions. A novel mathematical operation of multiplying the elements of a Kronecker product with their respective position numbers in the Kronecker product vector is also brought out which may find further applications in the future.

Memory-assisted Statistically-ranked RF Beam Training Algorithms for Sparse MIMO