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Communication at millimeter wave (mm-wave) bands is expected to become a key ingredient of the next generation (5G) wireless networks. Effective mm-wave communications require fast and reliable methods for beamforming at both the user equipment (UE) and the base station sides, in order to achieve a sufficiently large signal-to-noise ratio after beamforming. We refer to the problem of finding a pair of strongly coupled narrow beams at the transmitter and receiver as the beam alignment problem. In this paper, we propose an efficient BA scheme for single-carrier mm-wave communications. In the proposed scheme, the BS periodically probes the channel in the downlink via a pre-specified pseudo-random beamforming codebook and pseudo-random spreading codes, letting each UE estimate the angle-of-arrival/angle-of-departure (AoA-AoD) pair of the multipath channel for which the energy transfer is …