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The beam sweeping procedure estimates the beamforming directions, or beams, to be used for downlink millimeter-wave cellular transmissions to an incoming user entering the cell. We propose three new approaches for the choice of the sequence by which beams are explored (the beam-search sequence), in order to reduce the average time to find the directions. The proposed methods exploit a) the correlation among angles of departure of the incoming user and its nearest, already connected user, and b) the position of both the incoming and its nearest user. For point a), the nearest-neighbor-beam search method starts from the beam of the nearest user, and then explores other beams, with directions progressively farther away (in the angular domain) from the first beam. In the beam-and-angle search, the beam-search sequence is optimized by exploiting the knowledge of both users' position and the nearest …