This paper considers multiuser millimeter wave (mmWave) MIMO communication systems where both the base station (BS) and the user equipments (UEs) use analog beamforming (BF). We propose a beam acquisition approach to find the best directions for the narrow beams, required to achieve BS-UE links above a minimum signal-to-noise ratio (SNR) threshold. The multiple UEs first select their beams simultaneously, based on signals transmitted from the BS on wide training beams. The BS then switches to a beam acquisition mode in order to select the best beam direction for each UE, based on training signals the UEs send on the uplink. We propose a novel parallel beam acquisition scheme for this uplink phase. We also propose a user rejection policy, in which weak UEs that do not satisfy a target SNR threshold, equivalent to a certain bit error rate, are rejected. To do so, we derive the posterior probability that a BS beam has a resultant SNR below the target SNR threshold. We also propose a generalized likelihood ratio test (GLRT) to reduce the computational burden. We derive closed-form error probability expressions for the proposed GLRT approach, and examine the trade-off between the beam acquisition time and accuracy in selecting the beams. We show that the beam acquisition time of our proposed approach is as low as 3% of existing approaches.
