Multi-user Beam Alignment in Presence of Multi-path

To overcome the high path-loss and the intense shadowing in millimeter-wave (mmWave) communications, effective beamforming schemes are required which incorporate narrow beams with high beamforming gains. The mmWave channel consists of a few spatial clusters each associated with an angle of departure (AoD). The narrow beams must be aligned with the channel AoDs to increase the beamforming gain. This is achieved through a procedure called beam alignment (BA). Most of the BA schemes in the literature consider channels with a single dominant path while in practice the channel has a few resolvable paths with different AoDs, hence, such BA schemes may not work correctly in the presence of multi-path or at the least do not exploit such multipath to achieve diversity or increase robustness. In this paper, we propose an efficient BA schemes in presence of multipath. The proposed BA scheme transmits probing packets using a set of scanning beams and receives the feedback for all the scanning beams at the end of probing phase from each user. We formulate the BA scheme as minimizing the expected value of the average transmission beamwidth under different policies. The policy is defined as a function from the set of received feedback to the set of transmission beams (TB). In order to maximize the number of possible feedback sequences, we prove that the set of scanning beams (SB) has an special form, namely, Tulip Design. Consequently, we rewrite the minimization problem with a set of linear constraints and reduced number of variables which is solved by using an efficient greedy algorithm.