  Communication in Millimeter wave (mmWave) band relies on narrow beams due to
directionality, high path loss, and shadowing. One can use beam alignment (BA)
techniques to find and adjust the direction of these narrow beams. In this
paper, BA at the base station (BS) is considered, where the BS sends a set of
BA packets to scan different angular regions while the user listens to the
channel and sends feedback to the BS for each received packet. It is assumed
that the packets and feedback received at the user and BS, respectively, can be
correctly decoded. Motivated by practical constraints such as propagation
delay, a feedback delay for each BA packet is considered. At the end of the BA,
the BS allocates a narrow beam to the user including its angle of departure for
data transmission and the objective is to maximize the resulting expected
beamforming gain. A general framework for studying this problem is proposed
based on which a lower bound on the optimal performance as well as an
optimality achieving scheme are obtained. Simulation results reveal significant
performance improvements over the state-of-the-art BA methods in the presence
of feedback delay.
