  Directional transmission patterns (a.k.a. narrow beams) are the key to
wireless communications in millimeter wave (mmWave) frequency bands which
suffer from high path loss and severe shadowing. In addition, the propagation
channel in mmWave frequencies incorporates only a few number of spatial
clusters requiring a procedure to align the corresponding narrow beams with the
angle of departure (AoD) of the channel clusters. The objective of this
procedure, called beam alignment (BA) is to increase the beamforming gain for
subsequent data communication. Several prior studies consider optimizing BA
procedure to achieve various objectives such as reducing the BA overhead,
increasing throughput, and reducing power consumption. While these studies
mostly provide optimized BA schemes for scenarios with a single active user,
there are often multiple active users in practical networks. Consequently, it
is more efficient in terms of BA overhead and delay to design multi-user BA
schemes which can perform beam management for multiple users collectively. This
paper considers a class of multi-user BA schemes where the base station
performs a one shot scan of the angular domain to simultaneously localize
multiple users. The objective is to minimize the average of expected width of
remaining uncertainty regions (UR) on the AoDs after receiving users'
feedbacks. Fundamental bounds on the optimal performance are analyzed using
information theoretic tools. Furthermore, a beam design optimization problem is
formulated and a practical BA scheme, which provides significant gains compared
to the beam sweeping used in 5G standard is proposed.
