  Millimeter-wave (mm-wave) communications incur a high beam alignment cost in
mobile scenarios such as vehicular networks. Therefore, an efficient beam
alignment mechanism is required to mitigate the resulting overhead. In this
paper, a one-dimensional mobility model is proposed where a mobile user (MU),
such as a vehicle, moves along a straight road with time-varying and random
speed, and communicates with base stations (BSs) located on the roadside over
the mm-wave band. To compensate for location uncertainty, the BS widens its
transmission beam and, when a critical beamwidth is achieved, it performs
beam-sweeping to refine the MU position estimate, followed by data
communication over a narrow beam. The average rate and average transmission
power are computed in closed form and the optimal beamwidth for communication,
number of sweeping beams, and transmission power allocation are derived so as
to maximize the average rate under an average power constraint. Structural
properties of the optimal design are proved, and a bisection algorithm to
determine the optimal sweeping -- communication parameters is designed. It is
shown numerically that an adaptation of the IEEE 802.11ad standard to the
proposed model exhibits up to 90% degradation in spectral efficiency compared
to the proposed scheme.
