  Millimeter wave (mmWave) has been claimed to be the only viable solution for
high-bandwidth vehicular communications. However, frequent channel estimation
and beamforming required to provide a satisfactory quality of service limits
mmWave for vehicular communications. In this paper, we propose a novel channel
estimation and beam tracking framework for mmWave communications in a vehicular
network setting. For channel estimation, we propose an algorithm termed robust
adaptive multi-feedback (RAF) that achieves comparable estimation performance
as existing channel estimation algorithms, with a significantly smaller number
of feedback bits. We derive upper and lower bounds on the probability of
estimation error (PEE) of the RAF algorithm, given a number of channel
estimations, whose accuracy is verified through Monte Carlo simulations. For
beam tracking, we propose a new practical model for mmWave vehicular
communications. In contrast to the prior works, the model is based on position,
velocity, and channel coefficient, which allows a significant improvement of
the tracking performance. Focused on the new beam tracking model, we re-derive
the equations for Jacobian matrices, reducing the complexity for vehicular
communications. An extensive number of simulations is conducted to show the
superiority of our proposed channel estimation method and beam tracking
algorithm in comparison with the existing algorithms and models. Our
simulations suggest that the RAF algorithm can achieve the desired PEE, while
on average, reducing the feedback overhead by 75.5% and the total channel
estimation time by 14%. The beam tracking algorithm is also shown to
significantly improve beam tracking performance, allowing more room for data
transmission.
