  The sparsity and the severe attenuation of millimeter-wave (mmWave) channel
imply that highly directional communication is needed. The narrow beam produced
by large array requires accurate alignment, which is difficult to achieve when
serving fast-moving users. In this paper, we focus on accurate two-dimensional
(2D) beam and channel tracking problem aiming at minimizing exploration
overhead and tracking error. Using a typical frame structure with periodic
exploration and communication, a proven minimum overhead of exploration is
provided first. Then tracking algorithms are designed for three types of
channels with different dynamic properties. It is proved that the algorithms
for quasi-static channels and channels in Dynamic Case I are optimal in
approaching the minimum Cramer-Rao lower bound (CRLB). The computational
complexity of our algorithms is analyzed showing their efficiency, and
simulation results verify their advantages in both tracking error and tracking
speed.
