  Millimeter wave (mmWave) is an attractive candidate for high-speed mobile
communications in the future. However, due to the propagation characteristics
of mmWave, beam and and and and alignment becomes a key challenge for serving
users with fast moving speeds. In this paper, we develop a joint beam and
channel tracking algorithm that can track beams from the horizontal and
vertical directions by using two-dimensional (2D) phased antenna arrays. A
general sequence of optimal trial beamforming parameters is obtained to achieve
the minimum Cramer-Rao lower bound (CRLB) of joint beam and channel tracking
asymptotically as antenna number grows to infinity. This sequence is proved to
be asymptotically optimal in different conditions, e.g., channel coefficients,
path directions, and antenna array sizes. We prove that the proposed algorithm
converges to the minimum CRLB in static scenarios. Simulation results show that
our algorithm outperforms several existing algorithms in tracking accuracy and
speed band.
