  Analog beamforming is a low-cost architecture for millimeter-wave (mmWave)
mobile communications. However, it has two disadvantages for serving fast
mobility users: (i) the mmWave beam in the wireless channel and the beam
steered by analog beamforming have small angular spreads which are difficult to
align with each other and (ii) the receiver can only observe the mmWave channel
in one beam direction and rely on beam-probing algorithms to check other
directions. In this paper, we develop a beam probing and tracking algorithm
that can efficiently track fast-moving mmWave beams in three-dimensional (3D)
space. This algorithm has several salient features: (1) fading channel
supportive: it can simultaneously track the channel coefficient and
two-dimensional (2D) beam direction in fading channel environments; (2) low
probing overhead: it achieves the minimum probing requirement for joint beam
and channel tracking; (3) fast tracking speed and high tracking accuracy: its
tracking error converges to the minimum Cramer-Rao lower bound (CRLB) in static
scenarios in theory and it outperforms several existing tracking algorithms
with lower tracking error and faster tracking speed in simulations.
