  Millimeter Wave (mmWave) communications rely on highly directional beams to
combat severe propagation loss. In this paper, an adaptive beam search
algorithm based on spatial scanning, called Iterative Deactivation and Beam
Shifting (IDBS), is proposed for mmWave beam alignment. IDBS does not require
advance information such as the Signal-to-Noise Ratio (SNR) and channel
statistics, and matches the training overhead to the unknown SNR to achieve
satisfactory performance. The algorithm works by gradually deactivating beams
using a Bayesian probability criterion based on a uniform improper prior, where
beam deactivation can be implemented with low-complexity operations that
require computing a low-degree polynomial or a search through a look-up table.
Numerical results confirm that IDBS adapts to different propagation scenarios
such as line-of-sight and non-line-of-sight and to different SNRs. It can
achieve better tradeoffs between training overhead and beam alignment accuracy
than existing non-adaptive algorithms that have fixed training overheads.
