  Hierarchical beam search in mmWave communications incurs substantial training
overhead, necessitating deep learning-enabled beam predictions to effectively
leverage channel priors and mitigate this overhead. In this study, we introduce
a comprehensive probabilistic model of power distribution in beamspace, and
formulate the joint optimization problem of probing beam selection and
probabilistic beam prediction as an entropy minimization problem. Then, we
propose a greedy scheme to iteratively and alternately solve this problem,
where a transformer-based beam predictor is trained to estimate the conditional
power distribution based on the probing beams and user location within each
iteration, and the trained predictor selects an unmeasured beam that minimizes
the entropy of remaining beams. To further reduce the number of interactions
and the computational complexity of the iterative scheme, we propose a
two-stage probing beam selection scheme. Firstly, probing beams are selected
from a location-specific codebook designed by an entropy-based criterion, and
predictions are made with corresponding feedback. Secondly, the optimal beam is
identified using additional probing beams with the highest predicted power
values. Simulation results demonstrate the superiority of the proposed schemes
compared to hierarchical beam search and beam prediction with uniform probing
beams.
