Entropy-based Probing Beam Selection and Beam Prediction via Deep Learning

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.