Max-Min Hierarchical Codebooks for Millimeter-Wave Channel Sensing with Bandit Algorithms

We consider the problem of millimeter-wave beam alignment using only one RF chain and beamformers implementable with just phase shifters and antenna deactivation. Recent works have proposed Multi-Armed Bandit (MAB) based approaches for fast and efficient beam alignment. In this work, we investigate the role of codebook design in the performance of a specific MAB beam alignment algorithm called HOSUB which exploits the so-called “Unimodality” of rewards from hierarchical codebooks. We study the relationship between uni-modality and beampattern. Motivated by this analysis, we design a new hierarchical codebook for HOSUB that leverages our past design of robust analog beamformers. Extensive simulations are presented to showcase the efficacy of the proposed codebook in improving the performance of HOSUB in comparison to other hierarchical codebooks in the literature which obey the same hardware constraints.