Active Beam Training with Hierarchical Codebooks in Two-Dimensional Phased Arrays

Hierarchical codebooks enable simple beamformer design and time-efficient angle-of-arrival (AoA) acquisition in millimeter wave (mmWave) communication systems. In this paper, we study active beam training with hierarchical codebooks in two-dimensional (2D) phased arrays using the posterior matching algorithm. We focus on settings where a receiver employs analog beamforming and aims to steer its beam towards a transmitter that broadcasts pilot signals. We propose a new alternating hierarchical codebook design that sequentially decreases the beamwidth in both dimensions. The proposed alternating codebook outperforms an existing concatenated design, yielding increased beamforming gains in time-constrained beam training.