Hierarchical Codebook Design and Low-Overhead Beam Training for Near-Field Communications With Uniform Circular Arrays

Extremely large-scale multiple-input multiple-output (XL-MIMO) enables near-field location-specific beam focusing for sixth-generation (6G) communications. This paper proposes a resolution-aware hierarchical codebook for near-field uniform circular array (UCA) systems, in conjunction with an efficient two-stage beam training scheme aimed at significantly reducing training overhead. The minimum resolvable distance of UCA systems is characterized based on a geometric spherical-wave propagation model, highlighting their spatial resolution capability in the joint angle–distance domain. A UCA-specific hierarchical codebook is designed, where a power-efficient distance-robust beamforming (DRBF) codebook allows for coarse azimuth localization and a full-precision (FP) codebook offers refined angle–distance beam search. Regularized modal compensation techniques are employed to suppress weak-mode amplification while establishing a controllable tradeoff between absolute amplitude gain and distance robustness. The resulting hierarchical decoupled-architecture Bayesian regression (HDA-BAR) scheme enables swift and precise near-field beam training. For the defined array configuration, the HDA-BAR training procedure necessitates 384 probing slots, achieving a remarkable 99.66% reduction in overhead compared to conventional near-field exhaustive search benchmarks.