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

RESUMO

Extremely large-scale multiple-input multiple-output (XL-MIMO) enables near-field location-specific beam focusing for sixth-generation (6G) communications. Uniform circular arrays (UCAs), with rotational symmetry and uniform azimuth coverage, have emerged as a key enabling architecture for near-field XL-MIMO systems. In this paper, we propose a resolution-aware hierarchical codebook for near-field UCA systems, along with an efficient two-stage beam training scheme to significantly reduce the training overhead. Specifically, we characterize the minimum resolvable distance of UCA systems in the near-field region based on a geometric spherical-wave propagation model, revealing their spatial resolution capability in the joint angle--distance domain. Guided by this result, we design a UCA-specific hierarchical codebook, where a power-efficient distance-robust beamforming (DRBF) codebook provides coarse azimuth localization and a full-precision (FP) codebook sampled according to the minimum resolvable distance enables refined angle--distance beam search. The regularized modal compensation suppresses weak-mode amplification and provides a controllable tradeoff between absolute amplitude gain under unit-norm transmission and distance robustness. Based on this codebook, we develop a hierarchical decoupled-architecture Bayesian regression (HDA-BAR) scheme for fast and accurate near-field beam training. For the considered array configuration, the resulting HDA-BAR training procedure requires $384$ probing slots, corresponding to an approximately \(99.66\%\) overhead reduction relative to the conventional near-field exhaustive-search benchmark.