Beam-Steering Aided Hierarchical Codebook for Near-Field Beam Training

This paper explores efficient near-field beam training strategies for extremely large-scale multiple-input multiple-output (XL-MIMO) systems. The near-field beam training is decomposed into angle alignment (AA) and distance alignment (DA), with a focus on AA due to its more significant impact on training overhead. Drawing inspiration from conventional far-field beam steering (FFBS), we introduce the novel concept of near-field beam steering (NFBS), which enables the beam to cover arbitrary angular ranges across the entire near-field and far-field distance ranges. To realize NFBS under practical hybrid beamforming structures, we formulate the problem to approximate any target near-field beam pattern, for which an efficient codeword design approach is developed. Based on the proposed NFBS technique, a binary-tree hierarchical codebook (BTHC) and a mult-mainlobe hierarchical codebook (MMHC) are proposed to achieve efficient near-field AA under single-user equipment (UE) and multi-UE scenarios, respectively. Extensive numerical simulations are conducted, which first demonstrate that the proposed NFBS technique approximates the target near-field beam pattern well under various parameter settings. Subsequently, compared to existing benchmark schemes, the proposed BTHC achieves near-optimal achievable data rates with significantly reduced training overhead in single-UE scenarios. Moreover, the proposed MMHC scheme further reduces training and feedback overhead in multi-UE scenarios.