Angle–Distance Separated Hierarchical Beam Training With Multi-Focal and Defocal Beams for Large-Scale IRS-Aided Near-Field Communication

Intelligent reflecting surfaces (IRSs) have emerged as a promising technology for achieving high-capacity and reliable wireless communication in beyond 5G systems. However, as the size of IRSs increases to enhance the propagation environment, near-field effects become increasingly significant, rendering conventional beamforming based on far-field assumptions ineffective. Although beamfocusing can enhance near-field gain by considering both angle and distance, it necessitates extensive beam training across an extensive three-dimensional space, resulting in substantial overhead. To address this challenge, we propose a novel beam training framework, referred to as <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">separated hierarchical beam training</i>, which independently conducts hierarchical searches in both the angular and distance domains. To facilitate this separation, we introduce two key techniques: <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">multi-focusing</i>, which mitigates distance dependency by assigning multiple focal points across the IRS elements, and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">beamwidth expansion</i>, which enables broad beam coverage through intentional defocusing. These techniques facilitate the efficient construction of a hierarchical codebook tailored for near-field control. Simulation results demonstrate that the proposed method not only maintains high communication performance but also reduces beam training overhead by approximately five orders of magnitude compared with exhaustive search methods. This underscores the practicality and scalability of the proposed framework for near-field IRS systems within realistic training intervals defined by 3GPP standards.