Efficient Hybrid Near- and Far-Field Beam Training for XL-MIMO Communications

Hierarchical codebook-based beam training is gaining attention in near-field <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">extremely large-scale multiple-input multiple output</i> (XL-MIMO) communications because it can significantly reduce the beam training overhead. However, most of the current beam training schemes are designed for near-field domain and do not consider more practical scenarios, i.e., hybrid near- and far-field communications. Therefore, this paper proposes an efficient two-stage hybrid field beam training scheme based on rough beam sweeping and fine hierarchical codebook. In the first stage, we first modify the Rayleigh distance based on the beam gain, and a 3 dB spatial angle width is obtained by far-field beam sweeping with only some of the array antennas activated. The 3 dB spatial angle width is actually a rough angle range, which can be used to distinguish between near-field users (NUs) and far-field users (FUs). In the second stage, a fine hierarchical codebook is designed to further refine the beam training in the obtained polar coordinate domain. Simulation results validate the effectiveness of the proposed scheme in hybrid field and show that the proposed beam training method can achieve the performance of the near-field hierarchical codebook while significantly reducing the training overhead.