Extremely large-scale array (XL-array) has emerged as a promising technology to improve the spectrum efficiency and spatial resolution of future wireless systems. However, the huge number of antennas renders the users more likely to locate in the near-field (instead of the far-field) region of the XL-array with spherical wavefront propagation. This inevitably incurs prohibitively high beam training overhead since it requires a two-dimensional (2D) beam search over both the angular and distance domains. To address this issue, we propose in this paper an efficient two-stage hierarchical beam training method for near-field communications. Specifically, in the first stage, we employ the central sub-array of the XL-array to search for a coarse user direction in the angular domain with conventional far-field hierarchical codebook. Then, in the second stage, given the coarse user direction, we progressively search for the fine-grained user direction-and-distance in the polar domain with a dedicatedly designed codebook. Numerical results show that our proposed two-stage hierarchical beam training method can achieve over 99% training overhead reduction as compared to the 2D exhaustive search, yet achieving comparable rate performance.

翻译：超大规模阵列（XL-array）已成为提升未来无线系统频谱效率和空间分辨率的一项前景技术。然而，海量天线使得用户更可能位于XL-阵列的近场（而非远场）区域，此时波前传播呈现球面特性。这不可避免地导致波束训练开销剧增，因为需要在角度域和距离域进行二维（2D）波束搜索。为解决这一问题，本文针对近场通信提出了一种高效的两级分层波束训练方法。具体而言，在第一阶段，我们利用XL-阵列的中央子阵列，结合传统远场分层码本在角度域搜索用户的粗略方向。随后在第二阶段，根据该粗略方向，采用精心设计的码本在极域逐步搜索精细的用户角度与距离。数值结果表明，与二维穷举搜索相比，所提出的两级分层波束训练方法在实现可比的速率性能的同时，可降低超过99%的训练开销。