This paper investigates beam training for extremely large-scale multiple-input multiple-output systems. By considering both the near field and far field, a triple-refined hybrid-field beam training scheme is proposed, where high-accuracy estimates of channel parameters are obtained through three steps of progressive beam refinement. First, the hybrid-field beam gain (HFBG)-based first refinement method is developed. Based on the analysis of the HFBG, the first-refinement codebook is designed and the beam training is performed accordingly to narrow down the potential region of the channel path. Then, the maximum likelihood (ML)-based and principle of stationary phase (PSP)-based second refinement methods are developed. By exploiting the measurements of the beam training, the ML is used to estimate the channel parameters. To avoid the high computational complexity of ML, closed-form estimates of the channel parameters are derived according to the PSP. Moreover, the Gaussian approximation (GA)-based third refinement method is developed. The hybrid-field neighboring search is first performed to identify the potential region of the main lobe of the channel steering vector. Afterwards, by applying the GA, a least-squares estimator is developed to obtain the high-accuracy channel parameter estimation. Simulation results verify the effectiveness of the proposed scheme.

翻译：本文研究了超大规模多输入多输出系统的波束训练问题。通过同时考虑近场和远场，提出了一种三重精细化混合场波束训练方案，该方案通过三步渐进式波束细化获得高精度的信道参数估计。首先，提出了基于混合场波束增益（HFBG）的第一重精细化方法。基于HFBG分析，设计了第一重细化码本并据此进行波束训练，以缩小信道路径的潜在区域。随后，开发了基于最大似然（ML）和驻相原理（PSP）的第二重精细化方法。通过利用波束训练的测量值，采用ML估计信道参数。为避免ML的高计算复杂度，根据PSP推导了信道参数的闭式估计。此外，还提出了基于高斯近似（GA）的第三重精细化方法。首先执行混合场邻域搜索以识别信道导向矢量主瓣的潜在区域，随后应用GA开发了最小二乘估计器，实现高精度信道参数估计。仿真结果验证了所提方案的有效性。