Triple-Refined Hybrid-Field Beam Training for mmWave Extremely Large-Scale MIMO

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.