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

TL;DR

This work tackles CSI acquisition for XL-MIMO mmWave systems by introducing a triple-refined hybrid-field beam training (THBT) scheme that accounts for both near-field and far-field effects. The approach progresses from a HFBG-based first refinement to ML-based and PSP-based second refinements, and culminates in a GA-based third refinement with a hybrid-field neighboring search and LS-parameter estimation. Key contributions include: (i) a HFBG analysis and a carefully designed first-refinement codebook to narrow the potential channel region, (ii) ML-based and PSP-based second refinements for high-accuracy parameter estimation with closed-form alternatives to reduce complexity, and (iii) a GA-based third refinement with a neighboring search and LS estimation to finalize the channel parameters, achieving substantial reductions in training overhead while maintaining accuracy. Simulation results show that THBT-ML and THBT-PSP outperform existing hybrid-field beam training methods across beamforming gain, spectral efficiency, and positioning accuracy, particularly at SNRs above a few dB. The framework is adaptable to UPAs and is positioned to impact practical XL-MIMO deployments by enabling fast, high-precision beam alignment in hybrid near-field/far-field regimes.

Abstract

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.

Figures (13)

• Figure 1: Illustration of the system model.
• Figure 2: Comparison of the calculated and the approximated HFBGs.
• Figure 3: Illustration of the beam gain of $\boldsymbol{v}_m$ for $m = -M_1,\cdots,0,\cdots M_1$.
• Figure 4: Illustration of the second-refinement codebook and beam training.
• Figure 5: Illustration of the hybrid-field neighboring search.