Wavenumber-Domain Near-Field Channel Estimation: Beyond the Fresnel Bound

TL;DR

This work targets near-field channel estimation for extremely large antenna arrays in the reactive region below the Fresnel distance, where conventional Fresnel-based representations fail. It develops a wavenumber-domain ellipse-fitting (WD-EF) framework that derives closed-form spectrum boundaries (ellipses) governed by scatterer geometry and array layout via Weyl expansion, and then recovers scatterer coordinates by fitting observed boundaries to these ellipses. The method combines boundary extraction, ellipse fitting (DirectLSEllipseFitting), and a parametric inversion to estimate $(r^x_s,r^y_s,r^z_s)$ and convert to $(r_s, heta_s, frac{\,phi_s}{})$, achieving superior accuracy and robustness to distance and elevation compared with GMM-based baselines. Practically, WD-EF enables precise near-field channel estimation for ELAA/UPA systems, with potential benefits for localization and high-frequency 6G deployments where Fresnel limits are prohibitive.

Abstract

In the near-field context, the Fresnel approximation is typically employed to mathematically represent solvable functions of spherical waves. However, these efforts may fail to take into account the significant increase in the lower limit of the Fresnel approximation, known as the Fresnel distance. The lower bound of the Fresnel approximation imposes a constraint that becomes more pronounced as the array size grows. Beyond this constraint, the validity of the Fresnel approximation is broken. As a potential solution, the wavenumber-domain paradigm characterizes the spherical wave using a spectrum composed of a series of linear orthogonal bases. However, this approach falls short of covering the effects of the array geometry, especially when using Gaussian-mixed-model (GMM)-based von Mises-Fisher distributions to approximate all spectra. To fill this gap, this paper introduces a novel wavenumber-domain ellipse fitting (WDEF) method to tackle these challenges. Particularly, the channel is accurately estimated in the near-field region, by maximizing the closed-form likelihood function of the wavenumber-domain spectrum conditioned on the scatterers' geometric parameters. Simulation results are provided to demonstrate the robustness of the proposed scheme against both the distance and angles of arrival.

Figures (10)

• Figure 1: Physical boundaries of the $s$-th spherical wavefront.
• Figure 2: Corresponding elliptic boundaries of the wavenumber-domain spectrum area $\widetilde{\mathcal{K}}_s$.
• Figure 4: The wavenumber-domain spectrum.
• Figure 5: The non-zero indicators filtered by power threshold.
• Figure 6: The clustering results of the non-zero indicators using GMM guo-ICC24.