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

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.