Beyond Fresnel Approximation: High-Fidelity Near-Field Channel Estimation via Exact Polar Geometry

Abstract

Unlike 5G, 6G (fifth generation) sub-terahertz communications will alter the propagation environment fundamentally by bringing the user equipment into the radiating near field (Fresnel) region. Because of this the classical "far-field planar wavefront" assumptions are no longer valid, leading to high spatial defocusing and low beamforming gains. The commonly used Fresnel approximation, which aims to capture the spherical wavefront variations with a second order Taylor expansion, results in deterministic phase errors at large aperture corners and at small radial distances. To overcome the above mentioned modeling inaccuracies, this paper proposes a high fidelity near field channel estimation framework, using the exact polar-domain geometry. We systematically locate the spatial boundaries where the quadratic approximations diverge from the real physical distance equations, without any mathematical truncation. The numerical evaluations show that the proposed exact polar model is capable of perfectly removing the geometric mismatch, and the normalized mean squared error (NMSE) decreases continuously as the noise floor, and becomes less than 10-3 at 15 dB signal-to-noise ratio (SNR). On the other hand, the far-field and Fresnel baselines reach irreversible error floors in the high-SNR regime. The results clearly demonstrate that the exact polar formulation is an important benchmark for developing powerful, accurate near-field processing architectures.