When Near Becomes Far: From Rayleigh to Optimal Near-Field and Far-Field Boundaries

TL;DR

This paper redefines the boundary between near-field and far-field in wireless communications, proposing application-specific metrics and thresholds that often exceed classical Rayleigh limits, to improve 6G system design.

Contribution

It introduces a novel, application-oriented approach to determine the true near-field/far-field boundary using error-based metrics and Fresnel-zone analysis, with closed-form solutions for practical thresholds.

Findings

Proposed three mismatch metrics for near-field boundary detection.

Derived optimal transition distances exceeding Rayleigh limits by over an order of magnitude.

Provided numerical validation across diverse frequencies and array sizes.

Abstract

The transition toward 6G is pushing wireless communication into a regime where the classical plane-wave assumption no longer holds. Millimeter-wave and sub-THz frequencies shrink wavelengths to millimeters, while meter-scale arrays featuring hundreds of antenna elements dramatically enlarge the aperture. Together, these trends collapse the classical Rayleigh far-field boundary from kilometers to mere single-digit meters. Consequently, most practical 6G indoor, vehicular, and industrial deployments will inherently operate within the radiating near-field, where reliance on the plane-wave approximation leads to severe array-gain losses, degraded localization accuracy, and excessive pilot overhead. This paper re-examines the fundamental question: \emph{``Where does the far-field truly begin?''} Rather than adopting purely geometric definitions, we introduce an application-oriented approach based on user-defined error budgets and a rigorous Fresnel-zone analysis that fully accounts for both amplitude and phase curvature. We propose three practical mismatch metrics: worst-case element mismatch, worst-case normalized mean square error, and spectral efficiency loss. For each metric, we derive a provably optimal transition distance--the minimal range beyond which mismatch permanently remains below a given tolerance--and provide closed-form solutions. Extensive numerical evaluations across diverse frequencies and antenna-array dimensions show that our proposed thresholds can exceed the Rayleigh distance by more than an order of magnitude. By transforming the near-field from a design nuisance into a precise, quantifiable tool, our results provide a clear roadmap for enabling reliable and resource-efficient near-field communications and sensing in emerging 6G systems.