When Near Becomes Far: From Rayleigh to Optimal Near-Field and Far-Field Boundaries
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| Format: | Preprint |
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2025
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| _version_ | 1866916975456813056 |
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| author | Daei, Sajad Fodor, Gabor Skoglund, Mikael |
| author_facet | Daei, Sajad Fodor, Gabor Skoglund, Mikael |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_07743 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | When Near Becomes Far: From Rayleigh to Optimal Near-Field and Far-Field Boundaries Daei, Sajad Fodor, Gabor Skoglund, Mikael Signal Processing 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. |
| title | When Near Becomes Far: From Rayleigh to Optimal Near-Field and Far-Field Boundaries |
| topic | Signal Processing |
| url | https://arxiv.org/abs/2505.07743 |