Convexity Meets Curvature: Lifted Near-Field Super-Resolution
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| Format: | Preprint |
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2026
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| _version_ | 1866910023131594752 |
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| author | Daei, Sajad Fodor, Gábor Skoglund, Mikael |
| author_facet | Daei, Sajad Fodor, Gábor Skoglund, Mikael |
| contents | Extra-large apertures, high carrier frequencies, and integrated sensing and communications (ISAC) are pushing array processing into the Fresnel region, where spherical wavefronts induce a range-dependent phase across the aperture. This curvature breaks the Fourier/Vandermonde structure behind classical subspace methods, and it is especially limiting with hybrid front-ends that provide only a small number of pilot measurements. Consequently, practical systems need continuous angle resolution and joint angle-range inference where many near-field approaches still rely on costly 2D gridding. We show that convexity can meet curvature via a lifted, gridless superresolution framework for near-field measurements. The key is a Bessel-Vandermonde factorization of the Fresnel-phase manifold that exposes a hidden Vandermonde structure in angle while isolating the range dependence into a compact coefficient map. Building on this, we introduce a lifting that maps each range bin and continuous angle to a structured rank-one atom, converting the nonlinear near-field model into a linear inverse problem over a row-sparse matrix. Recovery is posed as atomic-norm minimization and an explicit dual characterization via bounded trigonometric polynomials yields certificate-based localization that super-resolves off-grid angles and identifies active range bins. Simulations with strongly undersampled hybrid observations validate reliable joint angle-range recovery for next-generation wireless and ISAC systems. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2602_14063 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Convexity Meets Curvature: Lifted Near-Field Super-Resolution Daei, Sajad Fodor, Gábor Skoglund, Mikael Signal Processing Information Theory Extra-large apertures, high carrier frequencies, and integrated sensing and communications (ISAC) are pushing array processing into the Fresnel region, where spherical wavefronts induce a range-dependent phase across the aperture. This curvature breaks the Fourier/Vandermonde structure behind classical subspace methods, and it is especially limiting with hybrid front-ends that provide only a small number of pilot measurements. Consequently, practical systems need continuous angle resolution and joint angle-range inference where many near-field approaches still rely on costly 2D gridding. We show that convexity can meet curvature via a lifted, gridless superresolution framework for near-field measurements. The key is a Bessel-Vandermonde factorization of the Fresnel-phase manifold that exposes a hidden Vandermonde structure in angle while isolating the range dependence into a compact coefficient map. Building on this, we introduce a lifting that maps each range bin and continuous angle to a structured rank-one atom, converting the nonlinear near-field model into a linear inverse problem over a row-sparse matrix. Recovery is posed as atomic-norm minimization and an explicit dual characterization via bounded trigonometric polynomials yields certificate-based localization that super-resolves off-grid angles and identifies active range bins. Simulations with strongly undersampled hybrid observations validate reliable joint angle-range recovery for next-generation wireless and ISAC systems. |
| title | Convexity Meets Curvature: Lifted Near-Field Super-Resolution |
| topic | Signal Processing Information Theory |
| url | https://arxiv.org/abs/2602.14063 |