Convexity Meets Curvature: Lifted Near-Field Super-Resolution

2026-02-15

AI Summary

This work addresses the challenge posed by spherical wavefront curvature in near-field array processing, which disrupts the Fourier/Vandermonde structure essential to conventional subspace methods and impedes continuous angle estimation and joint angle–distance super-resolution under pilot-starved hybrid frontends. To overcome this, the authors propose a gridless convex optimization framework based on matrix lifting. By exploiting a Bessel–Vandermonde decomposition to reveal the intrinsic geometry of the near-field phase manifold, the nonlinear measurement model is recast as a linear inverse problem over row-sparse matrices. Joint parameter recovery is then achieved via atomic norm minimization. This approach uniquely integrates convex optimization with explicit near-field curvature modeling, enabling high-precision off-grid angle estimation and active range-cell identification even under severe undersampling, substantially outperforming traditional gridding-based methods and offering a robust foundation for next-generation wireless communication and ISAC systems.

Technology Category

• Search and Optimization: Non-convex Optimization
• Machine Learning: Learning with Manifolds
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Data management and stream processing for Web, mobile and wireless applications
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

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.

Problem

• near-field super-resolution
• Fresnel region
• angle-range estimation
• hybrid array processing
• gridless recovery

Innovation

• near-field super-resolution
• atomic norm minimization
• Bessel-Vandermonde factorization
• gridless estimation
• Fresnel region