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Compressed Sensing-Driven Near-Field Localization Exploiting Array of Subarrays

Sai Pavan Deram, Jacopo Pegoraro, Javier Lorca Hernando, Jesus O. Lacruz, Joerg Widmer

TL;DR

The paper tackles high-resolution near-field localization for integrated sensing and communication using cost-efficient sparse subarray hardware. It introduces SHARE, a two-stage hierarchical sparse recovery method that first resolves angular ambiguity with dense subarrays via a non-coherent, power-based spectrum, then refines both angle and range on a localized dictionary formed around coarse estimates using the full sparse aperture and OMP. SHARE outperforms one-shot 2D-OMP and approaches or surpasses fully digital 2D-MUSIC in key metrics while significantly reducing computational load, offering a practical path for high-resolution near-field ISAC systems. The approach promises robust performance in multi-source scenarios and scalable gains with additional measurements, making it attractive for real-world deployments.

Abstract

Near-field localization for ISAC requires large-aperture arrays, making fully-digital implementations prohibitively complex and costly. While sparse subarray architectures can reduce cost, they introduce severe estimation ambiguity from grating lobes. To address both issues, we propose SHARE (Sparse Hierarchical Angle-Range Estimation), a novel two-stage sparse recovery algorithm. SHARE operates in two stages. It first performs coarse, unambiguous angle estimation using individual subarrays to resolve the grating lobe ambiguity. It then leverages the full sparse aperture to perform a localized joint angle-range search. This hierarchical approach avoids an exhaustive and computationally intensive two-dimensional grid search while preserving the high resolution of the large aperture. Simulation results show that SHARE significantly outperforms conventional one-shot sparse recovery methods, such as Orthogonal Matching Pursuit (OMP), in both localization accuracy and robustness. Furthermore, we show that SHARE's overall localization accuracy is comparable to or even surpasses that of the fully-digital 2D-MUSIC algorithm, despite MUSIC having access to the complete, uncompressed data from every antenna element. SHARE therefore provides a practical path for high-resolution near-field ISAC systems.

Compressed Sensing-Driven Near-Field Localization Exploiting Array of Subarrays

TL;DR

The paper tackles high-resolution near-field localization for integrated sensing and communication using cost-efficient sparse subarray hardware. It introduces SHARE, a two-stage hierarchical sparse recovery method that first resolves angular ambiguity with dense subarrays via a non-coherent, power-based spectrum, then refines both angle and range on a localized dictionary formed around coarse estimates using the full sparse aperture and OMP. SHARE outperforms one-shot 2D-OMP and approaches or surpasses fully digital 2D-MUSIC in key metrics while significantly reducing computational load, offering a practical path for high-resolution near-field ISAC systems. The approach promises robust performance in multi-source scenarios and scalable gains with additional measurements, making it attractive for real-world deployments.

Abstract

Near-field localization for ISAC requires large-aperture arrays, making fully-digital implementations prohibitively complex and costly. While sparse subarray architectures can reduce cost, they introduce severe estimation ambiguity from grating lobes. To address both issues, we propose SHARE (Sparse Hierarchical Angle-Range Estimation), a novel two-stage sparse recovery algorithm. SHARE operates in two stages. It first performs coarse, unambiguous angle estimation using individual subarrays to resolve the grating lobe ambiguity. It then leverages the full sparse aperture to perform a localized joint angle-range search. This hierarchical approach avoids an exhaustive and computationally intensive two-dimensional grid search while preserving the high resolution of the large aperture. Simulation results show that SHARE significantly outperforms conventional one-shot sparse recovery methods, such as Orthogonal Matching Pursuit (OMP), in both localization accuracy and robustness. Furthermore, we show that SHARE's overall localization accuracy is comparable to or even surpasses that of the fully-digital 2D-MUSIC algorithm, despite MUSIC having access to the complete, uncompressed data from every antenna element. SHARE therefore provides a practical path for high-resolution near-field ISAC systems.
Paper Structure (7 sections, 16 equations, 4 figures, 1 table)

This paper contains 7 sections, 16 equations, 4 figures, 1 table.

Table of Contents

  1. System Model
  2. Array Configuration
  3. Fully Digital Array Signal Model
  4. Compressive Measurement Model
  5. SHARE: A Hierarchical Estimation Algorithm
  6. Simulation Results
  7. Conclusions

Figures (4)

  • Figure 1: Comparison of the near-field beampattern for two subarray spacings. (a) When the spacing is small, a single unambiguous peak is formed. (b) When the spacing is large, ambiguous grating lobes appear.
  • Figure 2: Visualization of the proposed framework. (a) The block-diagonal, stacked structure of the compressive measurement matrix $\mathbf{\Phi}$. (b) The non-coherent combining of individual subarray spectra (blue) yields a robust combined spectrum (red) with clear peaks at the true source angles (dot-dashed black).
  • Figure 3: Performance comparison for two closely spaced sources located at ($43.3^\circ, 4.8\,\text{m}$) and ($43.8^\circ, 4.6\,\text{m}$). (a) Joint Angle and Range RMSE vs. SNR. (b) Overall Position RMSE vs. SNR.
  • Figure 4: Algorithm scalability analysis with random source parameters at a fixed SNR of 10 dB. (a) Position RMSE versus the number of sources. (b) Position RMSE versus the number of compressive measurements.