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

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.

Gridless Parameter Estimation in Partly Calibrated Rectangular Arrays

Spatial frequency estimation from a mixture of noisy sinusoids finds applications in various fields. While subspace-based methods offer cost-effective super-resolution parameter estimation, they demand precise array calibration, posing challenges for large antennas. In contrast, sparsity-based approaches outperform subspace methods, especially in scenarios with limited snapshots or correlated sources. This study focuses on direction-of-arrival (DOA) estimation using a partly calibrated rectangular array with fully calibrated subarrays. A gridless sparse formulation leveraging shift invariances in the array is developed, yielding two competitive algorithms under the alternating direction method of multipliers (ADMM) and successive convex approximation frameworks, respectively. Numerical simulations show the superior error performance of our proposed method, particularly in highly correlated scenarios, compared to the conventional subspace-based methods. It is demonstrated that the proposed formulation can also be adopted in the fully calibrated case to improve the robustness of the subspace-based methods to the source correlation. Furthermore, we provide a generalization of the proposed method to a more challenging case where a part of the sensors is unobservable due to failures.