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

Technical Summary: Compressed Sensing-Driven Near-Field Localization Exploiting Array of Subarrays

Problem Statement
The paper addresses the challenge of high-resolution near-field localization for Integrated Sensing and Communication (ISAC) systems. As wireless systems migrate to higher frequencies (mmWave and terahertz) and antenna arrays grow larger, the near-field region expands, necessitating the estimation of both angle and range. While fully-digital array architectures (where every antenna element has a dedicated RF chain) offer high resolution, they are prohibitively expensive and power-intensive for large apertures.

To mitigate hardware costs, sparse modular array architectures (partitioning a large array into smaller subarrays with fewer RF chains) are considered. However, these sparse configurations introduce severe spatial undersampling, resulting in grating lobes that cause significant ambiguity in parameter estimation. Existing methods struggle to balance the high hardware cost of fully-digital arrays with the ambiguity issues of sparse subarrays, particularly when using compressive sensing (CS) to further reduce data dimensions.

Methodology: The SHARE Algorithm
The authors propose SHARE (Sparse Hierarchical Angle-Range Estimation), a novel two-stage sparse recovery algorithm designed for a modular array architecture where $P$ subarrays, each containing $M_0$ elements, are connected to $P$ RF chains via analog combining networks. The system utilizes compressive sensing to acquire $K$ distinct measurement snapshots by varying analog phase shifters.

The algorithm operates as follows:

1. Stage 1: Coarse Unambiguous Angle Estimation

   • Objective: Resolve grating lobe ambiguities without a computationally expensive global search.
   • Mechanism: The algorithm treats each subarray individually. Since the intra-subarray aperture is small ($M_0$ elements), it is dense (spacing $d \le \lambda/2$) and free of grating lobes. Furthermore, sources are approximated as being in the far-field relative to the small subarray, allowing the use of a simplified range-independent steering vector.
   • Processing: The algorithm computes the power spectrum for each subarray independently using non-coherent combining. These individual power spectra are summed to create a robust combined spectrum ($P_{total}(\theta)$). The peaks of this spectrum provide coarse, unambiguous angle estimates ($\hat{\Theta}_0$). This stage avoids the circular dependency of coherent combining (which requires knowing the angle to compensate for phase) and effectively suppresses noise and spurious artifacts.

2. Stage 2: High-Resolution Joint Angle-Range Refinement

   • Objective: Leverage the full sparse aperture to estimate precise range and refine the angle.
   • Mechanism: Using the coarse angle estimates from Stage 1, the algorithm constructs a localized, fine-grained 2D search grid (a dictionary) only in the neighborhood of the estimated angles. This drastically reduces the search space compared to a global grid.
   • Processing: The problem is cast as a sparse recovery problem (Multiple Measurement Vector) over this localized dictionary. A greedy algorithm, such as Orthogonal Matching Pursuit (OMP), is used to find the sparse solution, yielding refined estimates for both angle and range simultaneously.

Key Contributions

• Low-Complexity Framework: The paper introduces a compressive sensing framework that processes signals from a large number of antennas using a small number of RF chains, significantly reducing hardware costs while maintaining a large aperture.
• Hierarchical Algorithm (SHARE): The authors propose a two-stage algorithm that decouples the estimation problem. It resolves angular ambiguities using dense subarrays (Stage 1) and then performs high-resolution joint refinement using the full sparse aperture (Stage 2).
• Performance Validation: Through extensive simulations, the paper demonstrates that SHARE outperforms conventional one-shot compressive methods (2D-OMP) and classical fully-digital algorithms (2D-MUSIC) in multi-source near-field scenarios.

Simulation Results
The authors evaluated SHARE against 2D-OMP (operating on the same compressive data) and 2D-MUSIC (operating on fully-digital data) using Monte Carlo simulations with $P=4$ subarrays and $M_0=16$ elements.

• Accuracy: In scenarios with closely spaced sources, 2D-OMP failed to resolve sources due to dictionary coherence, and 2D-MUSIC failed to estimate range accurately. SHARE successfully resolved both angle and range, achieving accuracy comparable to or surpassing 2D-MUSIC despite having access to less data.
• Robustness: SHARE demonstrated lower median Root Mean Squared Error (RMSE) in position estimation across varying numbers of sources and compressive measurements. Unlike 2D-OMP, whose performance plateaued with additional measurements, SHARE's accuracy improved as more measurements were provided.
• Computational Efficiency: SHARE significantly reduced computational complexity. By transforming a global 2D search into a coarse 1D search followed by a localized 2D search, SHARE was approximately 8 times more computationally efficient than 2D-OMP in the tested configuration, while being far more efficient than the $O(M^3)$ complexity of 2D-MUSIC.

Significance and Claims
The paper claims that SHARE provides a practical path for implementing high-resolution near-field ISAC systems. It addresses the trade-off between hardware cost and estimation ambiguity by leveraging the specific properties of subarray architectures. The authors assert that their hierarchical approach avoids the prohibitive computational cost of exhaustive 2D grid searches while preserving the resolution benefits of large apertures. They conclude that SHARE is not only more accurate and robust than brute-force compressive methods but also offers a scalable solution that makes high-performance near-field localization feasible with low-cost, sparse hardware.

Future work mentioned by the authors includes the design of optimized sensing matrices and the validation of the algorithm on a practical hardware testbed, specifically to account for mutual coupling effects and other hardware non-idealities.