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.

💡 Research Summary

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This paper tackles the challenge of high‑resolution near‑field localization for integrated sensing and communication (ISAC) systems, where large‑aperture antenna arrays are required to resolve both angle and range of sources. Fully‑digital implementations, which connect each antenna element to a dedicated RF chain, become prohibitively expensive and power‑hungry as the number of elements grows. To overcome this, the authors propose a hybrid architecture that partitions a large linear array into P sub‑arrays, each containing M₀ omnidirectional elements spaced at d ≤ λ/2. Within each sub‑array a single RF chain is used, and analog phase‑shifter networks provide K different linear projections over time, yielding a compressed measurement matrix Φ of size PK × M. This compressive sensing (CS) framework reduces hardware complexity from M RF chains to P while still capturing the spatial information needed for localization.

A key difficulty of sparse, widely‑spaced sub‑arrays (inter‑sub‑array spacing dₚ > M₀d) is the emergence of grating lobes, which cause severe angular ambiguities. The authors address this by introducing SHARE (Sparse Hierarchical Angle‑Range Estimation), a two‑stage algorithm that decouples angle and range estimation.

Stage 1 – Coarse, unambiguous angle estimation:
Each sub‑array’s aperture is small, guaranteeing a dense sampling (no grating lobes) and allowing the near‑field steering vector to be approximated by a far‑field model (Fresnel term negligible). For each sub‑array p, a power spectrum Pₚ(θ)=‖a_sub(θ)ᴴΦₚᴴŶₚ‖²_F is computed, where Ŷₚ contains the compressed measurements belonging to that sub‑array. Because only power is used, the unknown inter‑sub‑array phase offsets (functions of dₚ and the true angle) are eliminated. The spectra from all P sub‑arrays are summed non‑coherently: P_total(θ)=∑ₚPₚ(θ). This averaging suppresses noise and spurious peaks while reinforcing true source peaks. The L largest peaks of P_total(θ) provide a set of coarse angle estimates ĤΘ₀.

Stage 2 – High‑resolution joint angle‑range refinement:
Using each coarse angle θ₀ as a seed, the algorithm searches locally for a small angular correction δ and the corresponding range r. The measurement model Ŷ = Φ a(θ₀+δ, r) x + Z is nonlinear in δ and r, but for a given (θ, r) the optimal source waveform x has a closed‑form least‑squares solution. Therefore the problem reduces to a two‑dimensional search over (δ, r). To avoid exhaustive grid search, the authors construct a fine‑grained dictionary covering a small neighborhood around each θ₀ and perform a sparse recovery (e.g., 2D‑OMP) on the compressed data. This transforms the continuous optimization into a discrete CS problem, leveraging the Multiple Measurement Vector (MMV) structure to jointly estimate the waveform and improve robustness to noise.

Performance evaluation:
Simulations consider a linear array with M=128 elements, P=8 sub‑arrays (M₀=16), intra‑sub‑array spacing d=λ/2, and inter‑sub‑array spacing dₚ=4λ, creating a large aperture and pronounced grating lobes in a conventional full‑array view. Multiple near‑field sources (ranges 5–30 m, azimuths –30° to 30°) are tested over SNRs from 0 to 20 dB. SHARE is benchmarked against 2D‑OMP (single‑stage CS) and fully‑digital 2D‑MUSIC (spectral search on uncompressed data). Results show that SHARE achieves an average angle RMSE of ≈0.5°, compared with ≈2.5° for 2D‑OMP and ≈0.6° for MUSIC. Range RMSE is ≈0.3 m for SHARE, versus ≈1.0 m for 2D‑OMP and ≈0.35 m for MUSIC. Computationally, SHARE’s runtime (~0.12 s in MATLAB) is an order of magnitude lower than MUSIC (~1.4 s), while still outperforming 2D‑OMP in both accuracy and robustness. The non‑coherent power combination in Stage 1 effectively eliminates grating‑lobe ambiguities that cripple 2D‑OMP.

Insights and implications:

• Hardware efficiency: By reducing RF chains from M to P, the proposed architecture dramatically cuts cost and power consumption while preserving the large aperture needed for near‑field resolution.
• Ambiguity resolution: The hierarchical approach leverages dense sub‑arrays to obtain unambiguous coarse angles, sidestepping the grating‑lobe problem inherent in sparse apertures.
• Computational savings: Decoupling angle and range estimation avoids a full 2‑D exhaustive search; the second stage’s sparse recovery operates on a limited local grid, yielding near‑real‑time performance.
• Scalability: The method naturally extends to larger arrays (greater P or M₀) and higher frequencies (mmWave/THz), where hardware constraints are most severe.

Limitations and future work:
The current study assumes a linear 1‑D array and a single polarization, ignoring elevation angles and multipath effects. Extending SHARE to full 3‑D localization (azimuth, elevation, range) will increase dictionary size and demand more sophisticated CS algorithms. Real‑world implementation must address phase‑shifter quantization, calibration errors, and non‑idealities in the analog combining network, which were not modeled in the simulations. Finally, experimental validation with a hardware prototype and over-the‑air measurements in multipath‑rich environments is needed to confirm the simulated gains.

Conclusion:
SHARE presents a practical, low‑cost solution for high‑resolution near‑field localization in ISAC systems. By integrating a sparse sub‑array architecture with a two‑stage hierarchical CS algorithm, it achieves performance comparable to fully‑digital 2D‑MUSIC while using far fewer RF chains and substantially less computation. This makes it a strong candidate for deployment in future 6G networks where simultaneous sensing and communication demand both precision and efficiency.