HRIS-Aided Layered Sparse Reconstruction Hybrid Near- and Far-Field Source Localization Algorithm

YANG Qingqing; PU Xuelai; PENG Yi; LI Hui; YANG Qiuping

doi:10.11999/JEIT250429

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YANG Qingqing, PU Xuelai, PENG Yi, LI Hui, YANG Qiuping. HRIS-Aided Layered Sparse Reconstruction Hybrid Near- and Far-Field Source Localization Algorithm[J]. Journal of Electronics & Information Technology. doi: 10.11999/JEIT250429

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YANG Qingqing, PU Xuelai, PENG Yi, LI Hui, YANG Qiuping. HRIS-Aided Layered Sparse Reconstruction Hybrid Near- and Far-Field Source Localization Algorithm[J]. Journal of Electronics & Information Technology. doi: 10.11999/JEIT250429

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HRIS-Aided Layered Sparse Reconstruction Hybrid Near- and Far-Field Source Localization Algorithm

doi: 10.11999/JEIT250429 cstr: 32379.14.JEIT250429

1.
School of Information Engineering and Automation, Kunming University of Science and Technology, Kunming 650500, China
2.
Yunnan Provincial Key Laboratory of Computer Science, Kunming University of Science and Technology, Kunming 650500, China

Funds: The National Natural Science Foundation of China (62461030), The Key Basic Research Project of Yunnan Province (202401AS070105)

Received Date: 2025-05-19
Rev Recd Date: 2025-10-14

Available Online: 2025-10-22

Abstract

Abstract

Objective Advances in Reconfigurable Intelligent Surface (RIS) technology have enabled larger arrays and higher frequencies, which expand the near-field region and improve positioning accuracy. The fundamental differences between near- and far-field propagation necessitate hybrid localization algorithms capable of seamlessly integrating both regimes. Methods A localization framework for mixed near- and far-field sources is proposed by integrating Fourth-Order Cumulant (FOC) matrices with hierarchical sparse reconstruction. A hybrid RIS architecture incorporating active elements is employed to directly receive pilot signals, thereby reducing parameter-coupling errors that commonly occur in passive RIS over multi-hop channels and enhancing reliability in Non-Line-Of-Sight (NLOS) scenarios. Symmetrically placed active elements are employed to construct three FOC matrices for three-dimensional position estimation. The two-dimensional angle search is decomposed into two sequential one-dimensional searches, where elevation and azimuth are estimated separately to reduce computational complexity. The first FOC matrix (C1), formed from vertically symmetric elements, captures elevation characteristics. The second matrix (C2), constructed from centrally symmetric elements, suppresses nonlinear terms related to distance. The third matrix (C3) applies the previously estimated angles to select active elements, incorporates near-field effects, and enables accurate distance estimation as well as discrimination between near-field and far-field signals. To further improve the efficiency and accuracy of spectral searches, a hierarchical multi-resolution strategy based on sparse reconstruction is introduced. This method partitions the continuous parameter space into discrete intervals, incrementally generates a multi-resolution dictionary, and applies a progressive search procedure for precise position parameter estimation. During the search process, a tuning factor constrains the maximum reconstruction error between the sparse matrix and the projection of the original signal subspace. In addition, the algorithm exploits the orthogonality between the signal and noise subspaces to design a weight matrix, which reduces the effects of noise and position errors on the sparse solution. This hierarchical search enables rapid, coarse-to-fine parameter estimation and substantially improves localization accuracy. Results and Discussions The performance of the proposed algorithm is evaluated against Two-Stage Multiple Signal Classification (TSMUSIC), hybrid Orthogonal Matching Pursuit (OMP), and Holographic Multiple-Input Multiple-Output (HMIMO)-based methods with respect to noise resistance, convergence speed, and computational efficiency. Under varying SNR conditions (Fig. 5), traditional subspace methods exhibit degraded performance at low SNR because of reliance on signal–noise subspace orthogonality. In contrast, the proposed algorithm employs the FOC matrix to achieve accurate elevation and azimuth estimation while suppressing Gaussian noise. The hierarchical sparse reconstruction strategy further enhances estimation accuracy, resulting in superior far-field localization performance. Unlike the HMIMO-based algorithm, which depends on dynamic codebook switching, the proposed method retains nonlinear distance-dependent phase terms and constructs the distance codebook from initial angle estimates, thereby improving near-field localization accuracy. In Experiment 2, the effect of varying snapshot numbers on parameter estimation is examined. Owing to the angle-decoupling capability of the FOC matrix, the algorithm achieves rapid reduction in Root Mean Square Error (RMSE) even with a small number of snapshots. As the number of snapshots increases, estimation accuracy improves steadily and approaches convergence, indicating robustness against noise and fast convergence under low-snapshot conditions. Conventional methods typically require predefined near-field and far-field grids. By contrast, the nonlinear phase retention mechanism enables automatic discrimination between near-field and far-field sources without a predetermined distance threshold. While the nonlinear phase term introduces slightly slower convergence during distance decoupling, the proposed method still outperforms TSMUSIC and hybrid OMP. However, angle estimation errors during the decoupling process provide the HMIMO-based approach with a slight advantage in distance estimation accuracy (Fig. 6). Computational complexity is also compared between the hierarchical multi-resolution framework and traditional global search strategies (Fig. 7). Standard hybrid-field localization algorithms, such as TSMUSIC and hybrid OMP, require simultaneous optimization of angle and distance parameters, leading to exponential growth of computational cost. In contrast, the hierarchical strategy applies a phased search in which elevation and azimuth are estimated sequentially, reducing the two-dimensional angle spectrum search to two one-dimensional searches. The combination of progressive grid contraction, layer-by-layer tuning factors, and step-size decay narrows the search range efficiently, enabling rapid convergence through a three-layer dynamic grid structure. The distance dictionary constructed from angle estimates further removes redundant grids, thereby reducing complexity compared with global search methods. Conclusions This study presents a 3D localization framework for mixed near- and far-field sources in RIS-assisted systems by combining FOC decoupling with hierarchical sparse reconstruction. The method decouples angle and range estimation and uses a multi-resolution search strategy, achieving reliable performance and rapid convergence even under low SNR conditions and with limited snapshots. Simulation results demonstrate that the proposed approach consistently outperforms TSMUSIC, hybrid OMP, and HMIMO-based techniques, confirming its efficiency and robustness in mixed-field environments.
- Hybrid RIS,
- Mixed-field source localization,
- Hierarchical dictionary,
- Fourth-Order Cumulant (FOC),
- Sparse reconstruction

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References(17)

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