HRIS-Aided Layered Sparse Reconstruction Hybrid Near- and Far-Field Source Localization Algorithm
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摘要: 随着可重构智能超表面(RIS)技术的引入，更大的RIS阵列和更高的工作频率扩大了近场通信区域，而基于RIS的辅助定位技术也受到了极大关注。由于近场定位与传统的远场通信属于异构定位网络，其混合定位依赖于远场与近场通信系统网络融合的定位估计算法实现。因此，该文提出一种融合分层稀疏重构与4阶累积量(FOC)矩阵的混合场定位算法，通过引入混合型RIS(HRIS)架构捕获用户信号，有效解决了多跳信道累积误差的问题。该算法利用3组FOC矩阵，将二维角度谱搜索简化为两个一维谱搜索，分阶段实现仰角、方位角和距离参数的估计。在各阶段参数估计过程中结合分层稀疏字典与动态调谐因子衰减机制，逐层逼近真实参数，以进一步降低算法复杂度。仿真结果表明，在低信噪比与小快拍条件下，该文方法在大多数典型混合场景下，角度与距离估计的均方根误差(RMSE)均优于双阶段多重信号分类(TSMUSIC)算法与混合正交匹配追踪(OMP)算法以及基于全息多输入多输出(HMIMO)系统的混合场定位算法，同时展现出更强的抗噪性能与更低的计算开销，验证了其在复杂混合场场景下的有效性与鲁棒性。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. -
1 RIS辅助混合场源分级仰角估计算法
(1) 输入参数：$\Delta _0^\theta $; $\varepsilon _0^\theta $; $\delta _\Delta ^\theta $;$\delta _\varepsilon ^\theta $；码字索引$I = 0$；最大迭代层数$L_{\max }^\theta $；最小步长精度$\Delta _{\min }^\theta $； (2) 初始化参数：4阶累积量矩阵${{\boldsymbol{C}}_1}$,奇异值分解(SVD),获取信号子空间和噪声子空间；获取仰角范围${\varTheta ^1}$； (3) ${\text{while }}l \le {L_{\max }}{\text{ \& \& }}{\Delta ^{l + 1}} < \Delta _{\min }^\theta {\text{ do}}$ (4) $ {\boldsymbol{B}}_l^\theta = \left\{ {{\boldsymbol{b}}(\theta _{\min }^l),{\boldsymbol{b}}(\theta _{\min }^l + \Delta {\theta ^l}),} \right.\left. { \cdots ,{\boldsymbol{b}}(\theta _{\max }^l)} \right\} $，权重矩阵${\boldsymbol{W}}_l^\theta $ (5) $ {\text{if }}\left\| {{{{{\hat {\boldsymbol{C}}}}}_{{S_1}}} - {\boldsymbol{B}}_l^\theta {\boldsymbol{T}}_l^\theta } \right\| \le \sqrt {\varepsilon _l^\theta } {\text{ then}} $ (6) $ \mathop {\min }\limits_{{\boldsymbol{T}}_\theta ^{{l_2}}} {\left\| {{\boldsymbol{W}}_l^\theta {\boldsymbol{T}}_l^\theta } \right\|_1} $ (7) 计算码字能量：$ {\boldsymbol{E}}(q) = \sum\limits_{k = 1}^K {{{\left| {{\boldsymbol{T}}_l^\theta (q,k)} \right|}^2}} = \left\| {{\boldsymbol{T}}_l^\theta (q,:)} \right\|_2^2 $ (8) 能量升序排列返回索引：$[V,{\text{opt}}] = Sort[E({q_1}),E({q_2}), \cdots ,E({q_Q})]$ (9) 选择前$K$个能量构建信任区间：$ {\varTheta ^{l + 1}} = \mathop \cup \limits_{k = 1}^K {\left\{ {b({\theta _k} \pm {{\Delta _l^\theta } \mathord{\left/ {\vphantom {{\Delta _l^\theta } 2}} \right. } 2})} \right\}_{k \in \kappa }} $ (10) 更新调谐因子、步长、层数：$\varepsilon _{l + 1}^\theta = {\delta _\varepsilon } \cdot \varepsilon _l^\theta $，$\Delta _{l + 1}^\theta = {\delta _\Delta } \cdot \Delta _l^\theta $，$l = l + 1$ (11) ${\text{end while}}$ (12) 输出参数：$\stackrel \frown{\theta } $ 
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表 1 实验仿真参数设置
仿真参数/单位 取值 近场源${K_1}$(个) 2 远场源${K_2}$(个) 2 天线数量$N$(根) 64 反射单元数${N_R}$(个) 16×16 噪声功率${\sigma ^2}$(dBm) −174 最大层数${L_{\max }}$(层) 3 初始角度步长$\Delta _0^\theta $,$\Delta _0^\phi $(°) 10 初始距离步长$\Delta _0^d$(m) 0.5 步长缩减因子${\delta _\Delta }$ 0.5 正则化衰减率${\delta _\varepsilon }$ 0.5 初始调谐因子${\varepsilon _0}$ 0.1
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