利用自适应交叉近似驱动的测量矩阵插值加速目标宽带电磁散射特性分析

王仲根; 吴承钢; 聂文艳; 孙玉发

doi:10.11999/JEIT260392

利用自适应交叉近似驱动的测量矩阵插值加速目标宽带电磁散射特性分析

doi: 10.11999/JEIT260392 cstr: 32379.14.JEIT260392

1.
安徽理工大学电气与信息学院淮南 232001
2.
淮南师范学院机械与电气工程学院淮南 232001
3.
安徽大学电子信息工程学院合肥 230601

基金项目: 国家自然科学基金(62071004)，安徽省教育厅科学研究重点项目(2025AHGXZK31006)

详细信息

作者简介:
王仲根：男，教授，研究方向为计算电磁学、阵列信号处理

吴承钢：男，硕士生，研究方向为计算电磁学、电磁散射等

聂文艳：女，教授，研究方向为计算电磁学、电磁散射等

孙玉发：男，教授，研究方向为计算电磁学、天线理论及设计等

通讯作者:
王仲根　zgwang@ahu.edu.cn

中图分类号: TN011
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- 被引次数: 0
出版历程
- 收稿日期: 2026-04-07
- 修回日期: 2026-07-02
- 录用日期: 2026-07-03
- 网络出版日期: 2026-07-13

Accelerated Broadband Electromagnetic Scattering Analysis via ACA-Driven Measurement Matrix Interpolation

1.
College of Electrical and Information Engineering, Anhui University of Science and Technology, Huainan, Anhui 232001, China
2.
College of Mechanical and Electrical Engineering, Huainan Normal University, Huainan 232001, China
3.
College of Electronics and Information Engineering, Anhui University, Hefei 230601, China

Funds: The National Natural Science Foundation of China (62071004), The Natural Science Research Project of Anhui Educational Committee (2025AHGXZK31006)

摘要

摘要: 针对目标宽带电磁散射特性分析中待求频点阻抗矩阵重复计算、矩阵方程重复求解的问题，该文提出一种基于压缩感知框架的自适应交叉近似(ACA)驱动测量矩阵插值(MMI)的高效计算方法。该方法首先在最高频率点通过ACA提取主导行索引并全频段复用，实现测量矩阵确定性构建；其次采用MMI技术，通过少量采样频点的低维测量矩阵插值避免完整阻抗矩阵冗余计算；最后对插值后矩阵的远场组再次进行ACA分解，进一步加速矩阵向量积运算，实现传感矩阵的快速构建，将电流系数求解转换成压缩感知模型下超定方程的求解，实现待求频点电流快速求解。研究结果表明，该方法在保证计算精度的前提下，有效提高了测量矩阵的构造效率，显著降低插值的矩阵维数，大幅提升了目标宽带散射分析的效率。
- 宽带散射 /
- 压缩感知 /
- 自适应交叉近似 /
- 测量矩阵插值
Abstract: Objective Broadband electromagnetic scattering analysis is widely used in radar target recognition, stealth technology, and microwave imaging. Although the Method of Moments (MoM) provides high computational accuracy, it incurs substantial computational and memory costs for electrically large or geometrically complex targets because full impedance matrices must be constructed and solved. Existing acceleration techniques, including the MultiLevel Fast Multipole Method (MLFMM) and Adaptive Cross Approximation (ACA), reduce the computational burden but still require repeated matrix construction and equation solving at every frequency during wideband analysis. Methods such as Asymptotic Waveform Evaluation (AWE), Model-Based Parameter Estimation (MBPE), and impedance matrix interpolation have been proposed to reduce this redundancy. However, AWE is prone to error accumulation over wide frequency bands, MBPE requires expensive initial sampling, and conventional impedance matrix interpolation still requires the computation of full high-dimensional impedance matrices at the sampling frequencies. More recently, Compressive Sensing Method of Moments (CS-MoM) and its extension, CS-HBFM, have improved wideband analysis by employing Hyper-Basis Functions (HBFs). By constructing Characteristic Mode Basis Functions (CMBFs) only once at the highest frequency, CS-HBFM eliminates repeated basis-function generation. Nevertheless, existing CS-HBFM methods rely on nondeterministic random or uniform sampling, require expensive large-scale matrix-vector products, and repeatedly reconstruct and solve impedance equations throughout the frequency sweep. Methods A CS-ACA-MMI framework is proposed for broadband electromagnetic scattering analysis by combining dual ACA decomposition with Measurement Matrix Interpolation (MMI). First, CMBFs are constructed at the highest frequency, and dominant HBFs are selected according to the Modal Significance (MS) criterion. ACA is then applied to the full impedance matrix to extract deterministic row indices corresponding to the dominant Rao-Wilton-Glisson (RWG) basis functions. These indices are reused throughout the frequency band, eliminating nondeterministic sampling and repeated index extraction. Second, four sampling frequencies are selected using Chebyshev-Lobatto nodes. Low-dimensional measurement matrices are constructed directly from the extracted row indices, avoiding the generation of full high-dimensional impedance matrices. The measurement impedance elements at the sampling frequencies are corrected according to the geometric distance, interpolated to the target frequency, and then restored to the actual measurement impedance elements, thereby eliminating repeated construction of measurement matrices during frequency sweeping. Third, ACA is applied to the far-field component of the interpolated measurement matrix, converting large-scale matrix-vector products into low-dimensional matrix multiplications. The near-field sensing matrix is obtained directly by multiplying the measurement matrix by the basis functions, enabling rapid construction of the complete sensing matrix. Finally, the dense linear system is transformed into an overdetermined system under the compressive sensing framework, and the least-squares method is used to reconstruct the current coefficients, from which the broadband Radar Cross Section (RCS) is calculated. The Root Mean Square Error (RMSE) is used to evaluate numerical accuracy. Three representative targets, namely a cylinder, a slotted cone, and an almond, are analyzed. Broadband RCS, numerical accuracy, total computation time, and single-frequency measurement-matrix memory consumption are compared with those obtained using MoM and CS-HBFM to validate the proposed framework. Results and Discussions Three numerical examples, including a perfect electric conductor cylinder, a slotted cone, and an almond, are used to validate the proposed CS-ACA-MMI framework. The ACA-extracted row indices are concentrated near geometric boundaries and structural junctions, demonstrating the physical validity of the deterministic sampling strategy (Fig. 2). Parametric studies show that appropriate ACA thresholds and four sampling frequencies provide the best balance between computational efficiency and numerical accuracy (Figs. 3～5). The broadband RCS predicted by the proposed framework agrees closely with the MoM results over the entire frequency band (Figs. 6～8), and the RMSE remains low, demonstrating high numerical accuracy. Compared with CS-HBFM, the proposed framework reduces the total computation time by 93.4% for the cylinder, 96.7% for the slotted cone, and 81.0% for the almond (Table 2). These improvements result from deterministic index reuse, MMI, and dual ACA acceleration, which substantially reduce the computational cost of broadband frequency-sweeping analysis. Conclusions A CS-ACA-MMI framework is proposed by integrating ACA with MMI for efficient broadband electromagnetic scattering analysis. The proposed framework eliminates repeated matrix construction and equation solving during frequency sweeping while overcoming the nondeterministic sampling strategy and the high computational and memory costs of conventional CS-HBFM. Dominant row indices extracted by ACA at the highest frequency provide a deterministic measurement-matrix construction strategy and a stable physical basis for broadband interpolation. By shifting the interpolation target from full impedance matrices to low-dimensional measurement matrices, the computational complexity and redundant matrix construction are substantially reduced. A second ACA decomposition further accelerates sensing-matrix construction by converting large-scale matrix-vector products into low-dimensional matrix multiplications. Numerical results demonstrate that the proposed framework achieves numerical accuracy comparable to that of MoM while reducing total computation time by more than 81% and decreasing single-frequency measurement-matrix memory consumption by up to 65%. Because only the measurement matrices at four sampling frequencies need to be stored, the overall memory requirement is further reduced.
- Broadband scattering /
- Compressive Sensing(CS) /
- Adaptive Cross Approximation(ACA) /
- Measurement Matrix Interpolation(MMI)

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图 1 ACA测量矩阵构建示意图

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图 2 ACA全局行索引的高亮图

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图 3 行索引获取中不同ACA阈值下的时间和RMSE

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图 4 传感矩阵构建中不同ACA阈值下的时间和RMSE

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图 5 不同采样点数下的时间和RMSE

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图 6 圆柱体的宽带RCS

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图 7 带缝圆锥的宽带RCS

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图 8 杏仁体的宽带RCS

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表 1 两种方法的计算复杂度对比

方法	测量矩阵构建	近场传感矩阵构建	远场传感矩阵构建
CS-HBFM	$ O({N}_{f}MN) $	$ O((1-\eta ){N}_{f}MNK) $	$ O(\eta {N}_{f}MNK) $
CS-ACA-MMI	$ O(4SN) $	$ O((1-\eta ){N}_{f}SNK) $	$ O(\eta {N}_{f}RNK) $

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表 2 两种方法的计算时间对比

目标	方法	抽取行数	总时间(s)	RMSE(dBsm)	单频点测量矩阵的内存(GB)
圆柱体	CS-HBFM	3001	5285.27	0.46	0.46
圆柱体	CS-ACA-MMI	1104	349.33	0.4	0.16
带缝圆锥	CS-HBFM	4082	34991.7	0.04	0.83
带缝圆锥	CS-ACA-MMI	2839	1154.52	0.05	0.58
杏仁体	CS-HBFM	17633	180182.5	0.07	15.44
杏仁体	CS-ACA-MMI	13292	34316.2	0.05	11.64

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