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An algorithm of reconstructing phaseless radiation source based on singular value decomposition (SVD) regularization and fast iterative shrinkage-thresholding algorithm (FISTA) is proposed in this work, aiming at efficiently identifying electromagnetic interference (EMI) sources in integrated circuits (ICs). The method acquires electromagnetic field data through near-field scanning and reconstructs an equivalent dipole array on the surface of the radiation source by using the source reconstruction method (SRM). In the reconstruction process, the SVD regularization term enhances the algorithm's stability and noise resistance, while the FISTA accelerates the convergence speed. In order to validate the effectiveness of the proposed method, dipole array reconstruction is first performed using near-field data at a height of 5 mm for a patch antenna simulation model, followed by analyzing the magnetic field data at a 10 mm validation plane. At the 35th iteration, the total relative error of the reconstruction is 1.21%. The influence of the regularization parameter α on the result is then investigated, and it is found that when α = 0.05 the error is minimized. The method is also tested under different Gaussian white noise conditions, and the relative error is kept below 5%, which demonstrates strong robustness. Finally, the experiments on chips are conducted to verify the method. The proposed method converges stably within 35 iterations, with a relative error of 2.3% in the reconstruction results. The proposed method reduces the total iteration time to 61.7% of the single-layer phaseless interpolation algorithm, while achieving a 52% lower relative error than the double-layer phasless iteration algorithm. The experimental results show that the proposed method can reconstruct phaseless radiation source efficiently and accurately, and has good noise robustness, which is suitable for EMI analysis in ICs. -
Keywords:
- aingular value secomposition (SVD) /
- fast iterative shrinkage-thresholding algorithm (FISTA) /
- near-field scanning (NFS) /
- source reconstruction method (SRM)
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图 1 辐射源重构原理图
Figure 1. The radiation source reconstruction schematic.
图 2 所提算法流程图
Figure 2. Flowchart of the proposed algorithm.
图 3 贴片天线模型图 (a)三维图; (b)天线结构
Figure 3. Patch antenna model diagram: (a) Three-dimensional diagram; (b) antenna structure.
图 4 在z = 12 mm, f = 2.5 GHz下仿真和源重构的磁场分量幅值结果 (a)仿真的磁场分量幅值; (b)源重构的磁场分量幅值
Figure 4. Magnitude of magnetic field component for simulation and source reconstruction under z = 12 mm, f = 2.5 GHz: (a) Simulated magnetic field component amplitude; (b) magnetic field component amplitude of SRM.
图 5 在z = 12 mm, f = 2.5 GHz下源重构的相对误差 (a) 磁场分量的相对误差σHx, σHy和σHz; (b)总相对误差σH
Figure 5. Relative error of SRM at z = 12 mm, f = 2.5 GHz: (a) Relative error of magnetic field components σHx, σHy and σHz; (b) total relative error σH.
图 6 不同正则化参数对总相对误差的影响
Figure 6. Influence of different regularization parameters on total relative error.
图 7 在不同水平的高斯白噪声下z = 12 mm, f = 2.5 GHz磁场|Hx|幅值 (a) SNR = 30 dB; (b) SNR = 20 dB; (c) SNR = 10 dB; (d) SNR = 5 dB
Figure 7. Magnetic field $ \left|{H}_{x}\right| $ amplitude under different levels of white Gaussian noise, z = 12 mm, f = 2.5 GHz: (a) SNR = 30 dB; (b) SNR = 20 dB; (c) SNR = 10 dB; (d) SNR = 5 dB.
图 8 加入不同高斯白噪声后总的相对误差
Figure 8. Total relative error after adding different Gaussian white noise.
图 9 近场扫描实验设备 (a)近场扫描装置设备; (b)芯片模型
Figure 9. Near field scanning experimental equipment: (a) Near field scanning equipment; (b) chip model.
图 10 在z = 8.22 mm, f = 2 GHz下近场扫描和源重构的磁场分量幅值 (a)近场扫描的磁场分量幅值; (b)源重构的磁场分量幅值
Figure 10. Amplitude of magnetic field components in near-field scanning and SRM at z = 8.22 mm, f = 2 GHz: (a) Amplitude of magnetic field component in near-field scanning; (b) magnetic field component amplitude of SRM.
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