强稀疏低副瓣近场聚焦稀疏阵列三维成像

杨磊; 宋昊; 申瑞阳; 陈英杰; 胡仲伟; 霍鑫; 邢孟道

doi:10.11999/JEIT231278

强稀疏低副瓣近场聚焦稀疏阵列三维成像

doi: 10.11999/JEIT231278

1.
中国民航大学电子信息与自动化学院天津 300300
2.
西安电子科技大学雷达信号处理国家重点实验室西安 710071

基金项目: 国家自然科学基金(62271487)

详细信息

作者简介:
杨磊：男，教授，研究方向为高分辨SAR成像及机器学习理论应用

宋昊：男，硕士生，研究方向为毫米波成像与稀疏阵列构型设计

申瑞阳：男，硕士生，研究方向为毫米波成像与稀疏阵列构型设计

陈英杰：男，硕士生，研究方向为毫米波成像与稀疏阵列构型设计

胡仲伟：男，讲师，研究方向为高分辨SAR成像及优化学习理论

霍鑫：男，硕士生，研究方向为毫米波成像与稀疏阵列构型设计

邢孟道：男，教授，研究方向为雷达成像、动目标检测

通讯作者:
杨磊 email:　yanglei840626@163.com

中图分类号: TN957
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- 被引次数: 0
出版历程
- 收稿日期: 2023-11-20
- 修回日期: 2024-11-10
- 网络出版日期: 2024-11-19
- 刊出日期: 2025-12-01

High Sparsity and Low Sidelobe Near-field Focused Sparse Array for Three-Dimensional Imagery

1.
College of Electronic Information and Automation, Civil Aviation University of China, Tianjin 300300, China
2.
National Laboratory of Radar Signal Processing, Xidian University, Xi’an 710071, China

Funds: The National Natural Science Foundation of China (62271487)

摘要

摘要: 在主动式电扫描毫米波安检成像中，均匀阵列天线存在成本受限以及复杂度高等瓶颈问题，难以在实际工程中大规模运用。由此，该文提出一种强稀疏低副瓣的近场聚焦稀疏阵列设计方法，并进一步利用改进3维时域成像算法实现高精度3维重建。首先，以近场聚焦位置以及峰值旁瓣电平为约束，以权向量的$ {\ell _p} $(0<p<1)范数正则化为目标函数，构建近场聚焦稀疏阵列天线优化模型。然后，通过引入辅助变量，建立旁瓣及聚焦位置约束与辅助变量间的等价代换模型，解决阵列权向量目标函数与复杂约束耦合带来的求解难题，通过等价代换思想对模型化简并求解。接着，采用复数求导结合启发式近似方法对阵列激励以及位置进行优化选择。最后，利用交替方向多乘子法(ADMM)实现聚焦位置、峰值旁瓣约束以及阵列激励协同求解，通过改进3维时域成像算法实现稀疏阵列3维成像。仿真模拟实验结果显示，该方法可以在满足阵列天线辐射特性以及近场聚焦条件下，以更少的阵元数目获得更低的旁瓣电平。此外，采用实测数据验证稀疏阵列改进3维时域成像算法高精度、高效率的优势。
- 近场成像 /
- 稀疏阵列 /
- 3维成像 /
- 交替方向多乘子法
Abstract: In active electrical scanning millimeter-wave security imaging, the uniform array antenna has the bottleneck of uncontrolled cost and high complexity, which is difficult to be widely applied in practices. To this end, a near-field focused sparse array design algorithm for high sparsity and low sidelobes is proposed in this paper. It applies an improved three dimensional (3D) time-domain imaging algorithm to achieve high-accuracy 3D reconstruction. Firstly, the near-field focusing sparse array antenna model is constructed by taking the near-field focusing position and peak sidelobe level as constraints, where the $ {\ell _p} $(0<p<1) norm of the weight vector regularization is established as the objective function. Secondly, by introducing auxiliary variables and establishing equivalent substitution models between sidelobe and focus position constraints and auxiliary variables, the problem of solving the array weight vector in the coupling of the objective function and complex constraints is developed. The model is simplified and solved through the idea of equivalent substitution. Then, the array excitation and position are optimized using a combination of complex number differentiation and heuristic approximation methods. Finally, the Alternating Direction Method of Multipliers (ADMM) is employed to achieve the focus position, peak sidelobe constraint, and array excitation in a cooperative manner. The sparse array 3D imaging is realized by improving the 3D time-domain imaging algorithm. The experimental results show that the proposed method is capable of obtaining lower sidelobe level with fewer array elements under the condition of satisfying the radiation characteristics of array antenna and near-field focusing. Applying raw millimeter-wave data, the advantages of sparse array 3D time-domain imaging algorithm are verified in terms of high accuracy and high efficiency.
- Near field imaging /
- Sparse array /
- Three-dimensional imaging /
- Alternating Direction Method of Multipliers (ADMM)

HTML全文

图 1 圆柱体扫描毫米波安检成像几何示意图

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图 2 笛卡尔坐标系下近场线性阵列天线模型

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图 3 距离-高度维局部极坐标网格

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图 4 3维场景成像切片划分

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图 5 不同算法下天线方向图对比

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图 6 阵元位置分布及其对应激励值

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图 7 辅助变量收敛曲线

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图 8 均匀阵列与稀疏阵列成像结果对比

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图 9 均匀阵列与稀疏阵列点目标成像结果剖面图

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1 稀疏阵列优化算法

(1)初始化：$ {{\boldsymbol{\gamma}} ^{\mathrm{r}}}(0) $, $ {{\boldsymbol{\gamma}} ^{\mathrm{i}}}(0) $, $ {{\boldsymbol{\varsigma}} ^{\mathrm{r}}}(0) $, $ {{\boldsymbol{\varsigma}} ^{\mathrm{i}}}(0) $, $ {\boldsymbol{w}}(0) $，给定循环的迭代　次数$ K $, $ N $
(2) for $ i = 0,1, \cdots ,K $
步骤1　得到$ {q_0}(i + 1) $和$ {g_s}(i + 1) $通过式(12)–式(16)
步骤2　求解$ {\boldsymbol{w}}(i + 1) $
for $ k = 0,1, \cdots ,N $
(1)得到关于$ {\boldsymbol{w}} $非线性方程通过式(17)–式(21)
(2)确定$ {{\boldsymbol{w}}^{(k)}}(i + 1) $通过式(22)
End for $ k = N $
步骤3　通过式(23)更新$ {{\boldsymbol{\gamma}} ^{\mathrm{r}}}(i + 1) $, $ {{\boldsymbol{\gamma}} ^{\mathrm{i}}}(i + 1) $, $ {{\boldsymbol{\varsigma}} ^{\mathrm{r}}}(i + 1) $, $ {{\boldsymbol{\varsigma}} ^{\mathrm{i}}}(i + 1) $
end for $ i = K $
得到最终阵列权值向量的结果$ {\boldsymbol{w}} $

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表 1 圆周柱面阵列天线实测数据参数

雷达参数	数值	雷达参数	数值	雷达参数	数值
系统工作带宽	6.5 GHz	方位/俯仰波束角	55°/55°	旋转次数	314
工作频率	27 GHz	单脉冲采样点数	64	单次旋转角度	0.2867°
目标距离	0.4～0.8 m	阵元间距	0.0052 m	旋转半径	0.628 m

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表 2 均匀阵列与稀疏阵列点目标成像结果剖面图定量分析

点目标高度向成像结果	峰值旁瓣比(dB)	高度向分辨率(mm)
均匀阵列成像	–24.27	7.76
稀疏阵列RMA成像	–16.82	7.76
稀疏阵列改进3维时域成像	–20.32	7.76

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