一种基于信杂噪比准则的SAR波形和成像滤波器联合设计方法

张家伟; 孙婕; 徐华平; 李小龙

doi:10.12000/JR26117

一种基于信杂噪比准则的SAR波形和成像滤波器联合设计方法

DOI: 10.12000/JR26117 CSTR: 32380.14.JR26117

张家伟¹,
孙婕¹,
徐华平^2, ,,
李小龙^3, ,

1.
燕山大学信息科学与工程学院秦皇岛 066004
2.
北京航空航天大学电子信息工程学院北京 100191
3.
电子科技大学信息与通信工程学院成都 611731

基金项目: 国家自然科学基金( U2241202)，河北省自然科学基金(F2026203047)

详细信息

作者简介:
张家伟，博士，副教授，主要研究方向为合成孔径雷达成像处理、雷达波形设计和最优化算法等

孙　婕，硕士研究生，主要研究方向为雷达波形设计

徐华平，教授，博士生导师，主要研究方向为微波成像雷达新体制、成像处理和图像处理等

李小龙，教授，博士生导师，主要研究方向为机动目标探测、微弱目标检测跟踪和分布式雷达探测技术等

通讯作者:
徐华平 xuhuaping@buaa.edu.cn

李小龙 xiaolongli@uestc.edu.cn

责任主编：王伟 Corresponding Editor: WANG Wei

中图分类号: TN951
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出版历程
- 收稿日期: 2026-06-26

Joint Design of SAR Waveform and Imaging Filter Based on the Signal-to-Clutter-Plus-Noise Ratio Criterion

ZHANG Jiawei¹,
SUN Jie¹,
XU Huaping^{2
, ,},
LI Xiaolong^{3
, ,}

1.
School of Information Science and Engineering, Yanshan University, Qinhuangdao 066004, China
2.
School of Electronics and Information Engineering, Beihang University, Beijing 100191, China
3.
School of Information and Communication Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China

Funds: The National Natural Science Foundation of China (U2241202), The Hebei Natural Science Foundation (F2026203047)

More Information

Corresponding author: XU Huaping xuhuaping@buaa.edu.cn; LI Xiaolong xiaolongli@uestc.edu.cn

摘要

摘要: 针对合成孔径雷达(SAR)在弱目标成像时目标回波信号易被背景杂波淹没的问题，该文提出了一种基于信杂噪比准则的SAR波形与成像滤波器联合设计方法。该方法首先建立以信杂噪比为目标函数的联合优化模型，综合考虑了恒模、主瓣峰值、旁瓣电平及目标散射不确定性等约束条件，形成了具有极大极小结构的非凸多约束优化问题。为求解该复杂非凸恒模问题，该文发展了一种序贯交替迭代框架，将原问题分解为波形与滤波器两个子问题，采用上镜图变换与MM算法相结合的策略，实现分式目标函数解耦和非凸约束条件转化；通过引入辅助变量以扩展可行域，保证初始迭代时的可行性，再添加随迭代次数递增的惩罚项，最终迫使辅助变量趋于零，实现原始问题的求解，并从理论上分析了算法的收敛性和计算复杂度。实验结果表明：与同参数的线性调频信号相比，联合设计方案在仿真、半物理及外场真实试验中均表现出显著的杂波抑制能力，SAR图像的信杂比可提升3.2 dB以上，为改善SAR系统对弱目标的探测与成像性能提供了工程可行的技术途径。
- 合成孔径雷达 /
- 联合设计 /
- 波形设计 /
- 接收滤波器 /
- 优化算法
Abstract: To address the critical issue of weak-target imaging performance in synthetic aperture radar (SAR), this paper proposes a method for jointly designing the SAR waveform and imaging filter based on the signal-to-clutter-plus-noise ratio (SCNR) criterion. The method first establishes a joint optimization model aimed at maximizing the SCNR. This model comprehensively considers constant modulus constraints, mainlobe peak constraints, sidelobe levels, and target scattering uncertainty, resulting in a nonconvex, multiconstrained optimization problem with a max– min structure. To solve this problem, this paper develops a sequential alternating optimization framework that decomposes the original problem into two subproblems: waveform design and filter design. A strategy combining the epigraph transformation with the majorization–minimization algorithm is employed to handle the nonconvex fractional objective function and constraints. Auxiliary variables are introduced to extend the feasible region, thereby guaranteeing feasibility at the initial iteration. A penalty term that increases progressively with the number of iterations is then incorporated, ultimately forcing the auxiliary variables to approach zero and thereby enabling the solution of the original problem. The convergence and computational complexity of the proposed algorithm are also analyzed. Experimental results demonstrate that, compared with traditional linear frequency-modulated signals with identical parameters, the joint design scheme exhibits pronounced performance advantages in simulated, semi-physical, and field scenarios. The proposed method improves the SCNR of SAR images by more than 3.2 dB, providing an engineering-feasible approach for enhancing the detection and imaging performance of SAR systems for weak targets.
- Synthetic Aperture Radar (SAR) /
- Joint design /
- Waveform design /
- Receive filter /
- Optimization algorithm

HTML全文

图 1 迭代循环$ {\mathcal{L}}_{2} $与$ {\mathcal{L}}_{3} $中目标函数值及其下限随迭代次数的变化情况

Figure 1. Change of the objective function and its lower limit with respect to the iteration number in $ {\mathcal{L}}_{2} $ and $ {\mathcal{L}}_{3} $

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图 2 $ {\mathcal{L}}_{2} $中松弛变量$ ||\boldsymbol{u}|{|}_{1} $随迭代次数m的变化情况

Figure 2. Change in the slack variable $ ||\boldsymbol{u}|{|}_{1} $ with respect to the iteration number m in $ {\mathcal{L}}_{2} $

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图 3 目标函数值随迭代次数k变化

Figure 3. Convergence comparison of the objective function with respect to the iteration numberk

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图 4 不同初值下的目标函数序列

Figure 4. Objective function sequences generated from different initial values

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图 5 不同参数取值下CCF的比较

Figure 5. Comparison of CCF under different parameter values

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图 6 优化波形的实部、虚部、时频关系

Figure 6. Real and imaginary parts of proposed waveform, as well as time-frequency characteristics

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图 7 舰船目标模型

Figure 7. Ship models

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图 8 不同波形的SAR图像

Figure 8. SAR images with different waveforms.

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图 9 不同背景强度下的SCR

Figure 9. SCRs with different background scattering

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图 10 目标模型和不同波形的SAR图像

Figure 10. Target models and SAR images with different waveforms

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图 11 任意相位编码信号SAR硬件平台

Figure 11. Arbitrary phase-coded signal SAR hardware platform

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图 12 参考波形与硬件回传信号对比

Figure 12. The comparison between the reference signal and the hardware-returned signal

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图 13 外场试验目标

Figure 13. Target of field experiment

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图 14 外场试验SAR成像结果

Figure 14. SAR images of the field experiment

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1 联合优化算法

1. Joint optimization algorithm

设置参数：$ {E}_{0} $，$ \delta $，e，$ {e}^{\prime} $，$ \varepsilon $，$ {\tau }_{0} $，$ {\lambda }^{(0)} $和$ \omega $。
1：初始化$ {\boldsymbol{x}}_{(0)} $和$ {\boldsymbol{w}}_{(0)} $，设置迭代索引$ k=1 $，开启外层迭代$ {\mathcal{L}}_{1} $。
2：repeat固定$ \boldsymbol{w}={\boldsymbol{w}}^{\left(k-1\right)} $，构造$ {\mathcal{P}}_{2} $。
3：　令$ m=0 $，开启迭代循环$ {\mathcal{L}}_{2} $，$ {\lambda }^{(m)}={\lambda }^{(0)} $，　　　$ {\boldsymbol{x}}_{(m)}={\boldsymbol{x}}^{(k-1)} $，$ {\tau }_{(m)}={\tau }_{0} $。
4：　repeat引入松弛变量$ \boldsymbol{u} $，构造$ {\mathcal{P}}_{4} $，求解得到$ {\boldsymbol{x}}^{*} $。
5：　　更新$ {\lambda }^{(m)} $，$ {\boldsymbol{x}}_{(m)} $，$ {\tau }_{(m)} $，$ m=m+1 $。
6：　until$ \|\|\boldsymbol{u}\|{\|}_{1}\leq e $触发停止条件。
7：　更新波形$ {\boldsymbol{x}}^{\left(k\right)}={\boldsymbol{x}}^{\ast } $。
8：　固定$ \boldsymbol{x}={\boldsymbol{x}}^{\left(k\right)} $，构造$ {\mathcal{P}}_{5} $。
9：　令$ n=0 $，开启迭代$ {\mathcal{L}}_{3} $，$ {\boldsymbol{w}}_{(n)}={\boldsymbol{w}}^{(k-1)} $，　　　 $ {\tau }_{(n)}={\tau }_{(m)} $。
10： repeat构造$ {\mathcal{P}}_{6} $，求解得到$ {\boldsymbol{w}}^{\ast } $。
11：　更新$ {\boldsymbol{w}}_{(n)} $，$ {\tau }_{(n)} $，$ n=n+1 $。
12： until$ {\tau }_{(n)}-{\tau }_{(n-1)}\leq {e}^{\prime} $触发停止条件。
13：更新滤波器$ {\boldsymbol{w}}^{\left(k\right)}={\boldsymbol{w}}^{\ast } $，$ {\tau }_{0}={\tau }_{(n)} $。
14：until $ f({\boldsymbol{x}}^{(k)},{\boldsymbol{w}}^{(k)})-f({\boldsymbol{x}}^{(k-1)},{\boldsymbol{w}}^{(k-1)})\leq \varepsilon $触发$ {\mathcal{L}}_{1} $的停　止条件。
15：输出优化波形与滤波器解对$ ({\boldsymbol{x}}^{\left(k\right)}，{\boldsymbol{w}}^{\left(k\right)}) $

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表 1 SAR系统参数

Table 1. List of SAR parameters

参数		取值
平台高度	H₀	6 km
天线长度	D	2 m
有效雷达速率	v	150 m/s
视角	$ \theta $	30°
斜视角	$ \phi $	0°
中心频率	$ {f}_{0} $	5.3 GHz
脉冲持续时间	T	1 μs
距离带宽	$ {B}_{\text{r}} $	100 MHz
距离采样率	$ {F}_{\text{r}} $	120 MHz
方位采样率	$ {F}_{\text{a}} $	180 Hz
距离线数量	$ {N}_{\mathrm{a}} $	256
每个距离线的采样点数	$ {N}_{\text{r}} $	256

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表 2 外场试验参数

Table 2. List of field experiment parameters

参数	数值
平台高度	1.5 m
场景中心距	20 m
载波频率	5.5 G
信号带宽	100 MHz
脉冲时宽	2 us
采样率	122882080 Hz
方位向步长	0.05 m
合成孔径长度	11 m
天线物理口径	0.15 m

下载: 导出CSV

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