一种快速抗间歇采样转发干扰波形和滤波器联合设计算法

周凯; 何峰; 粟毅

doi:10.12000/JR22015

一种快速抗间歇采样转发干扰波形和滤波器联合设计算法

DOI: 10.12000/JR22015

国防科技大学电子科学学院长沙 410073

基金项目: 国家自然科学基金(61771478, 61901501, 62001488)

详细信息

作者简介:
周　凯(1993–)，男，湖南岳阳人，现为国防科技大学电子科学学院博士研究生，研究方向为雷达波形设计、雷达电子抗干扰技术和合成孔径雷达成像

何　峰(1976–)，男，湖北孝感人，博士，现为国防科技大学电子科学学院研究员，研究方向为合成孔径雷达成像、雷达多维波形编码设计

粟　毅(1961–)，男，山东泰安人，博士，现为国防科技大学电子科学学院教授，博士生导师，研究方向为新体制雷达系统、雷达信号处理

通讯作者:
何峰 hefeng@nudt.edu.cn

粟毅 yi.su@yeah.net

责任主编：崔国龙 Corresponding Editor: CUI Guolong
中图分类号: TN972
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- 被引次数: 10
出版历程
- 收稿日期: 2022-01-16
- 修回日期: 2022-03-17
- 网络出版日期: 2022-04-06
- 刊出日期: 2022-04-28

Fast Algorithm for Joint Waveform and Filter Design against Interrupted Sampling Repeater Jamming

College of Electronic Science, National University of Defense Technology, Changsha 410073, China

Funds: The National Natural Science Foundation of China (61771478, 61901501, 62001488)

More Information

Corresponding author: HE Feng, hefeng@nudt.edu.cn; SU Yi, yi.su@yeah.net

摘要

摘要: 该文研究了一种快速的抗间歇采样转发干扰波形和滤波器联合设计方法。基于罚函数和帕累托最优化原理给出了联合设计模型的优化数学模型。推导优化波形和滤波器过程中矩阵迹的解析表达式，有效降低了算法的计算复杂度。提出了一种基于平方迭代加速方法，解决了主分量最小化方法目标函数近似造成的算法收敛速度降低问题，进一步加快了算法运行速度。仿真结果表明，该文所提出的算法比传统方法具有更快的运行速度。同时，当干扰目标和真实目标在距离上不可分时，该文方法仍能够有效抑制间歇采样转发干扰。
- 波形设计 /
- 滤波器设计 /
- 间歇采样转发干扰 /
- 主分量最小化 /
- 平方迭代加速方法
Abstract: To suppress interrupted sampling jamming, a joint waveform and filter design method was proposed in this study. A fast algorithm was also suggested to design sequences with large code lengths. The joint design problem was formulated on the basis of the penalty function and Pareto optimization method. By deriving the theoretical solution of the trace of matrices in each iteration, the computation order of the proposed algorithm was decreased significantly compared to that of the conventional algorithm. Moreover, an accelerated scheme based on the squared iterative method, which further improves the running speed of the algorithm, was proposed. Simulation results demonstrate that the proposed algorithm runs faster than traditional algorithms. Moreover, the designed waveform and filter can be applied to suppress interrupted sampling repeater jamming when the false targets are inseparable from the true targets in time-frequency domains.
- Waveform design /
- Filter design /
- Interrupted Sampling Repeater Jamming (ISRJ) /
- Majorization minimization /
- Squared iterative method

HTML全文

图 1 非匹配滤波性能随着权值的变化曲线

Figure 1. Curves of mismatch output performance versus Pareto weights

下载: 全尺寸图片幻灯片

图 2 波形实部幅度图

Figure 2. The amplitude of the real part of waveform

下载: 全尺寸图片幻灯片

图 3 波形和干扰信号非匹配滤波输出(N=512)

Figure 3. Mismatch output of the waveform and jamming signal (N=512)

下载: 全尺寸图片幻灯片

图 4 积分旁瓣比和积分能量比随峰值增益损耗变化

Figure 4. Integrated sidelobe levels and integrated levels versus loss of processing gain

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图 5 运行时间对比图

Figure 5. Comparison of running time

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图 6 不同波形长度下的运行时间图

Figure 6. Running time versus different code length

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图 7 波形和干扰信号非匹配滤波输出(N=800)

Figure 7. Mismatch output of waveform and jamming signal (N=800)

下载: 全尺寸图片幻灯片

图 8 抗间歇采样转发干扰评估

Figure 8. Evaluation of interrupted sampling repeater jamming suppression

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图 9 干扰机位置对抗干扰性能的影响

Figure 9. Jamming suppression performance versus location of jammer

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图 10 干扰峰值随着重复周期和占空比的估计误差变化图

Figure 10. Jamming peak versus the relative error of pulse repetition period and duty ratio

下载: 全尺寸图片幻灯片

表 1 快速抗间歇采样转发干扰波形和滤波器联合设计算法

Table 1. Fast algorithm for joint waveform and filter design against interrupted sampling repeater jamming

输入：波形和滤波器长度N
1：用随机相位编码序列初始化 ${{\boldsymbol{x}}^{\left( 0 \right)}}$ 和 ${{\boldsymbol{h}}^{\left( 0 \right)}}$ ；
2：重复
3：　 ${{\boldsymbol{h}}_1} = F\left( {{{\boldsymbol{h}}^{\left( l \right)}},{{\boldsymbol{x}}^{\left( l \right)}}} \right)$
4：　 ${{\boldsymbol{h}}_2} = F\left( {{{\boldsymbol{h}}_1},{{\boldsymbol{x}}^{\left( l \right)}}} \right)$
5：　 ${{\boldsymbol{r}}_1} = {{\boldsymbol{h}}_1} - {{\boldsymbol{h}}^{\left( l \right)}}$
6：　 ${{\boldsymbol{v}}_1} = {{\boldsymbol{h}}_2} - {{\boldsymbol{h}}_1} - {{\boldsymbol{r}}_1}$
7：　 ${\alpha _1} = - {{{{\left\\| {{{\boldsymbol{r}}_1}} \right\\|}_2}} \mathord{\left/ {\vphantom {{{{\left\\| {{{\boldsymbol{r}}_1}} \right\\|}_2}} {{{\left\\| {{{\boldsymbol{v}}_1}} \right\\|}_2}}}} \right. } {{{\left\\| {{{\boldsymbol{v}}_1}} \right\\|}_2}}}$
8：　 ${{\boldsymbol{h}}^{\left( {l + 1} \right)}} = F\left( {{{\boldsymbol{h}}^{\left( l \right)}} - 2{\alpha _1}{{\boldsymbol{r}}_1} + \alpha _1^2{{\boldsymbol{v}}_1},{{\boldsymbol{x}}^{\left( l \right)}}} \right)$
9：　若 $f\left( {{{\boldsymbol{x}}^{\left( l \right)}},{{\boldsymbol{h}}^{\left( {l + 1} \right)}}} \right) > f\left( {{{\boldsymbol{x}}^{\left( l \right)}},{{\boldsymbol{h}}^{\left( l \right)}}} \right)$ ，循环
10：　　 ${\alpha _1} \leftarrow {{\left( {{\alpha _1} - 1} \right)} \mathord{\left/ {\vphantom {{\left( {{\alpha _1} - 1} \right)} 2}} \right. } 2}$
11：　　 ${{\boldsymbol{h}}^{\left( {l + 1} \right)}} = F\left( {{{\boldsymbol{h}}^{\left( l \right)}} - 2\alpha {{\boldsymbol{r}}_1} + {\alpha ^2}{{\boldsymbol{v}}_1},{{\boldsymbol{x}}^{\left( l \right)}}} \right)$
12：　结束
13：　 ${{\boldsymbol{x}}_1} = G\left( {{{\boldsymbol{h}}^{\left( {l + 1} \right)}},{{\boldsymbol{x}}^{\left( l \right)}}} \right)$
14：　 ${{\boldsymbol{x}}_2} = G\left( {{{\boldsymbol{h}}^{\left( {l + 1} \right)}},{{\boldsymbol{x}}_1}} \right)$
15：　 ${{\boldsymbol{r}}_2} = {{\boldsymbol{x}}_1} - {{\boldsymbol{x}}^{\left( l \right)}}$
16：　 ${{\boldsymbol{v}}_2} = {{\boldsymbol{x}}_2} - {{\boldsymbol{x}}_1} - {{\boldsymbol{r}}_1}$
17：　 ${\alpha _2} = - {{{{\left\\| {{{\boldsymbol{r}}_2}} \right\\|}_2}} \mathord{\left/ {\vphantom {{{{\left\\| {{{\boldsymbol{r}}_2}} \right\\|}_2}} {{{\left\\| {{{\boldsymbol{v}}_2}} \right\\|}_2}}}} \right. } {{{\left\\| {{{\boldsymbol{v}}_2}} \right\\|}_2}}}$
18：　 ${{\boldsymbol{x}}^{\left( {l + 1} \right)}} = G\left( {{{\boldsymbol{h}}^{\left( {l + 1} \right)}},{{\boldsymbol{x}}^{\left( l \right)}} - 2{\alpha _2}{{\boldsymbol{r}}_2} + \alpha _2^2{{\boldsymbol{v}}_2}} \right)$
19：　若 $f\left( {{{{\boldsymbol{\tilde x}}}^{\left( l \right)}},{{\boldsymbol{h}}^{\left( {l + 1} \right)}}} \right) > f\left( {{{\boldsymbol{x}}^{\left( l \right)}},{{\boldsymbol{h}}^{\left( {l + 1} \right)}}} \right)$ ，循环
20: 　　 ${\alpha _2} \leftarrow {{\left( {{\alpha _2} - 1} \right)} \mathord{\left/ {\vphantom {{\left( {{\alpha _2} - 1} \right)} 2}} \right. } 2}$
21：　　 ${{\boldsymbol{x}}^{\left( {l + 1} \right)}} = G\left( {{{\boldsymbol{h}}^{\left( {l + 1} \right)}},{{\boldsymbol{x}}^{\left( l \right)}} - 2{\alpha _2}{{\boldsymbol{r}}_2} + \alpha _2^2{{\boldsymbol{v}}_2}} \right)$
22：　结束
23：　 $l \leftarrow l + 1$
24：直至收敛
输出：波形和滤波器。

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表 2 算法性能对比

Table 2. Performance comparison of tested algorithms

方法	LPG (dB)	ISLR (dB)	ILs (dB)	干扰峰值(dB)	Running time (s)
文献[17]	–1.73	–10.71	–10.77	–30	1329.51
文献[18]	–1.71	–11.16	–11.34	–28.75	214.32
本文方法	–1.71	–11.17	–11.70	–29.73	38.80

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表 3 仿真参数

Table 3. Simulation parameters

参数	数值
时宽(μs)	40
带宽(MHz)	20
采样重复周期(μs)	10
采样信号时宽(μs)	2.5
雷达位置(m)	(0,0,0)
干扰机位置(m)	(0,2000,0)
目标位置(m)	(0,3000,0)
干扰机时延(μs)	2

下载: 导出CSV

表 4 两组波形和非匹配滤波器性能对比

Table 4. The mismatch output performance of designed waveform via tested algorithms

方法	LPG (dB)	ISLR (dB)	ILs (dB)	Peak interference (dB)
文献[17]	–1.61	–11.73	–14.29	–30.00
本文方法	–1.61	–12.60	–14.52	–29.99

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表 5 抗干扰性能对比

Table 5. Performance comparison of jamming suppression

方法	信号处理损耗(dB)	干扰峰值(dB)
文献[13]	0	–0.19
文献[10]	0	–14.96
文献[17]	–1.40	–9.16
本文方法	–1.11	–10.55

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