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Article(id=1253997370597896752, tenantId=1146029695717560320, journalId=1251234736404742242, issueId=1253997366797857283, articleNumber=null, orderNo=null, doi=10.3969/j.issn.1672-2337.2025.05.008, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1737475200000, receivedDateStr=2025-01-22, revisedDate=1745769600000, revisedDateStr=2025-04-28, acceptedDate=null, acceptedDateStr=null, onlineDate=1776905871295, onlineDateStr=2026-04-23, pubDate=null, pubDateStr=null, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1776905871295, onlineIssueDateStr=2026-04-23, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1776905871295, creator=13041195026, updateTime=1776905871295, updator=13041195026, issue=Issue{id=1253997366797857283, tenantId=1146029695717560320, journalId=1251234736404742242, year='2025', volume='23', issue='5', pageStart='473', pageEnd='590', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=1, specialIssue=null, createTime=1776905870387, creator=13041195026, updateTime=1777355497251, updator=13041195026, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1255883238690702048, tenantId=1146029695717560320, journalId=1251234736404742242, issueId=1253997366797857283, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1255883238690702049, tenantId=1146029695717560320, journalId=1251234736404742242, issueId=1253997366797857283, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=540, endPage=550, ext={EN=ArticleExt(id=1253997371038298677, articleId=1253997370597896752, tenantId=1146029695717560320, journalId=1251234736404742242, language=EN, title=ECA-CMAP Clutter Suppression Method for Passive Bistatic Radar, columnId=null, journalTitle=Radar Science and Technology, columnName=null, runingTitle=null, highlight=null, articleAbstract=

Passive bistatic radar (PBR) avoids electromagnetic interference to a great extent because of the layout mode of transmitting and receiving separately. However, it faces a lot of short-range ground clutter interference in its work, and it is difficult to detect the target when it is submerged in a lot of clutter, especially for PBR with pulse radar as its external radiation source, the clutter processing is more difficult. In this paper, a time-domain monopulse extensive cancellation algorithm-clutter map (ECA-CMAP) clutter suppression method is proposed for PBR with pulse radar as external radiation source, aiming at the problem that it faces a large number of short-range ground clutter to cover up the target in practical work. Firstly, based on the classical time domain clutter suppression method ECA (extensive cancellation algorithm), an improved scheme based on clutter time delay estimation is proposed, which can suppress short-range ground clutter and keep the target intact, and the signal-to-clutter ratio is increased by nearly 50dB, and the target detection probability is further improved by using Nitzberg clutter map algorithm. Simulation and result of measured data processing verify the effectiveness of the algorithm.

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非合作双基地雷达收发分置的布局模式很大程度上规避了电磁干扰，然而其在工作中面临大量的近程地杂波干扰，目标淹没在大量杂波中难以检测，尤其对于以脉冲雷达为外辐射源的非合作双基地雷达而言，杂波的处理更加困难。本文面向以脉冲雷达为外辐射源的非合作双基地雷达，针对其实际工作中面临大量近程地杂波掩盖目标的问题，提出了时域单脉冲ECA-CMAP杂波抑制方法。首先在经典的时域杂波抑制方法ECA的基础上提出了基于杂波时延估计的改进方案，在抑制近程地杂波的同时将目标完整地保留下来，且将信杂比提升约50dB；其次，提升目标信杂比后结合使用Nitzberg杂波图算法进一步提高目标检测概率。仿真和实测数据处理验证了算法的有效性。

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梁师源 男，硕士研究生，主要研究方向为自动目标识别。

潘嘉蒙 男，博士，讲师，主要研究方向为雷达信号处理。

鲍庆龙 男，博士，副教授，主要研究方向为雷达信号处理。

肖怀铁 男，博士，教授，主要研究方向为自动目标识别。

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梁师源 男，硕士研究生，主要研究方向为自动目标识别。

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梁师源 男，硕士研究生，主要研究方向为自动目标识别。

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潘嘉蒙 男，博士，讲师，主要研究方向为雷达信号处理。

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潘嘉蒙 男，博士，讲师，主要研究方向为雷达信号处理。

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鲍庆龙 男，博士，副教授，主要研究方向为雷达信号处理。

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鲍庆龙 男，博士，副教授，主要研究方向为雷达信号处理。

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肖怀铁 男，博士，教授，主要研究方向为自动目标识别。

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肖怀铁 男，博士，教授，主要研究方向为自动目标识别。

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参数参数值
脉宽/μs10
带宽/MHz2
载频/GHz1.5
脉冲重复间隔（PRI）/μs200
采样率/MHz5
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辐射源仿真参数

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参数参数值
脉宽/μs10
带宽/MHz2
载频/GHz1.5
脉冲重复间隔（PRI）/μs200
采样率/MHz5
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种类参数
距离单元原始幅度/dB
直达波170
杂波13530
杂波24531
杂波35533
杂波46529
杂波57526
杂波68523
杂波79530
杂波810545
杂波911535
杂波1012529
目标68-20
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杂波和目标仿真参数

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种类参数
距离单元原始幅度/dB
直达波170
杂波13530
杂波24531
杂波35533
杂波46529
杂波57526
杂波68523
杂波79530
杂波810545
杂波911535
杂波1012529
目标68-20
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参数参数值
虚警率Pf10-6
遗忘因子w0.0625
门限因子T18.125
雷达扫描次数L50
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杂波图参数

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虚警率Pf10-6
遗忘因子w0.0625
门限因子T18.125
雷达扫描次数L50
), ArticleFig(id=1253999621311754568, tenantId=1146029695717560320, journalId=1251234736404742242, articleId=1253997370597896752, language=EN, label=null, caption=null, figureFileSmall=null, figureFileBig=null, tableContent=
种类参数
距离单元原始幅度/dB
直达波170
多径1227
多径2331
多径3430
多径4526
多径5629
多径6739
多径7831
多径898
多径91025
多径101129
目标6831
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直达波及其多径、目标仿真参数

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种类参数
距离单元原始幅度/dB
直达波170
多径1227
多径2331
多径3430
多径4526
多径5629
多径6739
多径7831
多径898
多径91025
多径101129
目标6831
), ArticleFig(id=1253999621496303946, tenantId=1146029695717560320, journalId=1251234736404742242, articleId=1253997370597896752, language=EN, label=null, caption=null, figureFileSmall=null, figureFileBig=null, tableContent=
参数参数值
脉宽/μs100
带宽/MHz5
载频/GHz2.8
脉冲重复间隔（PRI）/μs1000
采样率/MHz10
), ArticleFig(id=1253999621609550155, tenantId=1146029695717560320, journalId=1251234736404742242, articleId=1253997370597896752, language=CN, label=表5, caption=

外辐射源信号参数

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参数参数值
脉宽/μs100
带宽/MHz5
载频/GHz2.8
脉冲重复间隔（PRI）/μs1000
采样率/MHz10
), ArticleFig(id=1253999621710213452, tenantId=1146029695717560320, journalId=1251234736404742242, articleId=1253997370597896752, language=EN, label=null, caption=null, figureFileSmall=null, figureFileBig=null, tableContent=
数据类型计算时间
改进前改进后
仿真数据12.7353.365
实测数据29.5787.391
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ECA改进前后计算速度对比

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数据类型计算时间
改进前改进后
仿真数据12.7353.365
实测数据29.5787.391
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非合作双基地雷达ECA-CMAP杂波抑制方法
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梁师源 , 潘嘉蒙 , 鲍庆龙 , 肖怀铁
雷达科学与技术 | 2025,23(5): 540-550
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雷达科学与技术 | 2025, 23(5): 540-550
非合作双基地雷达ECA-CMAP杂波抑制方法
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梁师源, 潘嘉蒙, 鲍庆龙, 肖怀铁
作者信息
  • 国防科技大学电子科学学院，湖南长沙 410073

    • 梁师源 男，硕士研究生，主要研究方向为自动目标识别。

    潘嘉蒙 男，博士，讲师，主要研究方向为雷达信号处理。

    鲍庆龙 男，博士，副教授，主要研究方向为雷达信号处理。

    肖怀铁 男，博士，教授，主要研究方向为自动目标识别。

ECA-CMAP Clutter Suppression Method for Passive Bistatic Radar
Shiyuan LIANG, Jiameng PAN, Qinglong BAO, Huaitie XIAO
Affiliations
  • College of Electronic Science and Technology, National University of Defense Technology, Changsha 410073, China
doi: 10.3969/j.issn.1672-2337.2025.05.008
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摘要
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非合作双基地雷达收发分置的布局模式很大程度上规避了电磁干扰，然而其在工作中面临大量的近程地杂波干扰，目标淹没在大量杂波中难以检测，尤其对于以脉冲雷达为外辐射源的非合作双基地雷达而言，杂波的处理更加困难。本文面向以脉冲雷达为外辐射源的非合作双基地雷达，针对其实际工作中面临大量近程地杂波掩盖目标的问题，提出了时域单脉冲ECA-CMAP杂波抑制方法。首先在经典的时域杂波抑制方法ECA的基础上提出了基于杂波时延估计的改进方案，在抑制近程地杂波的同时将目标完整地保留下来，且将信杂比提升约50dB；其次，提升目标信杂比后结合使用Nitzberg杂波图算法进一步提高目标检测概率。仿真和实测数据处理验证了算法的有效性。

非合作双基地雷达  /  运动目标检测  /  地杂波抑制  /  时域扩展相消  /  杂波图  /  单脉冲处理

Passive bistatic radar (PBR) avoids electromagnetic interference to a great extent because of the layout mode of transmitting and receiving separately. However, it faces a lot of short-range ground clutter interference in its work, and it is difficult to detect the target when it is submerged in a lot of clutter, especially for PBR with pulse radar as its external radiation source, the clutter processing is more difficult. In this paper, a time-domain monopulse extensive cancellation algorithm-clutter map (ECA-CMAP) clutter suppression method is proposed for PBR with pulse radar as external radiation source, aiming at the problem that it faces a large number of short-range ground clutter to cover up the target in practical work. Firstly, based on the classical time domain clutter suppression method ECA (extensive cancellation algorithm), an improved scheme based on clutter time delay estimation is proposed, which can suppress short-range ground clutter and keep the target intact, and the signal-to-clutter ratio is increased by nearly 50dB, and the target detection probability is further improved by using Nitzberg clutter map algorithm. Simulation and result of measured data processing verify the effectiveness of the algorithm.

passive bistatic radar  /  moving target detection  /  ground clutter suppression  /  time domain extensive cancellation  /  clutter map  /  monopulse processing
梁师源, 潘嘉蒙, 鲍庆龙, 肖怀铁. 非合作双基地雷达ECA-CMAP杂波抑制方法. 雷达科学与技术, 2025 , 23 (5) : 540 -550 . DOI: 10.3969/j.issn.1672-2337.2025.05.008
Shiyuan LIANG, Jiameng PAN, Qinglong BAO, Huaitie XIAO. ECA-CMAP Clutter Suppression Method for Passive Bistatic Radar[J]. Radar Science and Technology, 2025 , 23 (5) : 540 -550 . DOI: 10.3969/j.issn.1672-2337.2025.05.008
正文
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0　引言
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现代战争中雷达面临越来越多的新型干扰，非合作双基地雷达（PBR）只收不发的工作模式使其拥有良好的抗干扰性能，在实现隐蔽探测的同时，成本低、部署灵活且战场生存能力强，逐渐成为近年来雷达领域的研究热点[1]。非合作辐射源主要包括数字调频广播[2]、移动通信信号[3]和GNSS[4]等，近年来逐渐涌现以脉冲雷达为外辐射源的非合作双基地探测系统，相比于其他的连续波外辐射源，脉冲雷达发射功率大且方向增益高，系统可探测范围更广。然而在实际工作中，由于非合作辐射源波束扫描灵活，且与接收机距离较远，接收机得到的信号中存在大量的地杂波，而且这些杂波的能量通常较强，导致近程目标回波淹没在其中难以检测，因此非合作双基地雷达在做目标检测前，通常需要对监视通道进行杂波抑制处理[5]。杂波抑制通常包含两大阶段：1）信号处理阶段：空域上根据杂波干扰的不同方向进行抑制，时域上利用参考通道对监视通道滤波从而对消杂波，频域上采取距离多普勒处理实现目标与杂波的分离；2）数据处理阶段，通常采用恒虚警率检测的方法甄别目标和剩余杂波[6]。然而，以脉冲雷达为外辐射源的非合作双基地雷达杂波抑制仍存在很多难题：1）近程目标与杂波通常同时出现在主瓣，空域的旁瓣对消等方法无法处理主瓣杂波；2）时域处理通常使用一些滤波器来滤除杂波，但滤波器可能导致回波相位等关键信息的缺失或紊乱；3）脉冲信号可利用的数据长度很短，相参积累等频域处理往往效果不佳；4）能量微弱的目标淹没在大量强能量的杂波之中，只靠恒虚警率检测方法根本无法分辨强杂波和弱目标。尽管如此，仍可以从这些难题中找到突破口：地杂波虽然有高楼、山体等诸多种类，但其位置却是固定的，因此杂波环境是相对平稳的，杂波的到达时延固定。因此可以根据地杂波的这一特性进一步研究时域杂波抑制方法。
时域杂波抑制的典型方法有最小均方误差（Least Mean Square，LMS）、归一化最小均方误差（Normalized Least Mean Square，NLMS）、递归最小二乘法（Recursive Least Square，RLS）等[7]，这类算法统称为自适应维纳滤波类算法，需要设计合适阶数的滤波器，运算量通常较大且在实际使用中有可能丢失相位信息。另一类算法是扩展相消算法（Extensive Cancellation Algorithm，ECA），最初由Colone等人[8]提出，该方法基于最小二乘算法，将回波投影至杂波子空间的正交空间中，从而实现杂波对消。为了提高算法的性能，该团队及其他研究人员在ECA的基础上又相继提出ECA-B （ECA-Batches）[8]、ECA-S（ECA-Sliding）[9]等快速算法，杂波消除效果良好。但由于ECA的提出主要针对连续波外辐射源，而脉冲信号可利用数据长度相比连续波非常短，尤其是当近程微弱目标混叠在大量强杂波之中时，扩展相消所使用的多普勒滤波器将失去作用，从而导致目标被一同抑制。通过改进ECA的扩展杂波子空间可以较好地解决上述问题，但杂波消除之后的杂波旁瓣和一些剩余杂波幅度依然高于目标，因此可以考虑结合杂波图算法提高目标的检测概率。
杂波图（Clutter Map）能够记录雷达检测环境中的杂波分布和强度，属于恒虚警率（CFAR）检测的一种，常用于实际工程中。杂波图分为静态杂波图和动态杂波图，静态杂波图在建立之后便不再更新，存储的是检测环境中固定的杂波强度与所处方位。而动态杂波图随着雷达波束扫描进行更新，在杂波稳定的检测环境之中，可以辅助动目标检测。Nitzberg杂波图检测技术是较为经典的杂波图算法[10]，它的原理是通过雷达每次扫描后的采样值不断更新判决门限，当有目标出现时则会超过门限从而完成检测。但由于强杂波会将判决门限抬得很高，在实际应用中单纯地使用杂波图算法仍不能检测到目标。
综上所述，本文提出了时域单脉冲ECACMAP（ECA-Clutter MAP）杂波抑制算法，首先针对ECA的扩展杂波子空间提出了基于杂波时延估计的改进子空间，在时域抑制大部分近程地杂波的同时，有效保留混叠在其中的目标分量；其次再结合Nitzberg杂波图检测算法辨别剩余杂波和感兴趣目标，提高目标检测概率。
1　信号处理模型
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1.1　信号接收模型
非合作双基地雷达在工作时，接收机分别设置参考通道和监视通道，参考通道波束对准外辐射源方向，直接接收辐射源发射的信号，其信号模型可以表示为
式中sd（t）为辐射源的直射信号，n（t）为噪声。而监视通道波束对准动目标所在空域，接收目标反射的回波，由于外辐射源的非合作形式，且距离较远，监视通道除了接收到动目标回波之外，还会接收到外辐射源的直射信号及大量的多径杂波[11]，其回波模型可以表示为
式中，sc（t）和st（t）分别是多径杂波信号和动目标回波信号，M、N分别是杂波和目标的数目，τm和τn分别为杂波和目标的时延，Ac，m和At，n为杂波和目标的复幅度。其中直达波、地杂波的能量通常强于目标回波，杂波的脉压旁瓣也会将回波的底噪抬高，影响目标的检测性能[12]。
1.2　扩展相消算法
时域扩展相消算法的核心思想是：利用参考通道信号构造时域扩展杂波子空间，利用最小二乘准则将回波信号投影至杂波子空间的正交空间之中，所得结果即为对消杂波后的信号。
假设监视通道采样信号ssurv表示为
若想对消掉R个距离单元内的地杂波，则需要对参考通道采样N+R-1个点：
式中sr(n)=0(n≤ 0）。
根据参考信号sref构建（N+R-1）×R维的时域扩展杂波子空间Sref：
式中，D是采样延迟矩阵，由0、1组成，定义如下：
考虑地杂波的相位漂移以及子空间冗余等问题，最终的杂波子空间X由下式获得：
式中，B是入射矩阵，确保算法作用于Sref的最后N行数据，如式（8）所示；Λp为第p个多普勒单元所对应的相位漂移对角矩阵，如式（9）所示。
因此最终构建的杂波子空间X为2(p+1）×R维的列向量矩阵，其中的每一个列向量代表一个子空间元素。对消杂波后的信号为
式中α是监视通道采样信号ssurv在杂波子空间X上的投影系向量。
1.3　Nitzberg杂波图算法
Nitzberg杂波图检测技术利用地杂波的时域相对平稳性[13]，在每一个杂波检测单元处利用一阶递归滤波器对杂波背景强度估计值进行迭代更新，即获得每个杂波检测单元独立的检测门限供后续目标检测，因此Nitzberg杂波图检测技术也称为杂波图点技术，其原理框图如图1所示。
图1中qn是杂波图输入：
式中，D，A分别是一个杂波检测单元内的距离单元与方位单元的个数，(a，d）为距离-方位单元的坐标，分别代表方位与距离。pn是杂波背景强度估计，遵循以下的更新准则：
pn（k）是第k个杂波检测单元、第n次扫描后的杂波背景强度估计值，w是遗忘因子，取值区间为（0，1）。
假设热噪声、杂波和目标的总和服从瑞利分布[14]，且雷达每一次扫描获得的回波数据独立同分布，目标的起伏模型符合SwerlingⅠ型。则每次扫描后的杂波图输入q的概率密度函数为
式中，μ为噪声与杂波的总功率强度，λ为目标相对于多径杂波的平均信杂比（SCR），H0表示假设当前检测单元中未检测到目标，H1则为假设检测单元中存在目标，自适应判决准则为
式中T为门限因子[15]。当检测结果为H1时表示检测到目标，此时不更新杂波图数据，否则根据式（12）更新检测门限，作为下一次扫描的判决标准。
经过推导，检测概率Pd和虚警概率Pf的表达式分别为
由式（16）可以看出，Pf不受杂波功率变化的影响，那么通过设定Pf的值便可以计算出门限因子T，再将T的值代入式（15）中就可得到检测概率Pd。将虚警概率Pf设为10-6，针对不同遗忘因子，图2示出了检测概率随信杂比变化的曲线关系图，从图中可以看出，随着遗忘因子的增大，要想获得相同的检测概率必须提高信杂比，即随着遗忘因子的增大，CFAR损失越大。
1.4　ECA-CMAP算法
如公式（5）所示，在时域处理中使用ECA算法抑制杂波时，其杂波子空间是由直达波信号在距离范围R内的依次时延信号构成的，由于单脉冲的多普勒分辨率不足，投影至该杂波子空间的所有信号分量都将被抑制。为了解决这一场景问题，本文根据ECA算法的杂波子空间构建原理，对式（5）提出如下改进：
式中，R1、R2…分别是Nc个杂波所处的距离单元，而-1和+1距离单元的设置是为了进一步抑制杂波的峰值旁瓣。杂波所处的距离单元由匹配滤波器输出的最大信噪比信号的峰值点估计所得，匹配滤波器采用如下的信号互相关执行：
式中，m代表匹配滤波后的信号采样点，n代表回波采样点。
式（17）中的杂波子空间针对的是参考通道直达波纯净的情况。但非合作双基地雷达在实际工作时，参考通道接收到的直达波通常伴随着多径干扰，难以精准提取直达波用以匹配滤波。考虑到目标混叠在大量到达时间相近的杂波之间，为了避免到达时延与杂波非常接近的目标被抑制，采用下式的杂波子空间进行对消：
由式（17）和式（19）可知，改进后的时域扩展杂波子空间摒弃了许多冗余的采样延迟信号，并且原来的（N+R-1）×R维矩阵变为（N+R-1）×Nc、（N+R-1）×3Nc维矩阵，最终的杂波子空间X由（2p+1）×R维列向量降低至（2p+1）×Nc、（2p+1）×3Nc维，矩阵计算的复杂度大幅降低，其中Nc≪R。这种对于杂波子空间的优化，能够较准确地消除强地杂波，同时最大程度保留混叠在其中的运动目标。
ECA-CMAP算法的总体执行步骤如图3所示，首先利用参考通道的直达波信号与回波通道信号进行匹配滤波，通过脉压信号的峰值点判断所有杂波分量所处的距离单元，从而估计杂波的到达时延，构建时延估计杂波子空间；其次，根据ECA的执行步骤抑制杂波；最后对杂波抑制后的信号使用Nitzberg杂波图算法进行门限检测，得到最终的目标检测结果。
2　仿真实验
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本文考虑到非合作雷达实际工作环境的非理想性，在2.1节和2.2节分别仿真分析了参考通道直达波无多径干扰、参考通道直达波存在多径干扰两种情况，以验证所提算法在理想状态和非理想状态下的有效性。
2.1　参考通道无多径
根据实际脉冲体制雷达的工作参数以及实际的工作环境，分别模拟了非合作辐射源信号、接收端参考通道和监视通道接收信号，其中参考通道包含直达波和噪声，监视通道包含直达波、多径杂波、目标回波和噪声，噪声均为高斯白噪声，辐射源仿真信号采用恒模线性调频信号，具体参数如表1所示，杂波和目标仿真参数如表2所示，目标速度为50m/s，处于第68距离单元，其中一个距离单元的长度为30m。非均匀环境下的地杂波的幅度分布通常用韦布尔分布[16]描述，因此表2中的杂波幅度均由韦布尔随机数生成器生成。
在杂波图算法处理中，雷达前5次扫描是对杂波背景幅度的估计与更新，从第6次扫描开始目标持续出现，杂波图算法的参数设置如表3所示。
匹配滤波是输出信噪比最大的最优滤波器，但若对回波信号直接进行匹配滤波，也很难在大片杂波中识别目标，不仅是因为目标信噪比远远低于杂波，而且杂波旁瓣会使得信号噪声基底抬高从而进一步遮掩目标，如图4所示。此时信杂比过小，直接使用杂波图算法也无法检测出目标。
使用ECA算法对消杂波可以取得较好的效果，但单脉冲处理时多普勒分辨率不足，因此混叠在大片杂波中的目标也会被一同抑制，如图5（a）所示。而本文提出的基于杂波时延估计的ECA在对消杂波的同时可以很好地保留目标，而且仿真计算时间由原先的12.735s提升至3.365s。如图5（b）所示，改进后的算法将目标信杂比提升了约50dB，此时应用杂波图算法可以有效检测到目标[17]。如图6所示，分别为雷达第1次、第6次和第50次扫描时的杂波图结果，经过前5次扫描对杂波背景强度的估计和更新，从第6次扫描开始，检测门限逐渐稳定并可以持续检测出目标所出现的距离单元。
目标检测结果如图7所示，可以直观看出从雷达第6次扫描开始持续检测出目标，但由于目标速度相对较低、雷达扫描次数较少，因此目标并没有出现距离单元走动。
2.2　参考通道有多径
考虑到实际非合作双基地雷达参考通道的直达波往往伴随着多径干扰，用于匹配滤波的直达波并不纯净，对此进行非纯净参考信号条件下ECA-CMAP算法的检测效果仿真，对比分析算法的性能。参考通道直达波及其多径、目标的仿真参数如表4所示，其余参数与2.1节一致。
由于参考通道多径信号密集，使用ECA等算法抑制多径极易破坏直达波的相位，因此直接截取直达波作为参考信号，以对回波信号进行匹配滤波，结果如图8所示。
参考信号受到多径影响，导致回波匹配滤波后的峰值、旁瓣以及噪声基底均被抬高，但改进后的ECA仍然可以将目标保留，如图9所示。ECACMAP算法的检测效果如图10所示，当目标在雷达第6次扫描中出现时，便可以立即被检测到，唯一与2.1节不同的是，由于用于匹配滤波的直达波并不纯净，信杂比的改善效果略有下降，且检测结果中存在大量的虚警点，如图11所示，算法要想获得较高检测概率需要目标具备更高的信杂比。
通过上述对比实验可以得出，与Nitzberg杂波图算法相比，ECA-CMAP算法在杂波背景下的目标检测概率有较大的优势。经过1000次蒙特卡洛仿真，ECA-CMAP算法仅需目标信杂比达到-15dB，便可获得较高且较稳定的检测概率。图12展示了在表3参数下，参考通道有/无多径情况下的ECA-CMAP算法、基于非线性映射的Nitzberg杂波图算法[18]以及Nitzberg杂波图算法的检测概率曲线，ECA-CMAP算法在低信杂比的条件下便可获得较高的检测概率。
在参考通道纯净和非纯净两种情况下，通过时延估计的ECA对消杂波后，公式（15）中的信杂比λ相应地提高约50dB，此时再使用杂波图算法目标的检测概率大幅增加，新的检测概率如下所示：
3　实测数据验证
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实测数据采用某非合作双基地雷达目标探测跟踪实验项目的数据，接收端分别设有参考通道和监视通道，参考通道对准外辐射源所在方位，监视通道对准目标所在空域，不区分波束。由第2节的仿真可知，使用参考通道中不纯净的直达波时算法性能有所下降，且实际环境中多径效应影响更大，因此本文使用重构的直达波作为参考信号，其中信号参数均由线性调频参数估计方法[19]得出，经验证与实际辐射源参数基本一致，如表5所示。杂波图算法参数设置与仿真一致，采用50次雷达扫描周期，其中前5次扫描是对杂波背景幅度的估计与更新，从第6次扫描开始进行杂波图检测，其余参数设置如表3所示。
回波信号直接进行匹配滤波的结果如图13所示，其中目标混叠在杂波区之中，目标信噪比约为10dB。图14分别给出了原ECA算法和本文所提基于杂波时延估计的ECA算法抑制杂波的结果，表6是算法在MATLAB软件中计算速度的对比，软件所在电脑平台使用基于x64的Intel Core i7-12700H处理器，机带RAM为32GB，内存为1TB。
在实测数据的处理中，经过杂波对消后，杂波的旁瓣和一些剩余杂波仍然对目标有很大的遮掩影响，匹配滤波结果中无法直接发现目标，但杂波对消后信杂比的提升使得Nitzberg杂波图算法检测目标的概率大大提升。如图15所示，分别是第1次、第6次和第50次扫描的杂波图检测结果。经过前5次的杂波背景估计与更新，从第6次扫描起便可检测到目标。图15（d）中第23.01km处的信号采样值通过检测门限，经验证后与真实目标所在的位置相同。
与2.2节的仿真结果类似，实测数据的检测结果中也存在大量的虚警点，如图16所示，因此实际应用ECA-CMAP算法时、尤其在复杂环境下，仍需要目标具备尽可能高的信噪比。
4　结束语
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非合作双基地雷达在利用第三方脉冲雷达辐射源进行目标探测时，近程目标通常会淹没在大量的强地杂波中无法检测，经典的ECA是针对连续波信号设计的，而对线性调频脉冲信号做单脉冲处理时可利用的数据长度较短，无法获取有效的目标多普勒信息，为此本文在ECA的基础上提出了基于杂波时延估计的改进子空间，能够有针对性地消除强地杂波并且提高了矩阵计算效率。此外，为了处理对消后的剩余杂波，文中再度结合了Nitzberg杂波图检测技术，提出了ECA-CMAP算法。ECA-CMAP算法能够在低信杂比的条件下获得较大的目标检测概率，并且面对参考通道直达波不纯净的情况也有较好的检测性能。
尽管ECA-CMAP算法在仿真和实测数据中均有较好的表现，但在实测数据处理中仍然需要目标具备尽可能高的信杂比，才能保证较高且较稳定的检测概率，后续工作中还须进一步研究复杂杂波环境下的杂波子空间构建准则，实现有效、稳定的检测性能。
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2025年第23卷第5期
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doi: 10.3969/j.issn.1672-2337.2025.05.008
  • 接收时间：2025-01-22
  • 首发时间：2026-04-23
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  • 收稿日期：2025-01-22
  • 修回日期：2025-04-28
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鹅膏菌科Amanitaceae 2 11 5.26 鹅膏菌属 Amanita 10 4.78
小菇科 Mycenaceae 2 12 5.74 丝盖伞属 Inocybe 5 2.39
多孔菌科 Polyporaceae 8 14 6.70 蜡蘑属 Laccaria 5 2.39
红菇科 Russulaceae 3 23 11.00 小皮伞属 Marasmius 6 2.87
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光柄菇属 Pluteus 5 2.39
红菇属 Russula 17 8.13
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