基于混沌理论的MIMO雷达正交波形设计与目标检测技术研究
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摘要
正交波形设计与优化是MIMO（Multi-Input Multi-Output）雷达研究的基础性问题之一，在聚集式MIMO雷达和分散型MIMO雷达研究中均占有十分重要的地位。混沌信号产生简单、易于复制重现、数量多、类随机、遍历、无周期，在正交波形设计中具有天然优势。基于二者契合点，本文深入研究了基于混沌理论的MIMO雷达正交波形设计与优化问题，并将混沌理论推广应用于解决MIMO雷达非均匀分形杂波中目标检测问题。
本文首先阐述了研究背景和意义，介绍了MIMO雷达系统发展与正交波形设计优化技术，回顾了混沌研究的历程，就混沌理论在雷达波形设计中的应用进行了总结，指出混沌理论应用于MIMO雷达的可行性，最后介绍了论文的主要研究工作。
第二章主要研究正交发射波形与MIMO雷达定位、检测性能关系，为MIMO雷达正交波形设计与优化提供依据。建立了MIMO雷达一般信号观测模型，在此基础上分析其匹配滤波处理过程，并进一步推导得到MIMO参数估计的充分统计量。基于此，研究了发射波形互相关与MIMO雷达波束增益、高斯背景下目标检测性能、波达角（DOA）估计性能的关系，结果表明：当发射波形非理想正交时，收发波束宽度不变，但旁瓣水平抬高，在一定相关程度下旁瓣性能接近于发射理想正交波形。目标检测、DOA估计性能亦有类似结论。即无必要一味追求发射波形的正交性，可根据MIMO雷达探测需求和波形参数条件相应选择、设计和优化满足一定相关程度的波形集。
第三章主要分析混沌调制信号性能，基于雷达传统波形要求，从平均模糊函数、相关函数、频谱、距离分辨、速度分辨和信号处理等角度研究论证了信号作为MIMO雷达发射信号的可行性和优势。具体研究了三种信号形式：针对混沌调频信号，基于混沌各态历经理论研究了信号的统计特性，发现调制信号具有各态历经性。并以此进一步从理论上推导信号频谱、模糊函数和准正交性能，得到解析表达式，解释了信号距离旁瓣产生的原因；针对混沌离散频率编码信号，推导得到信号模糊函数，距离和速度分辨的解析表达式，考察了信号的正交性能。采用数值仿真方法，比较了四种混沌离散频率编码信号的性能；针对混沌随机频率步进信号，研究信号回波脉压处理方法，提出一种先匹配存储后脉压处理方法，指出当径向速度为0时，采用IFFT方法进行脉压，而存在径向速度时，需进行相位匹配，采用相关处理进行脉压。
第四章研究MIMO雷达混沌正交波形集设计。以相位编码信号为例，研究指出为获得最佳的正交性能，混沌编码信号在设计中需综合考虑混沌概率分布、编码方案选取、混沌选择与构造等因素，为混沌正交编码信号集设计提供了准则；基于混沌遍历、独立理论，提出一种基于序列抽样的混沌正交信号集设计方法。研究发现，当抽样间隔足够大时，同一混沌系统产生的两混沌序列近似独立和正交，其调制信号正交性能亦相应改善；从信号隐身和更好正交性能角度研究推导了混沌频率调制信号混沌行为保留的充分条件，定义和分析了混沌编码信号的混沌初值敏感度函数，指出不同混沌调制信号正交性能差异产生的原因，为混沌正交信号集的设计提供了指导。
第五章针对信号高距离旁瓣和多普勒敏感问题，主要研究波形优化。分析了正交多相编码信号速度、加速度敏感问题，采用更加灵活的分块编码方法增加信号优化自由度，在克隆选择算法中引入混沌，根据编码多样性测度进行自适应混沌变异操作，提出一种自适应混沌克隆选择算法，并基于此算法进行多目标联合优化问题求解，可同时获得距离旁瓣更低，速度、加速度容忍性更好的编码信号；基于互补编码思想，提出MIMO雷达在发射混沌相位编码之后，补充发射一组具有互补性质的编码信号，通过接收端联合处理，可较大程度降低距离旁瓣。其中，混沌相位编码信号的最佳互补码通过自适应混沌克隆选择算法优化求解得到。为降低信号多普勒敏感性，借鉴感知雷达闭环理念，提出一种多重假设检验自适应多普勒扩容方法。在MIMO雷达接收端进行多普勒滤波处理，通过假设检验测量获得目标多普勒相位估计值后，以闭环方式实时反馈到雷达发射端进行多普勒相位偏移预补偿，有效降低了信号对原多普勒偏移的敏感性。
第六章基于雷达自然背景杂波的分形特征，主要研究分形杂波中MIMO雷达目标检测问题。建立了分形杂波存在情况下MIMO雷达接收信号模型，基于混沌分形理论推导得到MIMO雷达接收信号的分形维均值，在此基础上设计了一种MIMO雷达分形检测器，并分析了其检测性能。结果表明，对于聚集式MIMO雷达，分形检测性能与其虚拟孔径大小无关；而对于分散型MIMO雷达，虚拟孔径越大，检测性能越好。研究为MIMO雷达分形杂波中目标检测提供了技术手段，拓展了MIMO雷达检测理论。
第七章对全文进行总结，并指出下一步可能的研究工作。
本课题的研究，具有理论和工程意义，一方面可以推动新型体制MIMO雷达技术发展，为MIMO雷达工程化应用提供可能的信号集；另一方面，亦可以拓宽和深化非线性科学-混沌分形理论的研究和工程应用。同时，课题对网络雷达（Netted Radar）信号设计、电子对抗、电磁隐身等领域的研究亦具有启发借鉴意义。
Orthogonal waveform design and optimization is a basic research issue for MIMOradar, which takes up quite an important status for colocated and statistic MIMO radaras well. Chaos presentes inherent property in orthogonal signal design for its easygeneration, easy copy, great number, randomicity, ergodicity and aperiodicity.Thus, thisthesis investigates the MIMO radar waveform design and optimization based on chaosand fractal theory which is also extended to MIMO radar target detection inunheterogeneous fractal clutter.
Background and siginificance of this thesis are first expounded, and then someMIMO radar sytem development and waveform design technique are introduced. Thestudy development of chaos is listed, especially its application in radar waveform isreviewed in detail and its feasibility for MIMO radar waveform is pointed out as well,followed with the main content introduction.
In charpter2, the relationship between transmitting unideal orthogonal waveformsand localization and detection performance of MIMO radar is investigated guiding forMIMO radar orthogonal waveform design and optimization. The general measuredsignal model is introduced, the course of matched processing is then presented, and thesufficient statistic for parameters estimation is induced in theory. Relationships betweenunideal orthogonal transmitting waveforms and MIMO radar beamforming, targetdetection in Gaussion noise and DOA estimation are mainly investigated. It can befound out that the sidelobe level is increased though its width is sustained fortransmit-receive beam with the correlation increases, which trend is similar to targetdetection and DOA estimation performance. Therefore, there is no necessary forpursuing fully orthogonal tramsmitting signals, which should be chosen, design andoptimizasion according to requirements of MIMO radar localization and detection.
Based on the analysis in chapter2, performances of chaos based modulated signalsincluding average ambiguity function, correlation, spectrum, range and velocityresolution, and echo waveform signal processing are mainly investigated in chapter3,and their feasibility and superiority are also pointed out. As to the chaos basedfrequence modulated signal, the signal model is introduced, statistic characteristic basedon ergodicity theory is investigated, based on these, its spectrum, average ambiguityfunction, and psudo-orthogonality are induced in theory. As to the chaos based discretefrequency coded signal, its chaotic coding method is presented, then performancesincluding the ambiguity function, the range and velocity resolution, and orthogonalityare investigated. Numerical simulation based on four chaotic maps has validated theanalyzing. As to the chaos based frequency stepped signal, an echo signal processingmethod is proposed, which carries our matched saving before pluse compression. Whenthere is no range velocity, FFT is utilized for pluse compression; otherwise, it takes the correlation processing.
In charpter4, MIMO radar orthogonal waveform design based on chaos theory ismainly inveatigated. Taking the poly phase coded signal as an example, the probabilitydensity, coding method and chaos chosn and construction are synthetically considered,which provides a design guidance for MIMO radar orthogonal waveform design. Basedon the ergodicity and independence theory, a chaos series sampling method is proposedfor orthogonal waveform set design. It is found out that, when the sampling distance islarge enough, two chaotic signals generated from the same chaos system are notcorrelated, which show better modulated orthogonal performance. Further, a sufficientcondition for chaos sustaining for chaotic frequency modulated signals is induced andan inititial condition sensitivity function for chaotic coded signals is defined. Thereasons for varying performance of different chaos are thus analyzed, which can guidefor MIMO radar chaotic orthogonal waveform design.
In charpter5, MIMO radar orthogonal waveform optimization based on chaostheory is mainly inveatigated. Velocity and accelerate velocity intolerance are firstanalyzed for poly phase coded waveforms. An improved clonal seneltion algorithm isproposed by introducing chaos. Based on this algorithm combining more flexiblecoding to increase signal design freedom, a combined optimization method is thusproposed and waveforms with lower sidelobe level, more velocity and acceleratevelocity intolerance are obtained. Based on the complementary coding idea, a chaosbased complementary codes are transmitted for MIMO radar after transmitting itcorresponding chaos codes and much lower sidelobe level is obtained shown bynumerical simulations. Further, a multiple hypothesis testing at MIMO radartransmitters is proposed for Doppler tolerance increasing,which carrys out Dopplerfiltering and gets a Doppler estimation firstly, and then is is feeded back to MIMO radartransmitters in a closed loop for Doppler precompensation. Numerical simulations showgreatly improvements have been obtained.
Fractal geometry has been used as an effective tool to improve target detectionperformance in radar system, since most non-homogeneous clutter generated by naturalsurface is demonstrated to be fractal by recent researches. In charpter6, we mainlyconsider MIMO radar target detection in fractal clutter. Target and clutter model isproposed for high resolution MIMO radar. Based on this model, a fractal dimensionestimation method is discussed, which is further investigated and deduced inmulti-channel systems with antennas being placed colocated and distributed,respectively. Fractal detectors for both colocated and statistical MIMO radars are thendesigned based on the statistic theory. The likelihood ratio threshold, false alarmprobability and detection probability are deduced according to the Neyman-Pearson (NP)Criteria, and the relationship between detection performances and the transmit-receivechannel number is analyzed as well. Additionally, we show that the fractal detector presents great capabilities in rejection of non-homogeneous clutter for MIMO radarsystem.
In charpter7, the summarization and the probable future work of this dissertationare discussed.
What need to be pointed out for supplement is that the study of this dissertation isof both theoretical and engineering sense. On one hand, it can promote the developmentof the new radar system-MIMO radar and provide waveform set for engineeringapplication. On the other hand, it can deepen and widen the non-linear science-chaosand fractal research in theory and engineering. Additionally, the research results canilluminate orthogonal waveform design of netted radars, electronic warfare, andelectromagnetism concealment. The obtained orthogonal waveform set can evendirectly be used in netted radar system.
本文首先阐述了研究背景和意义，介绍了MIMO雷达系统发展与正交波形设计优化技术，回顾了混沌研究的历程，就混沌理论在雷达波形设计中的应用进行了总结，指出混沌理论应用于MIMO雷达的可行性，最后介绍了论文的主要研究工作。
第二章主要研究正交发射波形与MIMO雷达定位、检测性能关系，为MIMO雷达正交波形设计与优化提供依据。建立了MIMO雷达一般信号观测模型，在此基础上分析其匹配滤波处理过程，并进一步推导得到MIMO参数估计的充分统计量。基于此，研究了发射波形互相关与MIMO雷达波束增益、高斯背景下目标检测性能、波达角（DOA）估计性能的关系，结果表明：当发射波形非理想正交时，收发波束宽度不变，但旁瓣水平抬高，在一定相关程度下旁瓣性能接近于发射理想正交波形。目标检测、DOA估计性能亦有类似结论。即无必要一味追求发射波形的正交性，可根据MIMO雷达探测需求和波形参数条件相应选择、设计和优化满足一定相关程度的波形集。
第三章主要分析混沌调制信号性能，基于雷达传统波形要求，从平均模糊函数、相关函数、频谱、距离分辨、速度分辨和信号处理等角度研究论证了信号作为MIMO雷达发射信号的可行性和优势。具体研究了三种信号形式：针对混沌调频信号，基于混沌各态历经理论研究了信号的统计特性，发现调制信号具有各态历经性。并以此进一步从理论上推导信号频谱、模糊函数和准正交性能，得到解析表达式，解释了信号距离旁瓣产生的原因；针对混沌离散频率编码信号，推导得到信号模糊函数，距离和速度分辨的解析表达式，考察了信号的正交性能。采用数值仿真方法，比较了四种混沌离散频率编码信号的性能；针对混沌随机频率步进信号，研究信号回波脉压处理方法，提出一种先匹配存储后脉压处理方法，指出当径向速度为0时，采用IFFT方法进行脉压，而存在径向速度时，需进行相位匹配，采用相关处理进行脉压。
第四章研究MIMO雷达混沌正交波形集设计。以相位编码信号为例，研究指出为获得最佳的正交性能，混沌编码信号在设计中需综合考虑混沌概率分布、编码方案选取、混沌选择与构造等因素，为混沌正交编码信号集设计提供了准则；基于混沌遍历、独立理论，提出一种基于序列抽样的混沌正交信号集设计方法。研究发现，当抽样间隔足够大时，同一混沌系统产生的两混沌序列近似独立和正交，其调制信号正交性能亦相应改善；从信号隐身和更好正交性能角度研究推导了混沌频率调制信号混沌行为保留的充分条件，定义和分析了混沌编码信号的混沌初值敏感度函数，指出不同混沌调制信号正交性能差异产生的原因，为混沌正交信号集的设计提供了指导。
第五章针对信号高距离旁瓣和多普勒敏感问题，主要研究波形优化。分析了正交多相编码信号速度、加速度敏感问题，采用更加灵活的分块编码方法增加信号优化自由度，在克隆选择算法中引入混沌，根据编码多样性测度进行自适应混沌变异操作，提出一种自适应混沌克隆选择算法，并基于此算法进行多目标联合优化问题求解，可同时获得距离旁瓣更低，速度、加速度容忍性更好的编码信号；基于互补编码思想，提出MIMO雷达在发射混沌相位编码之后，补充发射一组具有互补性质的编码信号，通过接收端联合处理，可较大程度降低距离旁瓣。其中，混沌相位编码信号的最佳互补码通过自适应混沌克隆选择算法优化求解得到。为降低信号多普勒敏感性，借鉴感知雷达闭环理念，提出一种多重假设检验自适应多普勒扩容方法。在MIMO雷达接收端进行多普勒滤波处理，通过假设检验测量获得目标多普勒相位估计值后，以闭环方式实时反馈到雷达发射端进行多普勒相位偏移预补偿，有效降低了信号对原多普勒偏移的敏感性。
第六章基于雷达自然背景杂波的分形特征，主要研究分形杂波中MIMO雷达目标检测问题。建立了分形杂波存在情况下MIMO雷达接收信号模型，基于混沌分形理论推导得到MIMO雷达接收信号的分形维均值，在此基础上设计了一种MIMO雷达分形检测器，并分析了其检测性能。结果表明，对于聚集式MIMO雷达，分形检测性能与其虚拟孔径大小无关；而对于分散型MIMO雷达，虚拟孔径越大，检测性能越好。研究为MIMO雷达分形杂波中目标检测提供了技术手段，拓展了MIMO雷达检测理论。
第七章对全文进行总结，并指出下一步可能的研究工作。
本课题的研究，具有理论和工程意义，一方面可以推动新型体制MIMO雷达技术发展，为MIMO雷达工程化应用提供可能的信号集；另一方面，亦可以拓宽和深化非线性科学-混沌分形理论的研究和工程应用。同时，课题对网络雷达（Netted Radar）信号设计、电子对抗、电磁隐身等领域的研究亦具有启发借鉴意义。
Orthogonal waveform design and optimization is a basic research issue for MIMOradar, which takes up quite an important status for colocated and statistic MIMO radaras well. Chaos presentes inherent property in orthogonal signal design for its easygeneration, easy copy, great number, randomicity, ergodicity and aperiodicity.Thus, thisthesis investigates the MIMO radar waveform design and optimization based on chaosand fractal theory which is also extended to MIMO radar target detection inunheterogeneous fractal clutter.
Background and siginificance of this thesis are first expounded, and then someMIMO radar sytem development and waveform design technique are introduced. Thestudy development of chaos is listed, especially its application in radar waveform isreviewed in detail and its feasibility for MIMO radar waveform is pointed out as well,followed with the main content introduction.
In charpter2, the relationship between transmitting unideal orthogonal waveformsand localization and detection performance of MIMO radar is investigated guiding forMIMO radar orthogonal waveform design and optimization. The general measuredsignal model is introduced, the course of matched processing is then presented, and thesufficient statistic for parameters estimation is induced in theory. Relationships betweenunideal orthogonal transmitting waveforms and MIMO radar beamforming, targetdetection in Gaussion noise and DOA estimation are mainly investigated. It can befound out that the sidelobe level is increased though its width is sustained fortransmit-receive beam with the correlation increases, which trend is similar to targetdetection and DOA estimation performance. Therefore, there is no necessary forpursuing fully orthogonal tramsmitting signals, which should be chosen, design andoptimizasion according to requirements of MIMO radar localization and detection.
Based on the analysis in chapter2, performances of chaos based modulated signalsincluding average ambiguity function, correlation, spectrum, range and velocityresolution, and echo waveform signal processing are mainly investigated in chapter3,and their feasibility and superiority are also pointed out. As to the chaos basedfrequence modulated signal, the signal model is introduced, statistic characteristic basedon ergodicity theory is investigated, based on these, its spectrum, average ambiguityfunction, and psudo-orthogonality are induced in theory. As to the chaos based discretefrequency coded signal, its chaotic coding method is presented, then performancesincluding the ambiguity function, the range and velocity resolution, and orthogonalityare investigated. Numerical simulation based on four chaotic maps has validated theanalyzing. As to the chaos based frequency stepped signal, an echo signal processingmethod is proposed, which carries our matched saving before pluse compression. Whenthere is no range velocity, FFT is utilized for pluse compression; otherwise, it takes the correlation processing.
In charpter4, MIMO radar orthogonal waveform design based on chaos theory ismainly inveatigated. Taking the poly phase coded signal as an example, the probabilitydensity, coding method and chaos chosn and construction are synthetically considered,which provides a design guidance for MIMO radar orthogonal waveform design. Basedon the ergodicity and independence theory, a chaos series sampling method is proposedfor orthogonal waveform set design. It is found out that, when the sampling distance islarge enough, two chaotic signals generated from the same chaos system are notcorrelated, which show better modulated orthogonal performance. Further, a sufficientcondition for chaos sustaining for chaotic frequency modulated signals is induced andan inititial condition sensitivity function for chaotic coded signals is defined. Thereasons for varying performance of different chaos are thus analyzed, which can guidefor MIMO radar chaotic orthogonal waveform design.
In charpter5, MIMO radar orthogonal waveform optimization based on chaostheory is mainly inveatigated. Velocity and accelerate velocity intolerance are firstanalyzed for poly phase coded waveforms. An improved clonal seneltion algorithm isproposed by introducing chaos. Based on this algorithm combining more flexiblecoding to increase signal design freedom, a combined optimization method is thusproposed and waveforms with lower sidelobe level, more velocity and acceleratevelocity intolerance are obtained. Based on the complementary coding idea, a chaosbased complementary codes are transmitted for MIMO radar after transmitting itcorresponding chaos codes and much lower sidelobe level is obtained shown bynumerical simulations. Further, a multiple hypothesis testing at MIMO radartransmitters is proposed for Doppler tolerance increasing,which carrys out Dopplerfiltering and gets a Doppler estimation firstly, and then is is feeded back to MIMO radartransmitters in a closed loop for Doppler precompensation. Numerical simulations showgreatly improvements have been obtained.
Fractal geometry has been used as an effective tool to improve target detectionperformance in radar system, since most non-homogeneous clutter generated by naturalsurface is demonstrated to be fractal by recent researches. In charpter6, we mainlyconsider MIMO radar target detection in fractal clutter. Target and clutter model isproposed for high resolution MIMO radar. Based on this model, a fractal dimensionestimation method is discussed, which is further investigated and deduced inmulti-channel systems with antennas being placed colocated and distributed,respectively. Fractal detectors for both colocated and statistical MIMO radars are thendesigned based on the statistic theory. The likelihood ratio threshold, false alarmprobability and detection probability are deduced according to the Neyman-Pearson (NP)Criteria, and the relationship between detection performances and the transmit-receivechannel number is analyzed as well. Additionally, we show that the fractal detector presents great capabilities in rejection of non-homogeneous clutter for MIMO radarsystem.
In charpter7, the summarization and the probable future work of this dissertationare discussed.
What need to be pointed out for supplement is that the study of this dissertation isof both theoretical and engineering sense. On one hand, it can promote the developmentof the new radar system-MIMO radar and provide waveform set for engineeringapplication. On the other hand, it can deepen and widen the non-linear science-chaosand fractal research in theory and engineering. Additionally, the research results canilluminate orthogonal waveform design of netted radars, electronic warfare, andelectromagnetism concealment. The obtained orthogonal waveform set can evendirectly be used in netted radar system.
引文
[1]张明友.雷达系统[M].北京:电子工业出版社,第2版,2006.
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