面向任务的MIMO雷达波形设计方法研究
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摘要
随着雷达理论特别是信号处理算法和技术的日趋完善，通过改进接收端信号处理算法来提升雷达性能变得越来越困难，而通过雷达发射端特别是发射波形的设计和优化来提升雷达探测性能得到越来越多的重视。雷达根据环境变化自适应地调整自身发射波形，不仅可改善雷达检测、跟踪等方面的性能，同时使敌方的电子侦察及干扰更加困难。多输入多输出（Multiple-Input Multiple-Output，MIMO）雷达现已成为雷达技术领域的一个研究热点，它的发射天线和接收天线根据系统要求可以进行灵活布置并且每个辐射单元可以发射不同的信号波形，从而在抗截获、检测小雷达截面积（Radar Cross Section, RCS）目标、抑制杂波和提高目标参数估计精度等方面带来更好的性能。波形设计和优化是实现MIMO雷达波形分集优点的重要手段。目前，虽然很多学者对MIMO雷达波形设计方法进行了深入细致的研究，也取得了一些突破和成果，然而针对不同应用场合情况，以提高MIMO雷达探测性能为目的的波形设计与优化方法仍然有很多问题没有得到完全解决。
本文在前人工作的基础上，结合承担的科研项目，研究了针对不同应用场合下基于单站MIMO雷达的波形设计与优化方法，包括正交编码波形设计，方向图及其时域信号合成，面向检测与跟踪的MIMO雷达自适应波形设计等方面。具体工作概括如下：
首先，研究了雷达波形设计的基本方法。研究了论文中涉及到的几种信号形式的模糊函数，分析了它们的距离和多普勒分辨性能，并研究了频率分集MIMO雷达的空时频模糊函数。分析了在最大信杂噪比准则下频域波形与检测性能之间的关系；给出了在总能量约束下最优波形的能量谱密度；在此基础上，提出了在已知频域最优波形的情况下，一种时域调频信号的快速设计方法。
针对MIMO雷达正交波形设计与相关信号处理问题，提出了一种MIMO雷达正交多相码快速设计方法及相应的自适应脉压滤波方法。针对MIMO雷达正交码设计中信号自相关旁瓣和互相关最小化的多目标优化问题，采用一种基于分解的多目标进化算法进行解决。该方法将多目标问题转化为多个子问题并行求解，每个子问题的优化通过与近邻子问题之间的进化操作来完成，弥补了遗传算法计算量大、收敛速度慢、多样性不足等缺点。在接收处理端，考虑到由于设计出的波形无法做到完全正交，导致脉压后的回波中除了自相关旁瓣之外，MIMO雷达不同通道之间的回波还存在互相关干扰。针对以上问题，以最大化系统输出信号与干扰噪声比为准则，提出了一种基于迭代思想的MIMO雷达自适应脉冲压缩方法，该方法利用对目标不同距离单元回波信息进行多次估计，进而自适应地对距离旁瓣和互相关干扰进行抑制，在一定程度上弥补了发射波形不完全正交造成的缺陷。
针对MIMO雷达中发射能量空间分配问题，研究了MIMO雷达的方向图合成以及后续相位编码波形设计方法。在Fuhrmann等人的MIMO雷达方向图合成模型基础上提出了一种基于DFT拟牛顿法的方向图合成方法，这种方法以增加变量数为代价，将功率约束转化为无约束的优化问题；搜索方法上，用当前迭代时刻的负梯度和上时刻的共轭方向的线性组合代替了最陡下降法的固定步长，并且不需计算Hesse逆矩阵。基于合成的方向图，分别研究了两种相位编码波形设计方法：基于概率分配的相位编码波形设计方法与低峰值平均功率比约束下的相位编码设计方法，在讨论相应优化函数的基础上分别研究了其优化方法。
针对面向目标检测的MIMO雷达波形设计问题，提出了一种基于多相编码的MIMO雷达自适应波形设计方法和一种OFDM-MIMO雷达信号的子载波系数优化方法。对于多相编码设计，采用一种交替搜索与检测工作方式对目标一维距离像进行多次估计，以逐步提高目标检测性能。将最大化信杂噪比作为优化目标，并针对杂波的慢时变特性提出了次最优的优化函数，在对目标函数的波形相位域梯度进行推导的基础上提出了一种相位域恒模共轭梯度优化算法。对于频率正交信号，讨论了发射OFDM波形的MIMO雷达信号的数学模型，基于广义似然检测提出了子载波系数优化的目标函数，并通过遗传算法求解最优值，在此基础上讨论了杂波和噪声对OFDM-MIMO雷达检测性能的影响。
针对单站MIMO雷达跟踪下的自适应波形设计问题，分析了面向目标跟踪的自适应波形设计框架，在此基础上提出了一种基于粒子滤波的MIMO雷达自适应波形设计方法。首先基于单载频高斯包络脉冲信号分析了系统的状态模型和量测模型，将参数估计均方误差作为波形设计准则，在每一次滤波结束时计算最优发射波形参数并反馈到发射端，以此来提高目标跟踪精度。对于单站MIMO雷达发射波形为OFDM信号的情况下，考虑到系统可能的非线性和非高斯性，采用粒子滤波作为跟踪滤波方法，以总发射能量为约束条件对OFDM信号的子载波系数进行优化，目的是使每次对目标跟踪PCRB矩阵的迹最小，以此来提高MIMO雷达对目标跟踪的精度。
With the development of radar theory, especially signal processing algorithm andtechnology, enhancing radar performances by updating signal processing algorithm inradar receiver become more and more difficult. The research interest turns to transmitterfor the fact that waveform design and optimization can also enhance radar detectingperformance. Via alternating waveform according to the changing environment, theperformace of detecting, tracking and inference suppression is adaptively optimized andthe effects of electronic scouting and inference from enemy are reduced. Multiple-InputMultiple-Output radar has become a hotspot in radar technology. The transmit andreceive antenna of MIMO radar are configured flexibly according to systemrequirement and each unit transmits different waveform, in this way better performancesof low probility of interception, detecting target with low RCS, clutter suppression andtracking are obtained. Waveform design and optimization is crucial means to utilize theadvantages of waveform diversity of MIMO radar. Although many scholars haveinvestigate into MIMO radar waveform design algorithms and a number ofachievements have been acquired, there are still many problems to be solved, especiallyin the fields of waveform design and optimization for different specific applications.
Based on previous work and combined with my research jobs at present, thisdissertation focuses on the waveform design and optimization algorithms for co-locatedMIMO radar tasks, including orthogonal waveform design, beampattern andtime-domain signal synthesis, adaptive waveform design for detecting and tracking. Themain contents of this dissertation are summarized as follows:
Firstly，basic method for radar waveform design is analyzed. The ambiguityfunctions of the waveforms menthioned in the thesis are introduced to analyse theperformances of their range and Doppler resolutions. The relation betweenfrequency-domain waveform and detection performance is studied in maximumsignal-clutter-and-noise ratio rule. Energy spectrum density of optimum waveform isdeduced under energy constraint, based on that, a quick waveform design method fortime-domain frequency modulation signal is introduced.
Focused on orthogonal waveform design and related signal processing for MIMOradar, a novel method for orthogonal phase-coded waveform design and related adaptivepulse compression filter are introduced. To minimize the auto-correlation sidelobe andcross-correlation, a multi-objective evolutionary algorithm based on decomposition isintroduced. The algorithm decomposes muti-objective optimization problem into a number of scalar optimization subproblems and optimizes them simultaneously. Eachsubproblem is optimized by using information from several neighboring subproblems,so the disadvantages of computational complexity, slow convergence and lack ofdiversity in gene algorithm is reduced. For related signal processing, considering theinterferences from sidelobes and different channels caused by correlation of differentechos, a MIMO radar adaptive pulse compression algorithm based on iterative updatingis introduced, the algorithm utilizes the information from echos of a number of rangebins and then restrains the range sidelobe and cross-correlation interferences, in thisway it compensates the shortage caused by imperfect orthogonal waveforms.
Focused on the spatial distribution of transmitted energy for MIMO radar, amethod for beampattern synthesis and follow-up phase-coded signal design for coherentMIMO radar are studied. Under the beampattern synthesis scheme for MIMO radardeveloped by Fuhrman, a beampattern synthesis method based on DFT newton-likealgorithm is studied which transfoms power restraint problem into a problem withoutrestraints at the cost of increased the number of variables. It substitutes alterablesearching steps for fixed steps of steepest descent method without calculating Hessematrix. Based on the results of baeampattern synthesis, two phase-coded waveformdesign methods are studied: The first is phase-coded waveform based on probabilityoptimization, in which the correlation matrix is denoted with code set and probability,and code is obtained by gambling. The second is phase-coded waveform based on lowpeak average ratio, the related optimization function is introduced and optimized bycyclic optimization algotithm.
Focused on the waveform design of target detection for MIMO radar, a method ofadaptive waveform design for MIMO radar based on phase-coded signal and asub-carrier coefficients optimization method for spatial-diversed OFDM waveform arestudied. For the design of phase-coded waveform, a pattern of alternative searching anddetecting is introduced: Firstly an initial waveform is transmitted to get a primaryestimation of target range profile, then waveform is optimized to increase signal-clutterand noise ratio and a preciser estimation is obtained. This process is repeated to enhancedetection performance. Based on the phase-domain grads of optimization function, aphase-domain conjugated grads optimization algorithm is introduced. For thefrequency-coded waveform, MIMO radar model based on OFDM waveform is studied.The optimization object function of sub-carrier coefficients based on GeneralLikelihood Ratio Test is introduced and solved by gene algotithm. The effect of clutterand noise on the detection performance of OFDM-MIMO radar is shown at the end of this chapter.
Focused on the waveform design of adaptive tracking for colocated MIMO radar, aadaptive waveform design scheme for target tracking is analysed, on which a adaptivewaveform design algotithm for MIMO radar based on particle filtering is studied.Firstly the state model and measure model are analysed based on single-carrier gaussianpulse. Taking the mean square error of parameter estimation as waveform designstandard, the optimum transmitted waveform parameters are calculated and feed back tothe transmitter in the end of each filtering to increase the tracking precision. For thesituation of colocated MIMO radar which transmits OFDM waveform, particle filteringis taken account considering the possible nonlinear and nongaussian characteristic.Under the contraint of transmitted energy, the sub-carrier coefficients of OFDMwaveform are optimized to minimizing the trace of PCRB matrix. In this way thetracking accuracy is improved.
本文在前人工作的基础上，结合承担的科研项目，研究了针对不同应用场合下基于单站MIMO雷达的波形设计与优化方法，包括正交编码波形设计，方向图及其时域信号合成，面向检测与跟踪的MIMO雷达自适应波形设计等方面。具体工作概括如下：
首先，研究了雷达波形设计的基本方法。研究了论文中涉及到的几种信号形式的模糊函数，分析了它们的距离和多普勒分辨性能，并研究了频率分集MIMO雷达的空时频模糊函数。分析了在最大信杂噪比准则下频域波形与检测性能之间的关系；给出了在总能量约束下最优波形的能量谱密度；在此基础上，提出了在已知频域最优波形的情况下，一种时域调频信号的快速设计方法。
针对MIMO雷达正交波形设计与相关信号处理问题，提出了一种MIMO雷达正交多相码快速设计方法及相应的自适应脉压滤波方法。针对MIMO雷达正交码设计中信号自相关旁瓣和互相关最小化的多目标优化问题，采用一种基于分解的多目标进化算法进行解决。该方法将多目标问题转化为多个子问题并行求解，每个子问题的优化通过与近邻子问题之间的进化操作来完成，弥补了遗传算法计算量大、收敛速度慢、多样性不足等缺点。在接收处理端，考虑到由于设计出的波形无法做到完全正交，导致脉压后的回波中除了自相关旁瓣之外，MIMO雷达不同通道之间的回波还存在互相关干扰。针对以上问题，以最大化系统输出信号与干扰噪声比为准则，提出了一种基于迭代思想的MIMO雷达自适应脉冲压缩方法，该方法利用对目标不同距离单元回波信息进行多次估计，进而自适应地对距离旁瓣和互相关干扰进行抑制，在一定程度上弥补了发射波形不完全正交造成的缺陷。
针对MIMO雷达中发射能量空间分配问题，研究了MIMO雷达的方向图合成以及后续相位编码波形设计方法。在Fuhrmann等人的MIMO雷达方向图合成模型基础上提出了一种基于DFT拟牛顿法的方向图合成方法，这种方法以增加变量数为代价，将功率约束转化为无约束的优化问题；搜索方法上，用当前迭代时刻的负梯度和上时刻的共轭方向的线性组合代替了最陡下降法的固定步长，并且不需计算Hesse逆矩阵。基于合成的方向图，分别研究了两种相位编码波形设计方法：基于概率分配的相位编码波形设计方法与低峰值平均功率比约束下的相位编码设计方法，在讨论相应优化函数的基础上分别研究了其优化方法。
针对面向目标检测的MIMO雷达波形设计问题，提出了一种基于多相编码的MIMO雷达自适应波形设计方法和一种OFDM-MIMO雷达信号的子载波系数优化方法。对于多相编码设计，采用一种交替搜索与检测工作方式对目标一维距离像进行多次估计，以逐步提高目标检测性能。将最大化信杂噪比作为优化目标，并针对杂波的慢时变特性提出了次最优的优化函数，在对目标函数的波形相位域梯度进行推导的基础上提出了一种相位域恒模共轭梯度优化算法。对于频率正交信号，讨论了发射OFDM波形的MIMO雷达信号的数学模型，基于广义似然检测提出了子载波系数优化的目标函数，并通过遗传算法求解最优值，在此基础上讨论了杂波和噪声对OFDM-MIMO雷达检测性能的影响。
针对单站MIMO雷达跟踪下的自适应波形设计问题，分析了面向目标跟踪的自适应波形设计框架，在此基础上提出了一种基于粒子滤波的MIMO雷达自适应波形设计方法。首先基于单载频高斯包络脉冲信号分析了系统的状态模型和量测模型，将参数估计均方误差作为波形设计准则，在每一次滤波结束时计算最优发射波形参数并反馈到发射端，以此来提高目标跟踪精度。对于单站MIMO雷达发射波形为OFDM信号的情况下，考虑到系统可能的非线性和非高斯性，采用粒子滤波作为跟踪滤波方法，以总发射能量为约束条件对OFDM信号的子载波系数进行优化，目的是使每次对目标跟踪PCRB矩阵的迹最小，以此来提高MIMO雷达对目标跟踪的精度。
With the development of radar theory, especially signal processing algorithm andtechnology, enhancing radar performances by updating signal processing algorithm inradar receiver become more and more difficult. The research interest turns to transmitterfor the fact that waveform design and optimization can also enhance radar detectingperformance. Via alternating waveform according to the changing environment, theperformace of detecting, tracking and inference suppression is adaptively optimized andthe effects of electronic scouting and inference from enemy are reduced. Multiple-InputMultiple-Output radar has become a hotspot in radar technology. The transmit andreceive antenna of MIMO radar are configured flexibly according to systemrequirement and each unit transmits different waveform, in this way better performancesof low probility of interception, detecting target with low RCS, clutter suppression andtracking are obtained. Waveform design and optimization is crucial means to utilize theadvantages of waveform diversity of MIMO radar. Although many scholars haveinvestigate into MIMO radar waveform design algorithms and a number ofachievements have been acquired, there are still many problems to be solved, especiallyin the fields of waveform design and optimization for different specific applications.
Based on previous work and combined with my research jobs at present, thisdissertation focuses on the waveform design and optimization algorithms for co-locatedMIMO radar tasks, including orthogonal waveform design, beampattern andtime-domain signal synthesis, adaptive waveform design for detecting and tracking. Themain contents of this dissertation are summarized as follows:
Firstly，basic method for radar waveform design is analyzed. The ambiguityfunctions of the waveforms menthioned in the thesis are introduced to analyse theperformances of their range and Doppler resolutions. The relation betweenfrequency-domain waveform and detection performance is studied in maximumsignal-clutter-and-noise ratio rule. Energy spectrum density of optimum waveform isdeduced under energy constraint, based on that, a quick waveform design method fortime-domain frequency modulation signal is introduced.
Focused on orthogonal waveform design and related signal processing for MIMOradar, a novel method for orthogonal phase-coded waveform design and related adaptivepulse compression filter are introduced. To minimize the auto-correlation sidelobe andcross-correlation, a multi-objective evolutionary algorithm based on decomposition isintroduced. The algorithm decomposes muti-objective optimization problem into a number of scalar optimization subproblems and optimizes them simultaneously. Eachsubproblem is optimized by using information from several neighboring subproblems,so the disadvantages of computational complexity, slow convergence and lack ofdiversity in gene algorithm is reduced. For related signal processing, considering theinterferences from sidelobes and different channels caused by correlation of differentechos, a MIMO radar adaptive pulse compression algorithm based on iterative updatingis introduced, the algorithm utilizes the information from echos of a number of rangebins and then restrains the range sidelobe and cross-correlation interferences, in thisway it compensates the shortage caused by imperfect orthogonal waveforms.
Focused on the spatial distribution of transmitted energy for MIMO radar, amethod for beampattern synthesis and follow-up phase-coded signal design for coherentMIMO radar are studied. Under the beampattern synthesis scheme for MIMO radardeveloped by Fuhrman, a beampattern synthesis method based on DFT newton-likealgorithm is studied which transfoms power restraint problem into a problem withoutrestraints at the cost of increased the number of variables. It substitutes alterablesearching steps for fixed steps of steepest descent method without calculating Hessematrix. Based on the results of baeampattern synthesis, two phase-coded waveformdesign methods are studied: The first is phase-coded waveform based on probabilityoptimization, in which the correlation matrix is denoted with code set and probability,and code is obtained by gambling. The second is phase-coded waveform based on lowpeak average ratio, the related optimization function is introduced and optimized bycyclic optimization algotithm.
Focused on the waveform design of target detection for MIMO radar, a method ofadaptive waveform design for MIMO radar based on phase-coded signal and asub-carrier coefficients optimization method for spatial-diversed OFDM waveform arestudied. For the design of phase-coded waveform, a pattern of alternative searching anddetecting is introduced: Firstly an initial waveform is transmitted to get a primaryestimation of target range profile, then waveform is optimized to increase signal-clutterand noise ratio and a preciser estimation is obtained. This process is repeated to enhancedetection performance. Based on the phase-domain grads of optimization function, aphase-domain conjugated grads optimization algorithm is introduced. For thefrequency-coded waveform, MIMO radar model based on OFDM waveform is studied.The optimization object function of sub-carrier coefficients based on GeneralLikelihood Ratio Test is introduced and solved by gene algotithm. The effect of clutterand noise on the detection performance of OFDM-MIMO radar is shown at the end of this chapter.
Focused on the waveform design of adaptive tracking for colocated MIMO radar, aadaptive waveform design scheme for target tracking is analysed, on which a adaptivewaveform design algotithm for MIMO radar based on particle filtering is studied.Firstly the state model and measure model are analysed based on single-carrier gaussianpulse. Taking the mean square error of parameter estimation as waveform designstandard, the optimum transmitted waveform parameters are calculated and feed back tothe transmitter in the end of each filtering to increase the tracking precision. For thesituation of colocated MIMO radar which transmits OFDM waveform, particle filteringis taken account considering the possible nonlinear and nongaussian characteristic.Under the contraint of transmitted energy, the sub-carrier coefficients of OFDMwaveform are optimized to minimizing the trace of PCRB matrix. In this way thetracking accuracy is improved.
引文
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