MIMO雷达参数估计技术研究
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摘要
多输入多输出（MIMO，Multiple-Input Multiple-Output）雷达作为近年来学术界提出的一种新体制雷达，因具有常规雷达所不具备的优势，成为雷达界的研究热点。MIMO雷达可以实现灵活的发射分集设计，使用多个发射天线同时发射相互正交的信号，并使用多个接收天线接收目标反射的信号，在空间形成多个通道。与常规雷达系统相比，MIMO雷达能够增大系统自由度，提高参数估计的精度和空间分辨率，并增加可估计的最大信源数。本论文的研究工作围绕MIMO雷达的参数估计技术展开，主要工作包括以下几个方面：
1.研究了双基地MIMO雷达的相干源角度估计方法。在现有的DOA矩阵法基础上，首先在空间高斯白噪声背景下提出基于降维DOA矩阵的相干源角度估计方法。该方法利用MIMO雷达能够产生多个虚拟子阵的特点，对目标回波进行解相干处理，然后根据DOA矩阵法的思想构造估计矩阵，利用其与信号子空间的关系进行降维处理以获得降维DOA矩阵，有效降低原DOA矩阵法的运算量，并利用降维DOA矩阵的特征参数与待估参数间的特定关系实现相干目标DOD和DOA的联合估计。之后将空间高斯白噪声背景下的降维DOA矩阵方法推广至背景噪声为空间高斯色噪声的情况，利用MIMO雷达发射信号的正交性消除噪声影响，并利用降维DOA矩阵的特征参数与待估参数间的特定关系实现相干目标DOD和DOA的联合估计。所提方法无需二维谱峰搜索和参数配对，且在接收阵列为非等距线阵的条件下仍具有适用性。
2.研究了空间高斯色噪声背景下的双基地MIMO雷达角度和多普勒频率联合估计方法。分析了空间高斯色噪声背景下双基地MIMO雷达的信号模型特点，提出在时域噪声为高斯白噪声的假设下，利用不同时刻匹配滤波器输出的互相关消除空间色噪声的影响。基于此，提出一种基于同时奇异值分解的双基地MIMO雷达角度和多普勒频率联合估计方法。该方法利用相邻时刻匹配滤波器输出的互相关矩阵构造新矩阵，消除空间色噪声的影响。然后通过对所构造矩阵进行奇异值分解获得信号子空间，根据目标回波的时域结构信息，将相邻时刻匹配滤波器输出的时间相位差作为时间旋转因子，采用ESPRIT方法获得目标多普勒频率，DOD和DOA的联合估计。针对同时奇异值分解方法多普勒频率估计模糊范围小的问题，提出一种基于降维DOA矩阵的双基地MIMO雷达参数估计方法。该方法同样利用时域信息构造时间旋转因子并消除空间色噪声的影响，然后结合降维DOA矩阵法获得目标多普勒频率，DOD和DOA的联合估计。两种方法均可以消除空间色噪声影响，并在参数估计时没有阵列孔径损失，且目标多普勒频率，DOD和DOA可以自动配对。同时，所提方法均可扩展至时空域均为色噪声时的双基地MIMO雷达参数估计，并可应用于常规阵列空间色噪声背景下的角度估计中。最后推导了基于时空结构时双基地MIMO雷达角度和多普勒频率估计的克拉美·罗界（CRB,Cramer-Rao Bound）。
3.研究了L型阵列MIMO雷达的DOA矩阵方法。针对常规DOA矩阵方法在二维角度估计时存在角度兼并的问题，首先将L型阵列MIMO雷达所形成的二维虚拟平面阵列划分为两个子阵，并将DOA矩阵法扩展应用于其中，实现了无需参数配对的二维DOA估计。与常规DOA矩阵方法相比，该方法在很大程度上提高了阵元利用率，减少了阵列孔径损失，改善了角度估计性能。由于其仍存在角度兼并问题，进一步提出L型阵列MIMO雷达的联合对角化DOA矩阵方法。该方法通过构造4个虚拟子阵，并对其接收回波的协方差矩阵进行联合对角化处理估计目标二维角度。该方法可减少阵列孔径损失，有效地提高角度估计的精度，增加最大可检测目标个数，同时能够避免角度兼并问题，并保持常规DOA矩阵方法无需二维谱峰搜索和参数配对的优点。
4.研究了米波雷达低仰角波达方向估计方法。针对现有的线性预处理类算法（包括线性预处理方法和差分预处理方法）使预处理后的噪声具有相关性，从而影响低信噪比时角度估计性能的问题，提出基于白化处理的线性预处理算法和基于白化处理的差分预处理算法。该算法通过对预处理后的数据进行白化处理，消除相关噪声的影响，有效提高了原有线性预处理类算法的角度估计性能。针对线性预处理算法运算量太大的问题，进一步提出基于传播算子的快速线性预处理算法。该算法在每个搜索角度利用线性运算代替协方差矩阵的特征分解，大大降低了原有算法的运算量，利于工程实时处理。另外，由于对噪声进行了白化处理，其性能优于原有线性预处理算法，并与基于白化处理的线性预处理算法性能基本一致。
5.研究了米波MIMO雷达的低仰角估计方法。首先根据米波MIMO雷达低仰角目标的回波特点，建立了同时考虑发射多径和接收多径的信号模型。其次，将线性预处理算法推广应用于米波MIMO雷达中，提出基于二次差分预处理的米波MIMO雷达低仰角角度估计算法。该算法通过在米波MIMO雷达回波数据的接收端和发射端分别进行两次差分预处理，消除发射多径信号和接收多径信号的影响，利用白化处理消除差分预处理对噪声结构的影响，并结合传统的MUSIC算法获得目标低仰角估计。该方法能够有效克服多径效应的影响并估计目标角度，并且其处理过程不受反射因子的影响，即与信号所处环境无关，具有较好的稳健性。
As a new radar system, Multiple-Input Multiple-Output (MIMO) radar is becomingpopular in radar field since its unique advantages compared with the phased array radar.MIMO radar transmits multiple orthogonal transmitted waveforms and receivesreflected signals with multiple received arrays, which can form many channels betweentransmitting and receiving array, and can achieve flexible transmitting diversity design.In contrast with the conventional phased array radar, MIMO radar provides a noveltechnique for increasing the degrees of freedom of the radar system and improving theperformance of detection and parameter estimation. This dissertation mainly focuses onthe parameter estimation of MIMO radar. The main content of this dissertation issummarized as follows:
1. The method for angle estimation of coherent sources in bistatic MMO radar isresearched. Firstly, based on the existed DOA matrix method, a method for angleestimation of coherent sources based on dimension reduction DOA matrix in thepresence of spatially white Gauss noise is presented. The virtual array date ofmultitarget echoes in MIMO radar receivers is uncorrelated utilizing the virtualsubarrays formed by MIMO radar, and the DOA matrices are constructed. Thedimension reduction DOA matrices which reduce the computational complex areobtained by the relationship between signal subspace and DOA matrices, and the jointestimation of DOD and DOA can be obtained by the corresponding relationshipsbetween the eigenvalue or eigenvector and the estimated parameters. Secondly, thedimension reduction DOA matrix method in spatially white noise circumstance isextended to the spatially colored noise circumstance. The spatially colored noise iseliminated by using the orthogonality of the transmitted signals of MIMO radar, and thejoint estimation of DOD and DOA can be obtained by using dimension reduction DOAmatrix method. The proposed methods do not need the multi-dimensional peak search,and can estimate the parameters of coherent sources without pairing in both two noisecircumstances. Moreover, it is applicable to receiving arrays without an invariancestructure.
2. The method of joint estimation of angle and Doppler frequency for bistaticMIMO radar in spatial colored noise is researched. According to the characteristic of thesignal model of bistatic MIMO radar, the spatial colored noise can be eliminated byusing the cross-correlation of the match filter outputs in different time delay sampling.Firstly, a method of joint estimation of angle and Doppler frequency for bistatic MIMO radar in spatial colored noise based on simultaneously singular value decomposition isproposed. Utilizing the cross-correlation matrix which is formed by the adjacent outputsof match filters in the time domain, a new matrix is constructed to eliminate theinfluence of spatial colored noise, and the signal subspace is obtained from singularvalue decomposition (SVD) of it. Then angles and Doppler frequencies can beestimated based on ESPRIT using the rotational factor produced by adjacent outputs ofmatch filters. Secondly, a method of joint estimation of angle and Doppler frequency forbistatic MIMO radar in spatial colored noise based on dimension reduction DOA matrixis proposed. This method utilizing the temporal information to construct the temporalrotational factor, and angles and Doppler frequencies is obtained by using dimensionreduction DOA matrix. In the proposed tow methods, the spatial colored noise can beeliminated, and the angles and Doppler frequencies can be obtained simultaneously andautomatically paired without array aperture loss. Besides, the proposed methods can beextended to the circumstance of spatially and temporally colored noise, and can be usedfor angle estimation of conventional array in the presence of colored noise. The CRB ofthe angle and Doppler frequency of bistatic MIMO radar based on spatial-temporalstructure is proposed.
3. The DOA matrix method based on MIMO radar with L-shape arrays isresearched. Firstly, a two-dimension (2-D) angle estimation method for multiple inputmultiple output (MIMO) radar with L-shape arrays based on direction of arrival (DOA)matrix is proposed. This method divides the2-D virtual plane array which is generatedby MIMO radar into two overlapping subarrays, and constructs an estimation matrix toestimate the2-D angles. To solve the problem of angle annexation, a jointdiagonalization DOA matrix method is proposed later. This method generates foursubarrays from the2-D virtual plane array, and uses the joint diagonalization algorithmto estimate the2-D angles. The proposed method secures the advantages of the existingDOA matrix method such as no requirement of2-D angle search and autopairing ofparameters, avoids the angle annexation problem, reduces the loss of the array aperture,and improves the performance of the angle estimation effectively.
4. Low-angle estimation in VHF radar is researched. The effect of the existedlinear preprocessing method to the noise structure is analyzed. Aimed at thedisadvantage that the linear preprocessing method changed the white noise of the realarray data to correlated noise which reduces the performance of angle estimation in lowSNR, an improved linear preprocessing method is proposed. This method greatlyimproved the performance of the low-angle estimation through the whitened processing of the data after linear preprocessing without increasing the computational burdensignificantly. To reduce the computational burden of the linear preprocessing method, afast algorithm of linear preprocessing based on propagator method is proposed. Thisalgorithm replaces the eigendecomposition of the cross-correlation matrix with linearoperation in each searching angle, and greatly reduces the computational burden.Moreover, the performance of the proposed algorithm is much better than theconventional linear preprocessing method, and is identical with the improved linearpreprocessing method due to the whitened processing.
6. Low-angle estimation in VHF MIMO radar is researched. Firstly, the multipathsignal model for MIMO radar is constructed with both transmitted multipath andreceived multipath signals being considered. Secondly, a twice differentialpreprocessing method for low-angle estimation in VHF MIMO radar is proposed. Withtwice differencing preprocessing of the received echoes of the VHF MIMO radar, thetransmitted multipath signals and received multipath signals are eliminated, and theconventional MUSIC algorithm can be used to obtain the estimation of low-angle. Theproposed method can overcome multipath effect and estimate the low-angle of the targeteffectively, and is not sensitive to the signals environments.
1.研究了双基地MIMO雷达的相干源角度估计方法。在现有的DOA矩阵法基础上，首先在空间高斯白噪声背景下提出基于降维DOA矩阵的相干源角度估计方法。该方法利用MIMO雷达能够产生多个虚拟子阵的特点，对目标回波进行解相干处理，然后根据DOA矩阵法的思想构造估计矩阵，利用其与信号子空间的关系进行降维处理以获得降维DOA矩阵，有效降低原DOA矩阵法的运算量，并利用降维DOA矩阵的特征参数与待估参数间的特定关系实现相干目标DOD和DOA的联合估计。之后将空间高斯白噪声背景下的降维DOA矩阵方法推广至背景噪声为空间高斯色噪声的情况，利用MIMO雷达发射信号的正交性消除噪声影响，并利用降维DOA矩阵的特征参数与待估参数间的特定关系实现相干目标DOD和DOA的联合估计。所提方法无需二维谱峰搜索和参数配对，且在接收阵列为非等距线阵的条件下仍具有适用性。
2.研究了空间高斯色噪声背景下的双基地MIMO雷达角度和多普勒频率联合估计方法。分析了空间高斯色噪声背景下双基地MIMO雷达的信号模型特点，提出在时域噪声为高斯白噪声的假设下，利用不同时刻匹配滤波器输出的互相关消除空间色噪声的影响。基于此，提出一种基于同时奇异值分解的双基地MIMO雷达角度和多普勒频率联合估计方法。该方法利用相邻时刻匹配滤波器输出的互相关矩阵构造新矩阵，消除空间色噪声的影响。然后通过对所构造矩阵进行奇异值分解获得信号子空间，根据目标回波的时域结构信息，将相邻时刻匹配滤波器输出的时间相位差作为时间旋转因子，采用ESPRIT方法获得目标多普勒频率，DOD和DOA的联合估计。针对同时奇异值分解方法多普勒频率估计模糊范围小的问题，提出一种基于降维DOA矩阵的双基地MIMO雷达参数估计方法。该方法同样利用时域信息构造时间旋转因子并消除空间色噪声的影响，然后结合降维DOA矩阵法获得目标多普勒频率，DOD和DOA的联合估计。两种方法均可以消除空间色噪声影响，并在参数估计时没有阵列孔径损失，且目标多普勒频率，DOD和DOA可以自动配对。同时，所提方法均可扩展至时空域均为色噪声时的双基地MIMO雷达参数估计，并可应用于常规阵列空间色噪声背景下的角度估计中。最后推导了基于时空结构时双基地MIMO雷达角度和多普勒频率估计的克拉美·罗界（CRB,Cramer-Rao Bound）。
3.研究了L型阵列MIMO雷达的DOA矩阵方法。针对常规DOA矩阵方法在二维角度估计时存在角度兼并的问题，首先将L型阵列MIMO雷达所形成的二维虚拟平面阵列划分为两个子阵，并将DOA矩阵法扩展应用于其中，实现了无需参数配对的二维DOA估计。与常规DOA矩阵方法相比，该方法在很大程度上提高了阵元利用率，减少了阵列孔径损失，改善了角度估计性能。由于其仍存在角度兼并问题，进一步提出L型阵列MIMO雷达的联合对角化DOA矩阵方法。该方法通过构造4个虚拟子阵，并对其接收回波的协方差矩阵进行联合对角化处理估计目标二维角度。该方法可减少阵列孔径损失，有效地提高角度估计的精度，增加最大可检测目标个数，同时能够避免角度兼并问题，并保持常规DOA矩阵方法无需二维谱峰搜索和参数配对的优点。
4.研究了米波雷达低仰角波达方向估计方法。针对现有的线性预处理类算法（包括线性预处理方法和差分预处理方法）使预处理后的噪声具有相关性，从而影响低信噪比时角度估计性能的问题，提出基于白化处理的线性预处理算法和基于白化处理的差分预处理算法。该算法通过对预处理后的数据进行白化处理，消除相关噪声的影响，有效提高了原有线性预处理类算法的角度估计性能。针对线性预处理算法运算量太大的问题，进一步提出基于传播算子的快速线性预处理算法。该算法在每个搜索角度利用线性运算代替协方差矩阵的特征分解，大大降低了原有算法的运算量，利于工程实时处理。另外，由于对噪声进行了白化处理，其性能优于原有线性预处理算法，并与基于白化处理的线性预处理算法性能基本一致。
5.研究了米波MIMO雷达的低仰角估计方法。首先根据米波MIMO雷达低仰角目标的回波特点，建立了同时考虑发射多径和接收多径的信号模型。其次，将线性预处理算法推广应用于米波MIMO雷达中，提出基于二次差分预处理的米波MIMO雷达低仰角角度估计算法。该算法通过在米波MIMO雷达回波数据的接收端和发射端分别进行两次差分预处理，消除发射多径信号和接收多径信号的影响，利用白化处理消除差分预处理对噪声结构的影响，并结合传统的MUSIC算法获得目标低仰角估计。该方法能够有效克服多径效应的影响并估计目标角度，并且其处理过程不受反射因子的影响，即与信号所处环境无关，具有较好的稳健性。
As a new radar system, Multiple-Input Multiple-Output (MIMO) radar is becomingpopular in radar field since its unique advantages compared with the phased array radar.MIMO radar transmits multiple orthogonal transmitted waveforms and receivesreflected signals with multiple received arrays, which can form many channels betweentransmitting and receiving array, and can achieve flexible transmitting diversity design.In contrast with the conventional phased array radar, MIMO radar provides a noveltechnique for increasing the degrees of freedom of the radar system and improving theperformance of detection and parameter estimation. This dissertation mainly focuses onthe parameter estimation of MIMO radar. The main content of this dissertation issummarized as follows:
1. The method for angle estimation of coherent sources in bistatic MMO radar isresearched. Firstly, based on the existed DOA matrix method, a method for angleestimation of coherent sources based on dimension reduction DOA matrix in thepresence of spatially white Gauss noise is presented. The virtual array date ofmultitarget echoes in MIMO radar receivers is uncorrelated utilizing the virtualsubarrays formed by MIMO radar, and the DOA matrices are constructed. Thedimension reduction DOA matrices which reduce the computational complex areobtained by the relationship between signal subspace and DOA matrices, and the jointestimation of DOD and DOA can be obtained by the corresponding relationshipsbetween the eigenvalue or eigenvector and the estimated parameters. Secondly, thedimension reduction DOA matrix method in spatially white noise circumstance isextended to the spatially colored noise circumstance. The spatially colored noise iseliminated by using the orthogonality of the transmitted signals of MIMO radar, and thejoint estimation of DOD and DOA can be obtained by using dimension reduction DOAmatrix method. The proposed methods do not need the multi-dimensional peak search,and can estimate the parameters of coherent sources without pairing in both two noisecircumstances. Moreover, it is applicable to receiving arrays without an invariancestructure.
2. The method of joint estimation of angle and Doppler frequency for bistaticMIMO radar in spatial colored noise is researched. According to the characteristic of thesignal model of bistatic MIMO radar, the spatial colored noise can be eliminated byusing the cross-correlation of the match filter outputs in different time delay sampling.Firstly, a method of joint estimation of angle and Doppler frequency for bistatic MIMO radar in spatial colored noise based on simultaneously singular value decomposition isproposed. Utilizing the cross-correlation matrix which is formed by the adjacent outputsof match filters in the time domain, a new matrix is constructed to eliminate theinfluence of spatial colored noise, and the signal subspace is obtained from singularvalue decomposition (SVD) of it. Then angles and Doppler frequencies can beestimated based on ESPRIT using the rotational factor produced by adjacent outputs ofmatch filters. Secondly, a method of joint estimation of angle and Doppler frequency forbistatic MIMO radar in spatial colored noise based on dimension reduction DOA matrixis proposed. This method utilizing the temporal information to construct the temporalrotational factor, and angles and Doppler frequencies is obtained by using dimensionreduction DOA matrix. In the proposed tow methods, the spatial colored noise can beeliminated, and the angles and Doppler frequencies can be obtained simultaneously andautomatically paired without array aperture loss. Besides, the proposed methods can beextended to the circumstance of spatially and temporally colored noise, and can be usedfor angle estimation of conventional array in the presence of colored noise. The CRB ofthe angle and Doppler frequency of bistatic MIMO radar based on spatial-temporalstructure is proposed.
3. The DOA matrix method based on MIMO radar with L-shape arrays isresearched. Firstly, a two-dimension (2-D) angle estimation method for multiple inputmultiple output (MIMO) radar with L-shape arrays based on direction of arrival (DOA)matrix is proposed. This method divides the2-D virtual plane array which is generatedby MIMO radar into two overlapping subarrays, and constructs an estimation matrix toestimate the2-D angles. To solve the problem of angle annexation, a jointdiagonalization DOA matrix method is proposed later. This method generates foursubarrays from the2-D virtual plane array, and uses the joint diagonalization algorithmto estimate the2-D angles. The proposed method secures the advantages of the existingDOA matrix method such as no requirement of2-D angle search and autopairing ofparameters, avoids the angle annexation problem, reduces the loss of the array aperture,and improves the performance of the angle estimation effectively.
4. Low-angle estimation in VHF radar is researched. The effect of the existedlinear preprocessing method to the noise structure is analyzed. Aimed at thedisadvantage that the linear preprocessing method changed the white noise of the realarray data to correlated noise which reduces the performance of angle estimation in lowSNR, an improved linear preprocessing method is proposed. This method greatlyimproved the performance of the low-angle estimation through the whitened processing of the data after linear preprocessing without increasing the computational burdensignificantly. To reduce the computational burden of the linear preprocessing method, afast algorithm of linear preprocessing based on propagator method is proposed. Thisalgorithm replaces the eigendecomposition of the cross-correlation matrix with linearoperation in each searching angle, and greatly reduces the computational burden.Moreover, the performance of the proposed algorithm is much better than theconventional linear preprocessing method, and is identical with the improved linearpreprocessing method due to the whitened processing.
6. Low-angle estimation in VHF MIMO radar is researched. Firstly, the multipathsignal model for MIMO radar is constructed with both transmitted multipath andreceived multipath signals being considered. Secondly, a twice differentialpreprocessing method for low-angle estimation in VHF MIMO radar is proposed. Withtwice differencing preprocessing of the received echoes of the VHF MIMO radar, thetransmitted multipath signals and received multipath signals are eliminated, and theconventional MUSIC algorithm can be used to obtain the estimation of low-angle. Theproposed method can overcome multipath effect and estimate the low-angle of the targeteffectively, and is not sensitive to the signals environments.
引文
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