MIMO雷达成像的电磁分析与模拟
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摘要
MIMO(multiple input multiple output)雷达系统是国际上新兴的研究方向，在雷达成像领域得到了广泛的关注。相对于传统的单天线雷达，MIMO雷达在数据获取上具有明显的优势，但与MIMO技术在通信信号处理方面的应用相比，MIMO雷达的优越性及局限性还没有清晰的结论，而且很多传统的雷达成像算法并不适合MIMO雷达。本论文应用电磁数值方法建立MIMO雷达系统成像的数学模型，利用逆散射领域的最新理论研究MIMO雷达的成像算法，主要工作包括：MIMO雷达信号模型及成像基础、MIMO雷达数据的数值模拟、基于逆散射理论的MIMO雷达成像算法、MIMO雷达成像算法在井地雷达中的应用。
MIMO雷达成像算法研究的前提条件是获取雷达的数据。实际的MIMO雷达系统仍处于试验阶段，因而雷达探测数据需要通过数值模拟来获得。本论文首先建立了MIMO雷达信号的数学模型，然后推导了对于特殊目标散射场的级数解析解。在二维和三维的情况，解析解分别依赖于贝赛尔函数和球面贝赛尔函数。在研究三维散射问题的级数解时，推导了Mie级数新的迭代公式并利用此公式获取了精确的散射解。利用以上结果，可以获得较为准确的MIMO雷达数据。对于一般情况，利用麦克斯韦方程建立MIMO雷达模型，应用典型的电磁数值计算方法—有限元法处理目标的散射场，获取雷达成像所需的频域数据。
理论上，MIMO雷达可以根据其探测的海量数据提高成像分辨率。但传统的雷达成像算法一般基于单天线雷达。多重信号分类（MUSIC）算法可以处理MIMO雷达数据，但一般情况下只能处理目标是点状散射体的情况，对较大目标的成像效果并不是很好。本论文利用逆散射领域中的定性方法—线性采样法和对偶差异法进行MIMO雷达成像的研究。此类方法基于完整的非线性模型，算法实现简单，运算速度快，可以处理多个雷达天线的多点场值，因而非常适合MIMO雷达系统成像的研究，而且基本上不需要目标的先验信息。线性采样法的理论已经发展的比较成熟，可应用于MIMO雷达近远场成像，处理目标可以具有一定的大小和形状。对偶差异法是逆散射领域近几年发展的最新方法，它可以看做是线性采样法的近场延拓。论文利用MIMO雷达散射问题的解析解与模拟数据，研究了对偶差异法在MIMO雷达应用中的基本性质，包括稳定性、成像极限、对雷达波长的依赖等。与传统的雷达成像方法相比，对偶差异法具有如下的优点：可以准确地获得目标的确切形状、可以获取目标的物理信息、运算速度非常快。在MIMO雷达近场成像中，利用对偶差异法进行目标重构，可以获得较为理想的效果。
探地雷达在地雷探测、非破坏性结构探测，确定地下管线等方面都有重要应用。本论文将对偶差异法应用到研究探地雷达中的井地雷达成像。井地雷达具有多个接收和发射天线，属于MIMO雷达范畴。论文应用数值方法模拟井地雷达数据并利用对偶差异法对地下物体进行成像。针对井地雷达的背景通常较复杂的特点,论文提出了修正的对偶差异法，可以处理介质折射率随机扰动的情况，并减小了运算量。通过计算机仿真可以看到在井地雷达的目标成像中，利用修正的对偶差异法会取得较为理想的重构效果。
本论文包含了对MIMO雷达模拟与成像的深入研究，是关于MIMO雷达成像理论的早期工作，也是首次把逆散射中的最新结果应用在MIMO雷达研究中。
Multiple input and multiple output (MIMO) radar system is a cutting edge researchdirection which received a lot of international attention recently from the radar imagingcommunity. It is clear that more data is obtained using MIMO radar. However, comparingwith applications of MIMO system in communication singal processing, the fundamentaladvantages and limits of MIMO radar system are not clear yet. Furthermore, traditional radarimaging techneques cannot be applied to MIMO radar directly. In this thesis, we focus on themathematical theory and imaging algorithms for MIMO radar based on the recentdevelopments in the inverse scattering theory. In particular, we study the scattering model ofthe MIMO radar system, apply numerical methods to simulate MIMO radar data, developradar imaging methods for MIMO radar, and apply the result to surfact to borehole radar(GPR) imaging.
It is necessary to obtain radar data before we apply any imaging algorithms for objectdetection. Since the actual MIMO radar system is still in the experiment phase, we rely on thenumerical simulation to get MIMO radar data. We first start by deriving the analyticalsolutions of MIMO radar scattering problems in both two and three dimensions using Bessel’sfunctions and spherical Bessel’s fuctions respectively. In three dimension, we derive newrecursive formula for the Mie series. Using these results, we are able to obtain the exact noisefree radar data which can be used to study the fundamental features of the MIMO radarsystem. In general cases, the MIMO radar model, which is based on the Maxwell's equations,is simulated using a typical numerical method, i.e., the finite element method. Then thecomputed scattered field is used for radar imaging.
Since MIMO radar provides a much denser data set, it is expected that high resolutionimages could be obtained. Most traditional radar imaging methods deal with single inputsingle output (SISO) radar. MUSIC method can be used to process MIMO radar data.However, only point like objects can be effectively detected. We apply the recently developedqualitative methods in inverse scattering theory to MIMO radar. These methods are based onnon-linear models and are fast and easy to implement. In particular, they are well-suited toprocess MIMO radar data. Among them, the reciprocity gap method, as an extension of thelinear sampling method, is a newly developed imaging method in inverse scattering. Since themethod needs radar data at multiple locations, it fits the context of MIMO radar systemextremely well. Comparing to traditional radar imaging techniques, the reciprocity gap method has several advantages: little a prior information of the target is needed; exact shapeof the target can be reconstructed; addtional properties, such as the index of refraction, can beobtained; and the method is very fast in general and has the potential to be applied in real time.Using exact data and simulation data, we study the fundamental problems related to thereciprocity gap method including the ill-posed properties, the reconstruction limit, and thedependence on the wave length.
Ground penetrating radar (GPR) is a geophysical method that uses radar pulses to imagethe subsurface. It has many applictions such as detecting land mines, nondestructive testing ofstructures, locating buried utility lines, etc. In this thesis, we will study a spectial type of GPR,surface to borehole radar. Comparing to traditional single input single output GPR, surfact toborehole radar falls in the category of MIMO radar since it has multiple radar receivers andtransmitters. We use the developed numerical method to obtain radar data and apply thereciprocity gap method to image the buried objects. In the case of random inhomogeneousbackground, we propose a modified reciprocity gap method and obtain satisfactory imagingresults.
This thesis contains the advanced study of simulation and algorithms for MIMO radarsystem. To the author’s knowledge, it is among the earliest studies of MIMO radar imagingand is the first to apply the qualitative methods in inverse scattering theory to MIMO radarsystem.
MIMO雷达成像算法研究的前提条件是获取雷达的数据。实际的MIMO雷达系统仍处于试验阶段，因而雷达探测数据需要通过数值模拟来获得。本论文首先建立了MIMO雷达信号的数学模型，然后推导了对于特殊目标散射场的级数解析解。在二维和三维的情况，解析解分别依赖于贝赛尔函数和球面贝赛尔函数。在研究三维散射问题的级数解时，推导了Mie级数新的迭代公式并利用此公式获取了精确的散射解。利用以上结果，可以获得较为准确的MIMO雷达数据。对于一般情况，利用麦克斯韦方程建立MIMO雷达模型，应用典型的电磁数值计算方法—有限元法处理目标的散射场，获取雷达成像所需的频域数据。
理论上，MIMO雷达可以根据其探测的海量数据提高成像分辨率。但传统的雷达成像算法一般基于单天线雷达。多重信号分类（MUSIC）算法可以处理MIMO雷达数据，但一般情况下只能处理目标是点状散射体的情况，对较大目标的成像效果并不是很好。本论文利用逆散射领域中的定性方法—线性采样法和对偶差异法进行MIMO雷达成像的研究。此类方法基于完整的非线性模型，算法实现简单，运算速度快，可以处理多个雷达天线的多点场值，因而非常适合MIMO雷达系统成像的研究，而且基本上不需要目标的先验信息。线性采样法的理论已经发展的比较成熟，可应用于MIMO雷达近远场成像，处理目标可以具有一定的大小和形状。对偶差异法是逆散射领域近几年发展的最新方法，它可以看做是线性采样法的近场延拓。论文利用MIMO雷达散射问题的解析解与模拟数据，研究了对偶差异法在MIMO雷达应用中的基本性质，包括稳定性、成像极限、对雷达波长的依赖等。与传统的雷达成像方法相比，对偶差异法具有如下的优点：可以准确地获得目标的确切形状、可以获取目标的物理信息、运算速度非常快。在MIMO雷达近场成像中，利用对偶差异法进行目标重构，可以获得较为理想的效果。
探地雷达在地雷探测、非破坏性结构探测，确定地下管线等方面都有重要应用。本论文将对偶差异法应用到研究探地雷达中的井地雷达成像。井地雷达具有多个接收和发射天线，属于MIMO雷达范畴。论文应用数值方法模拟井地雷达数据并利用对偶差异法对地下物体进行成像。针对井地雷达的背景通常较复杂的特点,论文提出了修正的对偶差异法，可以处理介质折射率随机扰动的情况，并减小了运算量。通过计算机仿真可以看到在井地雷达的目标成像中，利用修正的对偶差异法会取得较为理想的重构效果。
本论文包含了对MIMO雷达模拟与成像的深入研究，是关于MIMO雷达成像理论的早期工作，也是首次把逆散射中的最新结果应用在MIMO雷达研究中。
Multiple input and multiple output (MIMO) radar system is a cutting edge researchdirection which received a lot of international attention recently from the radar imagingcommunity. It is clear that more data is obtained using MIMO radar. However, comparingwith applications of MIMO system in communication singal processing, the fundamentaladvantages and limits of MIMO radar system are not clear yet. Furthermore, traditional radarimaging techneques cannot be applied to MIMO radar directly. In this thesis, we focus on themathematical theory and imaging algorithms for MIMO radar based on the recentdevelopments in the inverse scattering theory. In particular, we study the scattering model ofthe MIMO radar system, apply numerical methods to simulate MIMO radar data, developradar imaging methods for MIMO radar, and apply the result to surfact to borehole radar(GPR) imaging.
It is necessary to obtain radar data before we apply any imaging algorithms for objectdetection. Since the actual MIMO radar system is still in the experiment phase, we rely on thenumerical simulation to get MIMO radar data. We first start by deriving the analyticalsolutions of MIMO radar scattering problems in both two and three dimensions using Bessel’sfunctions and spherical Bessel’s fuctions respectively. In three dimension, we derive newrecursive formula for the Mie series. Using these results, we are able to obtain the exact noisefree radar data which can be used to study the fundamental features of the MIMO radarsystem. In general cases, the MIMO radar model, which is based on the Maxwell's equations,is simulated using a typical numerical method, i.e., the finite element method. Then thecomputed scattered field is used for radar imaging.
Since MIMO radar provides a much denser data set, it is expected that high resolutionimages could be obtained. Most traditional radar imaging methods deal with single inputsingle output (SISO) radar. MUSIC method can be used to process MIMO radar data.However, only point like objects can be effectively detected. We apply the recently developedqualitative methods in inverse scattering theory to MIMO radar. These methods are based onnon-linear models and are fast and easy to implement. In particular, they are well-suited toprocess MIMO radar data. Among them, the reciprocity gap method, as an extension of thelinear sampling method, is a newly developed imaging method in inverse scattering. Since themethod needs radar data at multiple locations, it fits the context of MIMO radar systemextremely well. Comparing to traditional radar imaging techniques, the reciprocity gap method has several advantages: little a prior information of the target is needed; exact shapeof the target can be reconstructed; addtional properties, such as the index of refraction, can beobtained; and the method is very fast in general and has the potential to be applied in real time.Using exact data and simulation data, we study the fundamental problems related to thereciprocity gap method including the ill-posed properties, the reconstruction limit, and thedependence on the wave length.
Ground penetrating radar (GPR) is a geophysical method that uses radar pulses to imagethe subsurface. It has many applictions such as detecting land mines, nondestructive testing ofstructures, locating buried utility lines, etc. In this thesis, we will study a spectial type of GPR,surface to borehole radar. Comparing to traditional single input single output GPR, surfact toborehole radar falls in the category of MIMO radar since it has multiple radar receivers andtransmitters. We use the developed numerical method to obtain radar data and apply thereciprocity gap method to image the buried objects. In the case of random inhomogeneousbackground, we propose a modified reciprocity gap method and obtain satisfactory imagingresults.
This thesis contains the advanced study of simulation and algorithms for MIMO radarsystem. To the author’s knowledge, it is among the earliest studies of MIMO radar imagingand is the first to apply the qualitative methods in inverse scattering theory to MIMO radarsystem.
引文
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