MIMO雷达模型与信号处理研究
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摘要
多输入多输出(MIMO，Multiple-Input Multiple-Output)雷达使用多天线发射多重探测信号照射目标，并利用多天线接收目标反射的后向散射回波信号。与传统的相控阵雷达相比，MIMO雷达可以显著改善参数可辨识性，实现更为灵活的发射方向图设计，改进目标检测和参数估计性能，并可通过采用更灵活的发射波形设计以提高检测和估计性能。本文研究了MIMO雷达的模型、信号检测、参数估计以及优化波形设计等方面问题。
本文的主要工作包括以下几方面。
1．本文系统地研究和总结了现有的MIMO雷达信号模型，包括波形分集的共址MIMO雷达、发射和接收空间全分集的统计MIMO雷达和仅发射分集的统计MIMO雷达，以及基于共址MIMO雷达的MIMO-STAP雷达模型。在此基础上，本文在仅发射分集统计MIMO雷达的接收阵列引入了目标的角度扩展，提出了使用非相干子阵的共址MIMO雷达的等效模型，将MIMO-STAP模型拓展到多目标情况。
2．在共址MIMO雷达模型中，目标被建模为点目标，因此发射和接收的信号都是完全相干的；而在统计MIMO雷达模型中，目标被建模为具有丰富散射的扩展目标，因此发射和接收的信号分别是完全不相关的。本文在MIMO雷达模型中考虑了空间部分相干性，即阵列发射信号通过有限的路径照射到目标的多个散射点，而目标散射点的后向回波信号也通过有限的路径被阵列接收，因此目标相对于发射和接收阵列表现为有限的角度扩展。本文提出了MIMO雷达的参数物理模型来描述这种空间部分相干性。
3．现有的共址MIMO雷达模型、发射和接收全分集的和仅发射分集的统计MIMO雷达模型都是建立在实际物理散射过程的描述上。利用这些模型不便于获得目标散射特性的整体性质，因此在处理诸如优化波形设计等需要利用目标散射特性的问题时，需要特定的复杂技术。在MIMO雷达的参数物理模型的基础上，并借鉴MIMO无线通信理论和阵列信号处理中的波束域理论，本文提出了MIMO雷达的虚拟表示模型。这种表示方法是通过将各方向的探测信号以及目标在各方向的物理散射分别投影到固定的傅里叶方向，并利用虚拟的等效信道矩阵来描述目标的整体散射特性。
4．在MIMO雷达的虚拟表示模型基础上，本文进一步提出了MIMO雷达的标准模型。该模型将各方向的探测信号以及目标在各方向的物理散射分别投影到发射和接收特征方向，并利用散射矩阵来描述目标的整体散射特性。该模型提供了共址MIMO雷达模型、统计MIMO雷达模型，以及具有空间部分相干的MIMO雷达模型的统一描述，并有助于获得广泛适用的优化波形设计方案。
5．对于具有空间部分相干性的发射分集统计MIMO雷达，利用空间相干矩阵的Toeplitz结构、Toeplitz矩阵与轮换矩阵的渐近等价性，以及离散傅里叶变换矩阵对轮换矩阵的对角化性质，本文提出了一种具有较低计算量的渐近优化检测算法。
6．对共址MIMO雷达，本文研究了Capon、APES、GLRT和发射分集平滑等目标角度估计算法。对于使用非相干子阵的共址MIMO雷达，本文提出了一种结合发射分集平滑技术和广义MUSIC算法的参数估计算法。该算法不仅具有高分辨的角度估计性能，而且可根据需要选择使用某些特定的非相干子阵，从而实现灵活的发射和接收分集。
7．对于仅发射分集统计MIMO雷达，基于准静态衰落的假设下，本文提出了目标角度和衰落向量参数估计的两种渐近最大似然估计算法、CAPES算法、以及衰落向量参数估计的稳健的APES算法；基于目标随机快速衰落的假设，本文提出了子空间算法和协方差匹配技术两种方法；本文也将盲信号处理技术应用于MIMO雷达的参数估计问题中。仿真实验表明，发射分集可有效改善目标的角度估计性能。
8．基于MIMO雷达标准模型，本文应用极大化条件互信息量和极小化最小均方误差两种准则实现了MIMO雷达的优化估计波形的设计(designs of optimalestimation waveforms)。该设计结果不仅适用于统计MIMO雷达模型，还适于具有部分空间相干性的共址MIMO雷达。本文也提出将Kronecker结构的矩阵估计技术用于解决MIMO雷达的优化估计波形设计问题。
A Multiple-Input Multiple-Output (MIMO) radar transmits multiple probing sig-nals via multiple antennas,and receives the backscattered signals reflected from thetargets using multiple antennas.In contrast with the conventional phased array radar,the waveform diversity enables the MIMO radar with colocated antennas to have muchimproved capabilities including significantly improved parameter identifiability,muchenhanced flexibility for transmit beampattern design,and direct applicability of adap-tive array processing algorithms.The spatial diversity of the target's radar cross sectionobtained by the statistical MIMO radar enables improved detection and estimation per-formance.
The problems of modeling of MIMO radar,the target detection,the parameterestimation,and optimal waveform designs are considered herein.
The main contribution of this thesis are as follows.
1.The recent results on signal models of MIMO radars are systematically sum-marized,including the MIMO radars with colocated antennas with waveform diversity,the statistical MIMO radars with transmit and receive diversity,the statistical MIMOradars with transmit diversity only,and the MIMO-STAP radars with colocated an-tennas.The statistical MIMO radar model with transmit diversity only is generalizedby introducing the target angular spread at the receive array.The equivalent model ofthe MIMO radars equipped with noncoherent transmit and receive colocated antennasubarrays is proposed.The multiple-target model of the MIMO-STAP system is alsoproposed.
2.The point target model is used in the MIMO radars with colocated antennas,and hence the signals transmitted and received respectively via the transmit and re-ceive antenna arrays are fully coherent.In the statistical MIMO radars,the target ismodeled as extended with rich scattering,and the transmitted and received signals arecompletely decorrelated,respectively.This contribution introduces the partial spatialcoherence in the MIMO radars,i.e.,the signals illuminate on finite number of scat-terers of the target,while the backscattered signals are received via finite number of paths as well.Hence,the target exhibits finite angular spread with respect to both thetransmit and receive arrays.The parametric physical MIMO radar model is proposedto describe the partial spatial coherence.
3.The MIMO radar with colocatd antennas,the statistical MIMO radars withtransmit and receive diversity,and the statistical MIMO radars with transmit diver-sity only,are constructed based on the physical scattering description.However,thesemodels cannot effectively capture the scattering characteristics,and it is not easy tohandle the problems which needs these information,such as the optimal waveform de-sign.Based on the parametric physical model of MIMO radars,exploiting the theory ofMIMO wireless communications and that of the bearnspace in array signal processing,the virtual representation model is proposed.In this model,the probing and reflectedsignals in different directions are respectively projected onto fixed Fourier directions,and the equivalent channel model is used to describe the scattering characteristics ofthe target.
4.The canonical model of MIMO radars is further proposed,with the models ofMIMO radars with colocated antennas,the statistical MIMO radar,and that with partialspatial coherence as its special cases.The probing signals from different directionsare projected onto the transmit eigen directions,while the physical reflections of thetarget towards different directions are projected onto the receive eigen directions.Thescattering characteristics of different scatterers is described by a scattering matrix.Thismodel eases the universal optimal waveform design.
5.For the statistical MIMO radar with transmit diversity only and angular spreadat the receive array,an efficient asymptotically optimal detection algorithm is proposedby use of the Toeplitz structure of the spatial coherence matrix,and the asymptoticequivalence of Toeplitz and circulant matrices,where the circulant matrix is diago-nalised by the discrete Fourier transform matrix.
6.The direction finding algorithms,including Capon,APES,GLRT and transmitdiversity smoothing techniques are considered for the MIMO radars with colocatedantennas.The generalized MUSIC algorithm in conjunction with the transmissiondiversity smoothing technique are proposed in the parameter estimation problem of theMIMO radar with colocated antennas equipped with noncoherent transmit and receive colocated antenna subarrays.The spatial diversity at either the transmit or the receivecan be flexibly obtained by selecting certain transmit or receive subarrays.
7.Several algorithms are proposed to deal with the problem of parameter estima-tion of the statistical MIMO radar with transmit diversity only.Under the quasistaticfading assumption,this contribution proposes two asymptotical maximum likelihoodmethods,and the CAPES algorithm to obtain the angle and fading parameters estima-tion,as well as the robust APES algorithm for fading estimation.Under the stochasticfading assumption,the covariance matching technique and the subspace algorithm areproposed for angle estimation.The application of blind signal processing in the param-eter estimation problem is discussed as well.The performance improvement of angleestimation with transmit diversity is validated through simulations.
8.This contribution maximizes the conditional mutual information and minimizesminimum mean-square error respectively to obtain the optimal estimation waveformswith the canonical MIMO radar model.This result may be considered as a generalsolution to the statistical MIMO radar and MIMO radar with partial spatial coherence.The Kronecker structure matrix estimation technique is also applied to the problem ofoptimal waveform design.
本文的主要工作包括以下几方面。
1．本文系统地研究和总结了现有的MIMO雷达信号模型，包括波形分集的共址MIMO雷达、发射和接收空间全分集的统计MIMO雷达和仅发射分集的统计MIMO雷达，以及基于共址MIMO雷达的MIMO-STAP雷达模型。在此基础上，本文在仅发射分集统计MIMO雷达的接收阵列引入了目标的角度扩展，提出了使用非相干子阵的共址MIMO雷达的等效模型，将MIMO-STAP模型拓展到多目标情况。
2．在共址MIMO雷达模型中，目标被建模为点目标，因此发射和接收的信号都是完全相干的；而在统计MIMO雷达模型中，目标被建模为具有丰富散射的扩展目标，因此发射和接收的信号分别是完全不相关的。本文在MIMO雷达模型中考虑了空间部分相干性，即阵列发射信号通过有限的路径照射到目标的多个散射点，而目标散射点的后向回波信号也通过有限的路径被阵列接收，因此目标相对于发射和接收阵列表现为有限的角度扩展。本文提出了MIMO雷达的参数物理模型来描述这种空间部分相干性。
3．现有的共址MIMO雷达模型、发射和接收全分集的和仅发射分集的统计MIMO雷达模型都是建立在实际物理散射过程的描述上。利用这些模型不便于获得目标散射特性的整体性质，因此在处理诸如优化波形设计等需要利用目标散射特性的问题时，需要特定的复杂技术。在MIMO雷达的参数物理模型的基础上，并借鉴MIMO无线通信理论和阵列信号处理中的波束域理论，本文提出了MIMO雷达的虚拟表示模型。这种表示方法是通过将各方向的探测信号以及目标在各方向的物理散射分别投影到固定的傅里叶方向，并利用虚拟的等效信道矩阵来描述目标的整体散射特性。
4．在MIMO雷达的虚拟表示模型基础上，本文进一步提出了MIMO雷达的标准模型。该模型将各方向的探测信号以及目标在各方向的物理散射分别投影到发射和接收特征方向，并利用散射矩阵来描述目标的整体散射特性。该模型提供了共址MIMO雷达模型、统计MIMO雷达模型，以及具有空间部分相干的MIMO雷达模型的统一描述，并有助于获得广泛适用的优化波形设计方案。
5．对于具有空间部分相干性的发射分集统计MIMO雷达，利用空间相干矩阵的Toeplitz结构、Toeplitz矩阵与轮换矩阵的渐近等价性，以及离散傅里叶变换矩阵对轮换矩阵的对角化性质，本文提出了一种具有较低计算量的渐近优化检测算法。
6．对共址MIMO雷达，本文研究了Capon、APES、GLRT和发射分集平滑等目标角度估计算法。对于使用非相干子阵的共址MIMO雷达，本文提出了一种结合发射分集平滑技术和广义MUSIC算法的参数估计算法。该算法不仅具有高分辨的角度估计性能，而且可根据需要选择使用某些特定的非相干子阵，从而实现灵活的发射和接收分集。
7．对于仅发射分集统计MIMO雷达，基于准静态衰落的假设下，本文提出了目标角度和衰落向量参数估计的两种渐近最大似然估计算法、CAPES算法、以及衰落向量参数估计的稳健的APES算法；基于目标随机快速衰落的假设，本文提出了子空间算法和协方差匹配技术两种方法；本文也将盲信号处理技术应用于MIMO雷达的参数估计问题中。仿真实验表明，发射分集可有效改善目标的角度估计性能。
8．基于MIMO雷达标准模型，本文应用极大化条件互信息量和极小化最小均方误差两种准则实现了MIMO雷达的优化估计波形的设计(designs of optimalestimation waveforms)。该设计结果不仅适用于统计MIMO雷达模型，还适于具有部分空间相干性的共址MIMO雷达。本文也提出将Kronecker结构的矩阵估计技术用于解决MIMO雷达的优化估计波形设计问题。
A Multiple-Input Multiple-Output (MIMO) radar transmits multiple probing sig-nals via multiple antennas,and receives the backscattered signals reflected from thetargets using multiple antennas.In contrast with the conventional phased array radar,the waveform diversity enables the MIMO radar with colocated antennas to have muchimproved capabilities including significantly improved parameter identifiability,muchenhanced flexibility for transmit beampattern design,and direct applicability of adap-tive array processing algorithms.The spatial diversity of the target's radar cross sectionobtained by the statistical MIMO radar enables improved detection and estimation per-formance.
The problems of modeling of MIMO radar,the target detection,the parameterestimation,and optimal waveform designs are considered herein.
The main contribution of this thesis are as follows.
1.The recent results on signal models of MIMO radars are systematically sum-marized,including the MIMO radars with colocated antennas with waveform diversity,the statistical MIMO radars with transmit and receive diversity,the statistical MIMOradars with transmit diversity only,and the MIMO-STAP radars with colocated an-tennas.The statistical MIMO radar model with transmit diversity only is generalizedby introducing the target angular spread at the receive array.The equivalent model ofthe MIMO radars equipped with noncoherent transmit and receive colocated antennasubarrays is proposed.The multiple-target model of the MIMO-STAP system is alsoproposed.
2.The point target model is used in the MIMO radars with colocated antennas,and hence the signals transmitted and received respectively via the transmit and re-ceive antenna arrays are fully coherent.In the statistical MIMO radars,the target ismodeled as extended with rich scattering,and the transmitted and received signals arecompletely decorrelated,respectively.This contribution introduces the partial spatialcoherence in the MIMO radars,i.e.,the signals illuminate on finite number of scat-terers of the target,while the backscattered signals are received via finite number of paths as well.Hence,the target exhibits finite angular spread with respect to both thetransmit and receive arrays.The parametric physical MIMO radar model is proposedto describe the partial spatial coherence.
3.The MIMO radar with colocatd antennas,the statistical MIMO radars withtransmit and receive diversity,and the statistical MIMO radars with transmit diver-sity only,are constructed based on the physical scattering description.However,thesemodels cannot effectively capture the scattering characteristics,and it is not easy tohandle the problems which needs these information,such as the optimal waveform de-sign.Based on the parametric physical model of MIMO radars,exploiting the theory ofMIMO wireless communications and that of the bearnspace in array signal processing,the virtual representation model is proposed.In this model,the probing and reflectedsignals in different directions are respectively projected onto fixed Fourier directions,and the equivalent channel model is used to describe the scattering characteristics ofthe target.
4.The canonical model of MIMO radars is further proposed,with the models ofMIMO radars with colocated antennas,the statistical MIMO radar,and that with partialspatial coherence as its special cases.The probing signals from different directionsare projected onto the transmit eigen directions,while the physical reflections of thetarget towards different directions are projected onto the receive eigen directions.Thescattering characteristics of different scatterers is described by a scattering matrix.Thismodel eases the universal optimal waveform design.
5.For the statistical MIMO radar with transmit diversity only and angular spreadat the receive array,an efficient asymptotically optimal detection algorithm is proposedby use of the Toeplitz structure of the spatial coherence matrix,and the asymptoticequivalence of Toeplitz and circulant matrices,where the circulant matrix is diago-nalised by the discrete Fourier transform matrix.
6.The direction finding algorithms,including Capon,APES,GLRT and transmitdiversity smoothing techniques are considered for the MIMO radars with colocatedantennas.The generalized MUSIC algorithm in conjunction with the transmissiondiversity smoothing technique are proposed in the parameter estimation problem of theMIMO radar with colocated antennas equipped with noncoherent transmit and receive colocated antenna subarrays.The spatial diversity at either the transmit or the receivecan be flexibly obtained by selecting certain transmit or receive subarrays.
7.Several algorithms are proposed to deal with the problem of parameter estima-tion of the statistical MIMO radar with transmit diversity only.Under the quasistaticfading assumption,this contribution proposes two asymptotical maximum likelihoodmethods,and the CAPES algorithm to obtain the angle and fading parameters estima-tion,as well as the robust APES algorithm for fading estimation.Under the stochasticfading assumption,the covariance matching technique and the subspace algorithm areproposed for angle estimation.The application of blind signal processing in the param-eter estimation problem is discussed as well.The performance improvement of angleestimation with transmit diversity is validated through simulations.
8.This contribution maximizes the conditional mutual information and minimizesminimum mean-square error respectively to obtain the optimal estimation waveformswith the canonical MIMO radar model.This result may be considered as a generalsolution to the statistical MIMO radar and MIMO radar with partial spatial coherence.The Kronecker structure matrix estimation technique is also applied to the problem ofoptimal waveform design.
引文
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