综合孔径微波辐射计天线阵排列优化研究
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摘要
微波辐射计在地球遥感、深空探测、制导、安检、医疗等领域有着广泛应用。上世纪80年代末发展起来的综合孔径微波辐射计(ASR)引入射电天文学“孔径综合”的思想,通过阵列稀疏、相关接收等技术,有效解决了传统微波辐射计口径有限、机械扫描困难等问题,极大提高了观测的空间分辨率,因而成为近年来被动微波遥感的一个发展方向。
阵列排列优化是ASR的一项关键技术。它通过基线设计和组合,决定可见度函数采样分布,而可见度函数采样分布又决定图像重建的质量。本文着重研究综合孔径微波辐射计的天线阵稀疏排列优化方法：包括基于分辨率最佳的最小冗余天线阵排列优化方法；基于系统灵敏度最佳的天线阵排列优化方法。在此基础上,设计并实现了一种新型的综合孔径毫米波辐射计天线阵物理结构；最后,对最小冗余阵在其它领域的应用进行了拓展研究。本文主要内容包括：
在总结大阵元数低冗余线阵(LRLA)排列的一般结构的基础上,提出了一种排列结构与蚁群优化(ACO)相结合的约束搜索算法,其思想是利用LRLA排列的一般结构缩小解空间,在大大缩减求解规模从而减少计算时间的同时,使所得排列具有较低的冗余度。进一步地,归纳出多种适合任意阵元数LRLA排列的解析解。
针对U、T型阵冗余度较大的问题,提出了一种矩形平面阵排列方法。从理论上证明了该方法构造的二维稀疏阵UV覆盖的完备性,导出了由该方法构造的二维稀疏阵的冗余度理论上限,并证明其优于U、T型阵。针对均匀圆环阵(UCA)基线长度存在大量冗余的问题,以最小化UCA基线长度冗余为优化目标,提出了两种稀疏优化方法：一种是基于受限差基的半圆环阵稀疏方法；一种是基于循环差集的全圆环阵稀疏方法。这两种方法均可大大减小阵元数,节约硬件成本；且均可解析地求出稀疏阵元位置,适于任意大阵元数的圆环阵稀疏优化。运用微粒群(PSO)算法优化圆环阵阵元位置,以改善圆环阵UV覆盖。设计了一种新的衡量圆环阵UV覆盖均匀程度的目标函数,与现有文献采用的目标函数相比,其计算复杂度大大降低,且能更准确地度量圆环阵UV覆盖的均匀程度。
分析了冗余基线对ASR灵敏度的影响,并定义阵列退化因子(DF)来度量这种影响；以最小化DF为优化目标,提出两种寻求最小退化阵(MDA)以实现系统最佳灵敏度的方法：一是基于贪婪思想的构建性算法,二是基于模拟退火(SA)的随机优化方法,并比较两种算法的性能。为克服阵列填充率较大时DF优化缓慢的问题,提出增广最大基线的思想。进一步地,导出了DF的下界。仿真和实验验证了MDA设计对系统灵敏度的改善。
提出了一种一维实孔径/一维综合孔径的综合孔径毫米波辐射计天线阵结构：共享偏置抛物柱面的16单元毫米波稀疏天线阵。每个ASR天线单元由一个馈源喇叭和柱形反射面组成,提供系统所需的扇形波束。这些天线单元排成最小冗余线阵,共享同一个反射面。理论计算和测量结果均表明,该天线阵具有窄主瓣、低旁瓣、低驻波比的特点,适合高分辨率被动微波成像应用。
将最小冗余阵(MRA)的研究拓展到其它应用领域。以实现最小冗余MIMO虚拟阵为优化目标,提出了两种快速构造MIMO雷达天线阵的方法：一种是基于差基和循环差集的组合方法；一种是差基/循环差集约束的SA随机搜索方法。数值计算验证了这两种方法的有效性。还研究了MRA在波束形成中的应用：由阵列自相关函数(Coarray)与波束形成方向图之间的傅氏变换对出发,建立了方向图旁瓣分布与Coarray特性之间的定量关系。进一步地,导出了MRA峰值旁瓣电平(PSL)的理论上界。
During the past few decades, there has been growing interest in the use of microwave radiometers for remote sensing of the Earth, space exploration, navigation, survillance and medical imaging. In order to provide high spatial resolution without requiring the very large and massive scanning antenna of a real-aperture system, aperture synthesis radiometers (ASR) are proposed. ASR can synthesize a large aperture by sparsely arranging a number of small aperture antennas and cross-correlating of these antenna pairs.
As a crucial technique for ASRs, antenna array design plays an important role in radiometric imaging. In this thesis, several aspects of antenna array design in ASR are addressed, including different design criterions, new placement algorithms as well as corresponding array configurations, novel design of millimeter wave array antenna and so on. The main contributions of the thesis are presented as follows:
An ant-colony-optimization-based method exploiting the general structure of low-redundancy linear arrays (LRLAs) is proposed, which can ensure obtaining large LRLAs while greatly reducing the size of the search space, therefore greatly reducing computation time. Based on the method, several analytical patterns for LRLAs are further derived, which can yield various array configurations with very low redundancy in nearly zero computation time.
A combinatorial method for optimal thinned rectangular arrays is proposed. The completeness of (u,v) coverage provided by the thinned rectangular array constructed by the method is proved and the theoretical upper bound of the array's redundancy is derived, which is superior to that of U or T array.
Two combinatorial methods for optimal thinned circular arrays are proposed to achieve the least redundancy in baseline length (modulus of baseline vector). One is half-circle thinning based on the restricted difference basis, the other is full-circle thinning based on the cyclic difference set (CDS). Both methods can greatly reduce the number of antennas and channels and provide analytical solutions for the element positions of thinned circular arrays.
A particle-swarm-optimization-based method is proposed to optimize the element locations of the circular array for the uniform (u,v) coverage. By designing an effective objective function for the optimization procedure, the computational complexity is greatly reduced and more uniform (u,v) coverage is achieved compared to the previous methods in the literature.
The minimum degradation array (MDA) is suggested for the optimum radiometric sensitivity of ASR (△TASR). Aiming at minimizing DF which characterizes the effect of redundant baselines on△TASR, two methods are proposed to search for MDA:one is a greedy constructive algorithm; the other is a simulated-annealing-based method. Numerical comparison of both methods'performance is presented. To further improve DF especially for a densely populated array, a concept of augmented maximum baseline (CAMB) is proposed. Also, the lower bound of DF is derived. Simulation and experiment results demonstrate that the proposed MDA design can ensure the optimum sensitivity of ASR.
A novel antenna array for ASR prototype is presented, which is a sparse antenna array with an offset parabolic cylinder reflector at millimeter wave band. The characterization of the whole antenna array architecture and each part of it are detailed. All measured results indicate that the antenna array performs well with narrow main beamwidth, low peak sidelobe level and small VSWR, which are all desired for passive imaging radiometer.
Research on minimum redundancy array (MRA) is also extended to other fields like beamforming and MIMO radars. Antenna array design in minimum redundancy MIMO radars is addressed and two methods are proposed to achieve the minimum redundancy virtual array:one is the combinatorial method based on difference bases and CDSs; the other is the simulated-annealing-based method incorperating difference bases and CDSs as a-priori knowledge. Numerical studies show the effectiveness of both methods. Also, based on the Fourier properties of arrays with optimal coarray properties, the coarray properties of MRAs with minimum sidelobe level are presented for the first time. Further, the upper bound of the peak sidelobe level (PSL) of an MRA is derived.
阵列排列优化是ASR的一项关键技术。它通过基线设计和组合,决定可见度函数采样分布,而可见度函数采样分布又决定图像重建的质量。本文着重研究综合孔径微波辐射计的天线阵稀疏排列优化方法：包括基于分辨率最佳的最小冗余天线阵排列优化方法；基于系统灵敏度最佳的天线阵排列优化方法。在此基础上,设计并实现了一种新型的综合孔径毫米波辐射计天线阵物理结构；最后,对最小冗余阵在其它领域的应用进行了拓展研究。本文主要内容包括：
在总结大阵元数低冗余线阵(LRLA)排列的一般结构的基础上,提出了一种排列结构与蚁群优化(ACO)相结合的约束搜索算法,其思想是利用LRLA排列的一般结构缩小解空间,在大大缩减求解规模从而减少计算时间的同时,使所得排列具有较低的冗余度。进一步地,归纳出多种适合任意阵元数LRLA排列的解析解。
针对U、T型阵冗余度较大的问题,提出了一种矩形平面阵排列方法。从理论上证明了该方法构造的二维稀疏阵UV覆盖的完备性,导出了由该方法构造的二维稀疏阵的冗余度理论上限,并证明其优于U、T型阵。针对均匀圆环阵(UCA)基线长度存在大量冗余的问题,以最小化UCA基线长度冗余为优化目标,提出了两种稀疏优化方法：一种是基于受限差基的半圆环阵稀疏方法；一种是基于循环差集的全圆环阵稀疏方法。这两种方法均可大大减小阵元数,节约硬件成本；且均可解析地求出稀疏阵元位置,适于任意大阵元数的圆环阵稀疏优化。运用微粒群(PSO)算法优化圆环阵阵元位置,以改善圆环阵UV覆盖。设计了一种新的衡量圆环阵UV覆盖均匀程度的目标函数,与现有文献采用的目标函数相比,其计算复杂度大大降低,且能更准确地度量圆环阵UV覆盖的均匀程度。
分析了冗余基线对ASR灵敏度的影响,并定义阵列退化因子(DF)来度量这种影响；以最小化DF为优化目标,提出两种寻求最小退化阵(MDA)以实现系统最佳灵敏度的方法：一是基于贪婪思想的构建性算法,二是基于模拟退火(SA)的随机优化方法,并比较两种算法的性能。为克服阵列填充率较大时DF优化缓慢的问题,提出增广最大基线的思想。进一步地,导出了DF的下界。仿真和实验验证了MDA设计对系统灵敏度的改善。
提出了一种一维实孔径/一维综合孔径的综合孔径毫米波辐射计天线阵结构：共享偏置抛物柱面的16单元毫米波稀疏天线阵。每个ASR天线单元由一个馈源喇叭和柱形反射面组成,提供系统所需的扇形波束。这些天线单元排成最小冗余线阵,共享同一个反射面。理论计算和测量结果均表明,该天线阵具有窄主瓣、低旁瓣、低驻波比的特点,适合高分辨率被动微波成像应用。
将最小冗余阵(MRA)的研究拓展到其它应用领域。以实现最小冗余MIMO虚拟阵为优化目标,提出了两种快速构造MIMO雷达天线阵的方法：一种是基于差基和循环差集的组合方法；一种是差基/循环差集约束的SA随机搜索方法。数值计算验证了这两种方法的有效性。还研究了MRA在波束形成中的应用：由阵列自相关函数(Coarray)与波束形成方向图之间的傅氏变换对出发,建立了方向图旁瓣分布与Coarray特性之间的定量关系。进一步地,导出了MRA峰值旁瓣电平(PSL)的理论上界。
During the past few decades, there has been growing interest in the use of microwave radiometers for remote sensing of the Earth, space exploration, navigation, survillance and medical imaging. In order to provide high spatial resolution without requiring the very large and massive scanning antenna of a real-aperture system, aperture synthesis radiometers (ASR) are proposed. ASR can synthesize a large aperture by sparsely arranging a number of small aperture antennas and cross-correlating of these antenna pairs.
As a crucial technique for ASRs, antenna array design plays an important role in radiometric imaging. In this thesis, several aspects of antenna array design in ASR are addressed, including different design criterions, new placement algorithms as well as corresponding array configurations, novel design of millimeter wave array antenna and so on. The main contributions of the thesis are presented as follows:
An ant-colony-optimization-based method exploiting the general structure of low-redundancy linear arrays (LRLAs) is proposed, which can ensure obtaining large LRLAs while greatly reducing the size of the search space, therefore greatly reducing computation time. Based on the method, several analytical patterns for LRLAs are further derived, which can yield various array configurations with very low redundancy in nearly zero computation time.
A combinatorial method for optimal thinned rectangular arrays is proposed. The completeness of (u,v) coverage provided by the thinned rectangular array constructed by the method is proved and the theoretical upper bound of the array's redundancy is derived, which is superior to that of U or T array.
Two combinatorial methods for optimal thinned circular arrays are proposed to achieve the least redundancy in baseline length (modulus of baseline vector). One is half-circle thinning based on the restricted difference basis, the other is full-circle thinning based on the cyclic difference set (CDS). Both methods can greatly reduce the number of antennas and channels and provide analytical solutions for the element positions of thinned circular arrays.
A particle-swarm-optimization-based method is proposed to optimize the element locations of the circular array for the uniform (u,v) coverage. By designing an effective objective function for the optimization procedure, the computational complexity is greatly reduced and more uniform (u,v) coverage is achieved compared to the previous methods in the literature.
The minimum degradation array (MDA) is suggested for the optimum radiometric sensitivity of ASR (△TASR). Aiming at minimizing DF which characterizes the effect of redundant baselines on△TASR, two methods are proposed to search for MDA:one is a greedy constructive algorithm; the other is a simulated-annealing-based method. Numerical comparison of both methods'performance is presented. To further improve DF especially for a densely populated array, a concept of augmented maximum baseline (CAMB) is proposed. Also, the lower bound of DF is derived. Simulation and experiment results demonstrate that the proposed MDA design can ensure the optimum sensitivity of ASR.
A novel antenna array for ASR prototype is presented, which is a sparse antenna array with an offset parabolic cylinder reflector at millimeter wave band. The characterization of the whole antenna array architecture and each part of it are detailed. All measured results indicate that the antenna array performs well with narrow main beamwidth, low peak sidelobe level and small VSWR, which are all desired for passive imaging radiometer.
Research on minimum redundancy array (MRA) is also extended to other fields like beamforming and MIMO radars. Antenna array design in minimum redundancy MIMO radars is addressed and two methods are proposed to achieve the minimum redundancy virtual array:one is the combinatorial method based on difference bases and CDSs; the other is the simulated-annealing-based method incorperating difference bases and CDSs as a-priori knowledge. Numerical studies show the effectiveness of both methods. Also, based on the Fourier properties of arrays with optimal coarray properties, the coarray properties of MRAs with minimum sidelobe level are presented for the first time. Further, the upper bound of the peak sidelobe level (PSL) of an MRA is derived.
引文
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