独立信号与相干信号并存的测向算法研究
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摘要
波达方向(Direction of arrival, DOA)估计是阵列信号处理的重要研究方向之一，在雷达、被动声纳以及移动通信等军事和民用领域都有着广阔的应用前景。经过国内外学者多年来针对这一领域问题的研究，先后提出了一系列经典的超分辨率测向算法，在参数估计性能方面取得了重大的突破。但是，随着现代电磁技术的不断发展和应用，实际环境中的信号密度越来越大，且独立信号与相干信号交错并存。因此，经典的DOA估计算法大都不能满足实际应用背景的需求。尤其是针对独立信号与相干信号并存背景下的测向问题，在阵列利用率以及DOA估计性能等方面尚有很多实际问题亟待解决。本文针对这一问题展开了深入地研究和探讨，并提出了一系列性能优良的DOA估计算法。
独立信号与相干信号并存的测向问题，其核心思想是将一个阵列虚拟等效为两个阵列，用于分别对独立信号与相干信号进行DOA估计，进而可有效地提高阵列利用率。该思想涉及到独立信号的DOA估计、相干信号信息的分离和相干信号的DOA估计三个核心环节。针对独立信号与相干信号并存的测向问题，本文所做的主要工作如下：
首先，研究了相干信号测向问题。针对均匀线阵，通过利用大特征值对应的特征矢量及其反向矢量来构造解相干数据矩阵，提出了改进矢量重构方法。该方法在秉承传统算法解相干性能的同时，有效地提高了信号不完全相干时的测向性能。针对任意阵列，利用信号子空间作为测量矢量，提出了基于压缩感知理论的信号子空间测量模型。该方法有效地改善了已有单测量矢量模型和多测量矢量模型在低信噪比时的测向性能。理论分析和实验仿真验证了所提方法的优良性能。
其次，研究了独立信号与相干信号并存的一维测向问题。针对均匀线阵，利用Toeplitz矩阵特性分离法、root-MUSIC算法和改进矢量重构解相干方法，提出了均匀线阵的测向算法。该算法能够扩展阵列孔径，相比同类算法具有更高的阵列利用率和更好的估计性能。针对均匀圆阵列，采用模式空间变换技术，并结合所提均匀线阵的测向算法，提出了均匀圆阵列的测向算法。该算法能够弥补模式空间变换带来的阵列孔径损失，提高了估计性能，有效地降低了均匀圆阵列进行相干信号测向时的计算量。针对任意阵列，通过采用斜轴投影技术和基于压缩感知理论的信号子空间模型，提出了任意阵列的测向算法。该算法具有计算简便，可扩展阵列孔径等优良性能，且更适于工程实际应用，具有重要的实际意义。
再次，研究了独立信号与相干信号并存的二维DOA估计问题。针对L型阵列，在一维均匀线阵测向算法的基础上，通过选取计算简便的高性能测向算法，并分别提出高效的参数配对方法和解相干方法，分别提出了基于L型电磁矢量传感器阵列和L型标量传感器阵列的测向算法。这两种算法相对已有算法具有更高的阵列利用率和更好的估计性能。针对任意阵列，通过采用空时处理技术构造旋转不变关系，并巧妙地构造数据矩阵，提出了任意阵列的二维测向算法。该算法利用信号自身的特性即可分离出独立信号和相干信号的信息，且参数自动配对。与传统的任意阵列测向算法相比，该算法具有更小的计算量，且实际应用价值高。理论分析和实验仿真均表明该算法具有极大的阵列扩展潜能。
最后，研究了冲击噪声背景下的DOA估计问题。针对均匀线阵，采用去冲击预处理方法，提出了冲击噪声背景下的测向新算法。由于冲击噪声不具备二阶及其以上的矩，现有冲击噪声背景下的测向算法都是基于分数低阶统计量提出的。通过对阵列接收数据中信号成分的振幅进行估计，并采用归一化处理限定冲击噪声的最高振幅，冲击噪声强度被有效地削弱，则前面所提出的测向算法也可以适用于冲击噪声背景。理论分析和实验仿真表明，所提算法优于基于分数低阶统计量的测向算法，且具有计算简便，抗冲击性强等优点。
Direction of arrival (DOA) estimation is an important area in array signal processing,and has widely application in the field of military and civilian, such as radar, passive sonar,radio astronomy, communication, etc. During the past five decades, scholars at home andabroad have proposed a series of high resolution direction finding algorithms. And they havemade significant achievement in improving the performance of parameter estimation. Withthe development and application of electromagnetic technology, the density of signalsincrease greatly, and the uncorrelated and coherent signals always coexist. In this situation,the traditional DOA estimation algorithms fail or degrade since they can’t make full use of thearray aperture. In this paper, we focus on the direction finding issue for coexisted uncorrelatedand coherent signals, aiming to exploit the array aperture efficiently, and improving theperformance of estimation.
The main idea of DOA estimation for coexisted uncorrelated and coherent signals is toestimate the DOAs of the uncorrelated and coherent signals separately. In this way, the arrayaperture could be fully ultilized, and the performance of estimation will be improved. DOAestimation for coexisted uncorrelated and coherent signals is comprised of three key parts: theestimation of uncorrelated signals, the separation of coherent information, and the estimationof coherent signals. In this paper, we concentrate on investigating new methods to separatethe coherent information and estimate the coherent signals. The main work of this paper islisted as follows.
Firstly, we study the direction finding problem for coherent signals. For uniform lineararray, by exploiting the eigenvector corresponding to the big eigenvalues as well as itsbackward vector to construct the decorrelation data matrix, the improved vectorreconstruction method is proposed. It has better performance than the common methods forboth incompletely and completely coherent signals. For arbitrary array, we present a signalsubspace measurement model by regarding the signal subspace as compressed sensingmeasured vector. It can improve the DOA estimation performance of the single measurementvector model and multiple measurement vectors model greatly at low signal to noise ratio.Theoretical analysis and simulation results illustrate the good performance of the proposedmethods.
Secondly, we discuss the one-dimensional DOA estimation problems for coexisteduncorrelated and coherent signals. For uniform linear array, a new derection finding algorithm is proposed using the Toeplitz property separation method, the root-MUSIC algorithm as wellas the improved vector reconstruction method. Comparing with the similar algorithms, theproposed algorithm has higher array aperture and better performance of estimation. Foruniform circular array, the mode space transform technique is adopted, so that the algorithmfor uniform linear array could be implemented. This algorithm can cut down the computationcomplexity for coherent signals greatly and make up for the loss of array aperture. Forarbitrary array, the oblique projection technology and signal subspace measurement model areemployed to separate the coherent information and estimate the DOAs, respectively. Theproposed algorithm can expand the array aperture, and has much smaller computational loadthan the common DOA estimation algorithms for arbitrary array. Moreover, this algorithm ismore suitable for the practical application of engineering, which is of great practicalsignificance.
Thirdly, we research on the two-dimensional DOA estimation algorithms for coexisteduncorrelated and coherent signals. For L shape array, direction finding algorithms based onthe eletromagnetic vector sensor array and the scalar sensor array are proposed, respectively.Based on the one-dimensional DOA estimation algorithms of uniform linear array, the twoalgorithms make the following improvement. DOA estimation algorithms with smallcomputational complexity and good performance are chosen. Effective parameter pairmatching methods are proposed respectively. New decorrelation methods are proposedrespectively. Comparing with the similar algorithms, these two algorithms have higher arrayaperture and better performance. For arbitrary array, the space-time processing technology isimplemented, so that the rotational invariant relationship could be constructed to simplify theprocess of estimation. Moreover, by constructing the data matrix skillfully, the information ofthe uncorrelated and coherent signals could be separated according to their characteristics, andthe parameters are paired automatically. This algorithm cut down the computation load for thearbitrary array greatly. Theoretical analysis and simulation results illustrate that this algorithmhas great potential in expanding the array aperture.
Finally, we consider the DOA estimation in impulsive noise. And new direction findingalgorithms are proposed based on the second order statistics by employing the preprocessingmethod to weaken the impulsive noise. Since the impulsive noise doesn’t have second or highorder moment, the DOA estimation algorithms in impulsive noise are mostly based on thefractional lower order statistics. By estimating the amplitude of the signals and normalizingthe amplitude of the array received data, the strength of impulsive is weakened. In this way,the algorithms proposed before could be applied to impulsive noise. Simulation results illustrate that the proposed algorithms have small computation complexity and betterperformance than the algorithms based on the fractional lower order statistics, and is effectivein strong impulsive noise, too.
独立信号与相干信号并存的测向问题，其核心思想是将一个阵列虚拟等效为两个阵列，用于分别对独立信号与相干信号进行DOA估计，进而可有效地提高阵列利用率。该思想涉及到独立信号的DOA估计、相干信号信息的分离和相干信号的DOA估计三个核心环节。针对独立信号与相干信号并存的测向问题，本文所做的主要工作如下：
首先，研究了相干信号测向问题。针对均匀线阵，通过利用大特征值对应的特征矢量及其反向矢量来构造解相干数据矩阵，提出了改进矢量重构方法。该方法在秉承传统算法解相干性能的同时，有效地提高了信号不完全相干时的测向性能。针对任意阵列，利用信号子空间作为测量矢量，提出了基于压缩感知理论的信号子空间测量模型。该方法有效地改善了已有单测量矢量模型和多测量矢量模型在低信噪比时的测向性能。理论分析和实验仿真验证了所提方法的优良性能。
其次，研究了独立信号与相干信号并存的一维测向问题。针对均匀线阵，利用Toeplitz矩阵特性分离法、root-MUSIC算法和改进矢量重构解相干方法，提出了均匀线阵的测向算法。该算法能够扩展阵列孔径，相比同类算法具有更高的阵列利用率和更好的估计性能。针对均匀圆阵列，采用模式空间变换技术，并结合所提均匀线阵的测向算法，提出了均匀圆阵列的测向算法。该算法能够弥补模式空间变换带来的阵列孔径损失，提高了估计性能，有效地降低了均匀圆阵列进行相干信号测向时的计算量。针对任意阵列，通过采用斜轴投影技术和基于压缩感知理论的信号子空间模型，提出了任意阵列的测向算法。该算法具有计算简便，可扩展阵列孔径等优良性能，且更适于工程实际应用，具有重要的实际意义。
再次，研究了独立信号与相干信号并存的二维DOA估计问题。针对L型阵列，在一维均匀线阵测向算法的基础上，通过选取计算简便的高性能测向算法，并分别提出高效的参数配对方法和解相干方法，分别提出了基于L型电磁矢量传感器阵列和L型标量传感器阵列的测向算法。这两种算法相对已有算法具有更高的阵列利用率和更好的估计性能。针对任意阵列，通过采用空时处理技术构造旋转不变关系，并巧妙地构造数据矩阵，提出了任意阵列的二维测向算法。该算法利用信号自身的特性即可分离出独立信号和相干信号的信息，且参数自动配对。与传统的任意阵列测向算法相比，该算法具有更小的计算量，且实际应用价值高。理论分析和实验仿真均表明该算法具有极大的阵列扩展潜能。
最后，研究了冲击噪声背景下的DOA估计问题。针对均匀线阵，采用去冲击预处理方法，提出了冲击噪声背景下的测向新算法。由于冲击噪声不具备二阶及其以上的矩，现有冲击噪声背景下的测向算法都是基于分数低阶统计量提出的。通过对阵列接收数据中信号成分的振幅进行估计，并采用归一化处理限定冲击噪声的最高振幅，冲击噪声强度被有效地削弱，则前面所提出的测向算法也可以适用于冲击噪声背景。理论分析和实验仿真表明，所提算法优于基于分数低阶统计量的测向算法，且具有计算简便，抗冲击性强等优点。
Direction of arrival (DOA) estimation is an important area in array signal processing,and has widely application in the field of military and civilian, such as radar, passive sonar,radio astronomy, communication, etc. During the past five decades, scholars at home andabroad have proposed a series of high resolution direction finding algorithms. And they havemade significant achievement in improving the performance of parameter estimation. Withthe development and application of electromagnetic technology, the density of signalsincrease greatly, and the uncorrelated and coherent signals always coexist. In this situation,the traditional DOA estimation algorithms fail or degrade since they can’t make full use of thearray aperture. In this paper, we focus on the direction finding issue for coexisted uncorrelatedand coherent signals, aiming to exploit the array aperture efficiently, and improving theperformance of estimation.
The main idea of DOA estimation for coexisted uncorrelated and coherent signals is toestimate the DOAs of the uncorrelated and coherent signals separately. In this way, the arrayaperture could be fully ultilized, and the performance of estimation will be improved. DOAestimation for coexisted uncorrelated and coherent signals is comprised of three key parts: theestimation of uncorrelated signals, the separation of coherent information, and the estimationof coherent signals. In this paper, we concentrate on investigating new methods to separatethe coherent information and estimate the coherent signals. The main work of this paper islisted as follows.
Firstly, we study the direction finding problem for coherent signals. For uniform lineararray, by exploiting the eigenvector corresponding to the big eigenvalues as well as itsbackward vector to construct the decorrelation data matrix, the improved vectorreconstruction method is proposed. It has better performance than the common methods forboth incompletely and completely coherent signals. For arbitrary array, we present a signalsubspace measurement model by regarding the signal subspace as compressed sensingmeasured vector. It can improve the DOA estimation performance of the single measurementvector model and multiple measurement vectors model greatly at low signal to noise ratio.Theoretical analysis and simulation results illustrate the good performance of the proposedmethods.
Secondly, we discuss the one-dimensional DOA estimation problems for coexisteduncorrelated and coherent signals. For uniform linear array, a new derection finding algorithm is proposed using the Toeplitz property separation method, the root-MUSIC algorithm as wellas the improved vector reconstruction method. Comparing with the similar algorithms, theproposed algorithm has higher array aperture and better performance of estimation. Foruniform circular array, the mode space transform technique is adopted, so that the algorithmfor uniform linear array could be implemented. This algorithm can cut down the computationcomplexity for coherent signals greatly and make up for the loss of array aperture. Forarbitrary array, the oblique projection technology and signal subspace measurement model areemployed to separate the coherent information and estimate the DOAs, respectively. Theproposed algorithm can expand the array aperture, and has much smaller computational loadthan the common DOA estimation algorithms for arbitrary array. Moreover, this algorithm ismore suitable for the practical application of engineering, which is of great practicalsignificance.
Thirdly, we research on the two-dimensional DOA estimation algorithms for coexisteduncorrelated and coherent signals. For L shape array, direction finding algorithms based onthe eletromagnetic vector sensor array and the scalar sensor array are proposed, respectively.Based on the one-dimensional DOA estimation algorithms of uniform linear array, the twoalgorithms make the following improvement. DOA estimation algorithms with smallcomputational complexity and good performance are chosen. Effective parameter pairmatching methods are proposed respectively. New decorrelation methods are proposedrespectively. Comparing with the similar algorithms, these two algorithms have higher arrayaperture and better performance. For arbitrary array, the space-time processing technology isimplemented, so that the rotational invariant relationship could be constructed to simplify theprocess of estimation. Moreover, by constructing the data matrix skillfully, the information ofthe uncorrelated and coherent signals could be separated according to their characteristics, andthe parameters are paired automatically. This algorithm cut down the computation load for thearbitrary array greatly. Theoretical analysis and simulation results illustrate that this algorithmhas great potential in expanding the array aperture.
Finally, we consider the DOA estimation in impulsive noise. And new direction findingalgorithms are proposed based on the second order statistics by employing the preprocessingmethod to weaken the impulsive noise. Since the impulsive noise doesn’t have second or highorder moment, the DOA estimation algorithms in impulsive noise are mostly based on thefractional lower order statistics. By estimating the amplitude of the signals and normalizingthe amplitude of the array received data, the strength of impulsive is weakened. In this way,the algorithms proposed before could be applied to impulsive noise. Simulation results illustrate that the proposed algorithms have small computation complexity and betterperformance than the algorithms based on the fractional lower order statistics, and is effectivein strong impulsive noise, too.
引文
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