通信信号盲分离方法研究
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摘要
雷达、通信等各类电子系统的广泛应用，形成了时域高度密集、频谱严重混叠的复杂电磁环境，使得各类合作/非合作通信系统接收到时频重叠混合信号的概率大大增大。为了完成感兴趣的源信号的参数估计和信息提取，必须首先从混合信号中准确分离出源信号。盲信号分离（Blind Signal Separation, BSS），可以从观测到的混合信号中恢复出无法直接观测到的源信号。利用BSS方法可以大大提高各类通信系统对复杂电磁环境的适应能力，具有重要的实际意义。本文根据不同的接收阵列结构以及源信号否为稀疏信号的情况，分别针对特定阵列稀疏信号的欠定波达方向（Direction-of-Arrival, DOA）估计和盲分离、特定阵列非稀疏信号的欠定DOA估计和盲分离、任意阵列的欠定盲分离以及特定目标信号盲提取四个方面的问题进行了深入研究。主要研究内容概括如下：
第二章研究了特定阵列且源信号是稀疏信号的欠定DOA估计和盲分离问题。假设任意时频邻域内同时存在的源信号数目小于阵元数目，提出了基于稀疏重构和聚类验证的源个数、DOA与信号波形联合估计算法。首先将信号的时频支撑域划分成若干不相交的时频邻域，利用稀疏重构算法估计出每个时频邻域内不为零的源信号的DOA及其对应的时频域波形，然后利用聚类验证方法对所有时频邻域的DOA估计结果进行聚类分析，从而完成源个数和所有源信号DOA的联合估计。最后，根据DOA完成整个时频域上不同源信号波形的拼接，并通过逆变换求解源信号的时域波形。本章算法充分利用了源信号的时频稀疏性，同时实现了欠定混合条件下源个数、DOA以及信号波形的估计。在DOA估计方面，相比基于高阶累积量的欠定DOA估计算法，所需的样本点数更少，估计精度更高。相比基于聚类的欠定DOA估计方法，放宽了对源信号的稀疏性要求并克服了要求事先已知源个数的不足。在源信号分离方面，由于算法可以准确估计任意时频邻域内同时存在的源信号数目，相比具有相同稀疏性假设的子空间投影算法，提高了源信号的估计性能。仿真结果验证了算法的有效性。
第三章研究了特定阵列且源信号是非稀疏信号的欠定DOA估计和盲分离问题，提出了基于拓展循环自相关矩阵联合对角化的欠定DOA估计算法。首先计算信号在不同循环频率、不同时延处的循环自相关矩阵，利用代数方法将同一循环频率、不同时延处的循环自相关矩阵表示成拓展循环自相关矩阵形式，从而得到一组不同循环频率的拓展循环自相关矩阵集合；然后，利用联合对角化的方法估计出信号子空间和噪声子空间；最后根据子空间类方法估计出源信号的DOA。该算法通过代数手段实现了阵列的虚拟扩展，不要求源信号在时频域是稀疏的，可以有效地实现欠定条件下非稀疏源信号的DOA估计。同时，由于联合利用了多个不同循环频率的拓展循环自相关矩阵，显著提高了算法的DOA估计精度以及对色噪声的适应能力。在估计出源信号的DOA的基础上，提出了基于期望最大化和时频域最优波束形成的欠定盲分离算法。通过期望最大化算法估计出不同时频邻域内的各源信号和噪声的概率分布参数，在此基础上分别求解不同时频邻域内各源信号对应的最优波束形成器以完成源信号的分离。该算法充分利用了源信号和噪声的概率分布信息，可以有效实现欠定条件下非稀疏源信号的分离。仿真结果表明本章算法可以有效完成欠定条件下非稀疏源信号的DOA估计及盲分离。
第四章研究了任意阵列的欠定盲分离问题。假设所有源信号均存在时频单源点且任意时频邻域内同时存在的源信号数目不大于阵元数目，提出了基于时频单源点检测以及改进的矩阵对角化的欠定盲分离算法。首先计算混合信号的时频比矩阵，对时频比矩阵的实部和虚部进行直方图统计以完成时频单源点的检测。然后利用基于k均值的聚类验证算法对时频单源点集对应的奇异向量进行聚类分析从而完成源个数和混合矩阵的联合估计。该混合矩阵估计算法有两个优点：一是放宽了对源信号的稀疏性要求，只要求源信号存在离散的时频单源点；二是源个数估计过程中人工参数少且容易设置。在估计出混合矩阵后，针对单源邻域通过子空间投影算法估计该时频邻域内源信号对应的混合矢量；针对多源邻域，通过度量协方差矩阵对角线元素与非对角线元素之间的差异估计该时频邻域内不为零的源信号个数及其对应的混合矩阵。最后通过求解各时频邻域上混合矩阵的伪逆估计出源信号。由于该算法可以准确估计出任意时频邻域内同时存在的源信号数目，克服了原有方法设定固定的源数目而导致分离性能下降的不足。仿真结果验证了算法的有效性。
第五章研究了适定/超定条件下特定目标信号的盲提取问题。将基于线性瞬时混合模型的约束独立分量分析理论框架推广到线性延迟混合模型，总结了约束的类型和来源，并提出了两类新的求解方法。在此基础上，利用目标信号的循环平稳特性提出了基于循环平稳约束的盲信号提取算法并分析了算法的收敛条件以及约束条件中的人工参数的选取依据；利用目标信号波达方向信息提出了基于空域约束的盲信号提取算法并分析了算法的收敛条件以及约束条件中的人工参数的选取依据。由于约束独立分量分析算法将目标信号的先验信息与独立分量分析算法的学习过程相结合，保证算法可以收敛到满足约束条件的极值点，有效解决了盲信号分离存在的顺序模糊性问题，并提高了目标源信号的估计性能。仿真结果验证了算法的有效性。
The extensive use of the radar, communication and other electronic equipmentsmakes the electromagnetic environment more and more complex, where large numbersof signals are overlapped in the frequency domain at any same time. Thus, theprobability of receiving mixing signals overlapping in the time frequency domain byvarious communication systems increases dramatically. In order to estimate theparameters and extract the information from the signals of interest, the correspondingsignals must be separated from the mixtures firstly. Blind source separation (BSS) is asignal processing technique that consists of retrieving n unobservable sources fromm linear combinations provided by sensors. The adaption ability of the communicationsystems can be greatly improved by utilizing the BSS methods, which consists of majorsignificance in practical field. This paper is aiming to investigate the following fourproblems according to two different factors (e.g., the reception structure of multiplesensors and the sparseness property of signals):1) the problems related to both the DOAestimation and BSS for sparse signals based on controlled sensor arrangement;2) theproblems related to both the DOA estimation and BSS for non-sparse signals based oncontrolled sensor arrangement;3) the problems of BSS based on random receptionstructure of multiple sensors;4) the problems of extraction of the specific target signals.The content of the dissertation is as follows.
In chapter2, the problem related to both the DOA estimation and BSS, whichconsists in estimating the waveforms of signals and their physical directions ofpropagation and given a controlled sensor arrangement is investigated. A novelunderdetermined number of sources, DOA and waveforms of sources estimationalgorithm in the TF domain is proposed under the assumption that the number ofsources is less than that of sensors in each time frequency partition domain by utilizingthe concept and method of sparse signal representation. Firstly, partition the timefrequency support domain of the sources into disjointed time frequency neighborhoods,and estimate the DOA and the corresponding waveform of the active sources in eachtime frequency neighborhood domain by the sparse reconstruction method, and thenestimate the number of the source signals and the their DOA simultaneously by thecluster validation technique based on k-means clustering algorithm. Finally, the timefrequency transformation of each signal can be obtained by splicing the estimated resultin each time frequency partition domain while the permutation problem betweendifferent time frequency partition domain can be solved by the utilization of the DOAinformation and then the waveforms in the time domain of the source signals can beobtained by the inverse transform. The proposed algorithm can estimate the number of sources, the DOAs and waveforms of the source signals simultaneously in theunderdetermined case and the major advantages of the proposed algorithm are asfollows:1) Compared with the clustering-based DOA estimation algorithms, theproposed algorithm relaxes the necessary condition that the number of the signals is lessthan that of the sensors. Moreover, the number of the signals needs not to be known as apriori and can be obtained along with the DOA estimation process. Compared with thehigh-order cumulants based DOA estimation algorithms, the proposed algorithmrequires less number of samples and achieves higher DOA estimation accuracy.2) Theproposed algorithm provides better performance in separating source signals than thesubspace-based method which requires the same sparseness assumption as that in theproposed algorithm since it can estimate the number of active sources at any timefrequency partition domain. The simulation results show the efficacy and accuracy ofthe proposed algorithms.
In chapter3, the problem related to both the DOA estimation and BSS, whichconsists in estimating the waveforms of signals and their physical directions ofpropagation and given a controlled sensor arrangement is investigated, where the sourcesignals are not sparse in time or time frequency domain. A new method fordirection-of-arrival (DOA) estimation of cyclostationary signals is proposed. Based on ajoint diagonalization of combined set of extended cyclic autocorrelation matrices, theproposed DOA estimation algorithm can address for the underdetermined case. Firstly,calculate cyclic correlation matrix of the mixtures corresponding to different cyclefrequencies and time lags, stack the cyclic correlation matrices with the same cyclefrequency and different time lags into the extended cyclic correlation matrix form byalgebraic method. Then estimate the signal subspaces and the noise subspaces by jointdiagonalize a set of extended cyclic correlation matrices with different cycle frequencies.Finally estimate the DOAs by the conventional subspace-like methods. The proposedDOA estimation algorithm does not require the source signals to be sparse in the timefrequency domain and can estimate the DOAs in the underdetermined case bygenerating a virtual of both the effective aperture and the number of sensors of theconsidered array through the algebraic method. Furthermore, it is insensitive to thespatially correlated noise and its estimation performance can be improved greatly byutilizing multiple extended cyclic autocorrelation matrices of source signals. After theestimation of DOAs, a new method for source separation based on ExpectationMaximization (EM) algorithm and optimum beamforming in the time frequency domainis proposed. The source signals in each time frequency neighborhood can be extractedby obtaining the corresponding optimum beamformers. The probability densityparameters of the sources and noise required in the calculation of the optimumbeamformers can be estimated by the expectation maximization method. Simulationresults confirm the validity and high performance of the proposed algorithm.
In chapter4, the problem of underdetermined BSS in the case that the receptionstructure of multiple channels is random is investigated. A novel underdeterminedseparation algorithm based on single source point detection and improved matrixdiagonalization is proposed in the case of that there should be some single source pointsfor each source and the number of active sources at any time frequency neighborhooddoes not exceed that of sensors. Firstly, calculate the time frequency ratio matrix of themixtures and detect single source point of each source signal by hist stat. of the real partand imag part of the time frequency ratio matrix, then estimate the number of the sourcesignals and the mixing matrix simultaneously by clustering the mixing vectors in thecorresponding single source point set by utilizing the cluster validation technique basedon k-means clustering algorithm. The proposed mixing matrix estimation algorithm hastwo major advantanges:1) relaxes the sparsity requirement of the source signals and canestimate the mixing matrix under the assumption that there exist disjointed single sourcepoints for each source signal.2) user-parameters in the estimation process of number ofsources are easy to set. After the mixing matrix has been estimated, the source signalscan be obtained by the improved matrix diagonalization algorithm. For the single sourceneighborhood, the corresponding mixing vector can be obtained by the subspaceprojection method, and for the multiple source neighborhood where there are more thanone active sources, the corresponding mixing matrix can be obtained by measuring thedifferences between the diagonal elements and non-diagonal elements of the covariancematrix. Finally, the source signals in each time frequency neighborhood can beestimated by calculating the peuside inverse of the corresponding mixing matrix. Theproposed algorithm improves the accuracy over the matrix diagonalization basedalgorithm via estimating the number of active sources at any time frequencyneighborhood. Simulation results confirm the validity and high performance of theproposed algorithm.
In chapter5, the problem of the specific signal extraction in theoverdetermined/determined case is investigated. The constrained independentcomponent analysis (CICA) framework under the linear instantaneous mixing model isgeneralized to the linear delayed mixing model, the types and the sources of theconstraints are summarized, and two novel solutions to the CICA framework areproposed. Based on the new CICA framework, two new CICA algorithms are proposedby utilizing different prior information of the communication signals. One is CICAalgorithm with cyclosationary constraint which exploits the cyclostationary property ofthe target signals as prior information. The convergence condition and the selectionrules of user parameters are analyzed. The other is CICA algorithm with spatialconstraint which exploits the spatial information corresponding to the Directions ofArrival (DOAs) of the SOIs as prior information. The convergence condition and theselection rules of user parameters are analyzed. The CICA algorithms incorporate the a priori information about the desired signal as the additional constraints into theconventional ICA learning process and means that only a single statisticallyindependent component will be extracted for the given constraint, which effectivelysolve the order ambiguities in conventional BSS problem. The correspondingexperiment results show the efficacy and accuracy of the proposed algorithms.
第二章研究了特定阵列且源信号是稀疏信号的欠定DOA估计和盲分离问题。假设任意时频邻域内同时存在的源信号数目小于阵元数目，提出了基于稀疏重构和聚类验证的源个数、DOA与信号波形联合估计算法。首先将信号的时频支撑域划分成若干不相交的时频邻域，利用稀疏重构算法估计出每个时频邻域内不为零的源信号的DOA及其对应的时频域波形，然后利用聚类验证方法对所有时频邻域的DOA估计结果进行聚类分析，从而完成源个数和所有源信号DOA的联合估计。最后，根据DOA完成整个时频域上不同源信号波形的拼接，并通过逆变换求解源信号的时域波形。本章算法充分利用了源信号的时频稀疏性，同时实现了欠定混合条件下源个数、DOA以及信号波形的估计。在DOA估计方面，相比基于高阶累积量的欠定DOA估计算法，所需的样本点数更少，估计精度更高。相比基于聚类的欠定DOA估计方法，放宽了对源信号的稀疏性要求并克服了要求事先已知源个数的不足。在源信号分离方面，由于算法可以准确估计任意时频邻域内同时存在的源信号数目，相比具有相同稀疏性假设的子空间投影算法，提高了源信号的估计性能。仿真结果验证了算法的有效性。
第三章研究了特定阵列且源信号是非稀疏信号的欠定DOA估计和盲分离问题，提出了基于拓展循环自相关矩阵联合对角化的欠定DOA估计算法。首先计算信号在不同循环频率、不同时延处的循环自相关矩阵，利用代数方法将同一循环频率、不同时延处的循环自相关矩阵表示成拓展循环自相关矩阵形式，从而得到一组不同循环频率的拓展循环自相关矩阵集合；然后，利用联合对角化的方法估计出信号子空间和噪声子空间；最后根据子空间类方法估计出源信号的DOA。该算法通过代数手段实现了阵列的虚拟扩展，不要求源信号在时频域是稀疏的，可以有效地实现欠定条件下非稀疏源信号的DOA估计。同时，由于联合利用了多个不同循环频率的拓展循环自相关矩阵，显著提高了算法的DOA估计精度以及对色噪声的适应能力。在估计出源信号的DOA的基础上，提出了基于期望最大化和时频域最优波束形成的欠定盲分离算法。通过期望最大化算法估计出不同时频邻域内的各源信号和噪声的概率分布参数，在此基础上分别求解不同时频邻域内各源信号对应的最优波束形成器以完成源信号的分离。该算法充分利用了源信号和噪声的概率分布信息，可以有效实现欠定条件下非稀疏源信号的分离。仿真结果表明本章算法可以有效完成欠定条件下非稀疏源信号的DOA估计及盲分离。
第四章研究了任意阵列的欠定盲分离问题。假设所有源信号均存在时频单源点且任意时频邻域内同时存在的源信号数目不大于阵元数目，提出了基于时频单源点检测以及改进的矩阵对角化的欠定盲分离算法。首先计算混合信号的时频比矩阵，对时频比矩阵的实部和虚部进行直方图统计以完成时频单源点的检测。然后利用基于k均值的聚类验证算法对时频单源点集对应的奇异向量进行聚类分析从而完成源个数和混合矩阵的联合估计。该混合矩阵估计算法有两个优点：一是放宽了对源信号的稀疏性要求，只要求源信号存在离散的时频单源点；二是源个数估计过程中人工参数少且容易设置。在估计出混合矩阵后，针对单源邻域通过子空间投影算法估计该时频邻域内源信号对应的混合矢量；针对多源邻域，通过度量协方差矩阵对角线元素与非对角线元素之间的差异估计该时频邻域内不为零的源信号个数及其对应的混合矩阵。最后通过求解各时频邻域上混合矩阵的伪逆估计出源信号。由于该算法可以准确估计出任意时频邻域内同时存在的源信号数目，克服了原有方法设定固定的源数目而导致分离性能下降的不足。仿真结果验证了算法的有效性。
第五章研究了适定/超定条件下特定目标信号的盲提取问题。将基于线性瞬时混合模型的约束独立分量分析理论框架推广到线性延迟混合模型，总结了约束的类型和来源，并提出了两类新的求解方法。在此基础上，利用目标信号的循环平稳特性提出了基于循环平稳约束的盲信号提取算法并分析了算法的收敛条件以及约束条件中的人工参数的选取依据；利用目标信号波达方向信息提出了基于空域约束的盲信号提取算法并分析了算法的收敛条件以及约束条件中的人工参数的选取依据。由于约束独立分量分析算法将目标信号的先验信息与独立分量分析算法的学习过程相结合，保证算法可以收敛到满足约束条件的极值点，有效解决了盲信号分离存在的顺序模糊性问题，并提高了目标源信号的估计性能。仿真结果验证了算法的有效性。
The extensive use of the radar, communication and other electronic equipmentsmakes the electromagnetic environment more and more complex, where large numbersof signals are overlapped in the frequency domain at any same time. Thus, theprobability of receiving mixing signals overlapping in the time frequency domain byvarious communication systems increases dramatically. In order to estimate theparameters and extract the information from the signals of interest, the correspondingsignals must be separated from the mixtures firstly. Blind source separation (BSS) is asignal processing technique that consists of retrieving n unobservable sources fromm linear combinations provided by sensors. The adaption ability of the communicationsystems can be greatly improved by utilizing the BSS methods, which consists of majorsignificance in practical field. This paper is aiming to investigate the following fourproblems according to two different factors (e.g., the reception structure of multiplesensors and the sparseness property of signals):1) the problems related to both the DOAestimation and BSS for sparse signals based on controlled sensor arrangement;2) theproblems related to both the DOA estimation and BSS for non-sparse signals based oncontrolled sensor arrangement;3) the problems of BSS based on random receptionstructure of multiple sensors;4) the problems of extraction of the specific target signals.The content of the dissertation is as follows.
In chapter2, the problem related to both the DOA estimation and BSS, whichconsists in estimating the waveforms of signals and their physical directions ofpropagation and given a controlled sensor arrangement is investigated. A novelunderdetermined number of sources, DOA and waveforms of sources estimationalgorithm in the TF domain is proposed under the assumption that the number ofsources is less than that of sensors in each time frequency partition domain by utilizingthe concept and method of sparse signal representation. Firstly, partition the timefrequency support domain of the sources into disjointed time frequency neighborhoods,and estimate the DOA and the corresponding waveform of the active sources in eachtime frequency neighborhood domain by the sparse reconstruction method, and thenestimate the number of the source signals and the their DOA simultaneously by thecluster validation technique based on k-means clustering algorithm. Finally, the timefrequency transformation of each signal can be obtained by splicing the estimated resultin each time frequency partition domain while the permutation problem betweendifferent time frequency partition domain can be solved by the utilization of the DOAinformation and then the waveforms in the time domain of the source signals can beobtained by the inverse transform. The proposed algorithm can estimate the number of sources, the DOAs and waveforms of the source signals simultaneously in theunderdetermined case and the major advantages of the proposed algorithm are asfollows:1) Compared with the clustering-based DOA estimation algorithms, theproposed algorithm relaxes the necessary condition that the number of the signals is lessthan that of the sensors. Moreover, the number of the signals needs not to be known as apriori and can be obtained along with the DOA estimation process. Compared with thehigh-order cumulants based DOA estimation algorithms, the proposed algorithmrequires less number of samples and achieves higher DOA estimation accuracy.2) Theproposed algorithm provides better performance in separating source signals than thesubspace-based method which requires the same sparseness assumption as that in theproposed algorithm since it can estimate the number of active sources at any timefrequency partition domain. The simulation results show the efficacy and accuracy ofthe proposed algorithms.
In chapter3, the problem related to both the DOA estimation and BSS, whichconsists in estimating the waveforms of signals and their physical directions ofpropagation and given a controlled sensor arrangement is investigated, where the sourcesignals are not sparse in time or time frequency domain. A new method fordirection-of-arrival (DOA) estimation of cyclostationary signals is proposed. Based on ajoint diagonalization of combined set of extended cyclic autocorrelation matrices, theproposed DOA estimation algorithm can address for the underdetermined case. Firstly,calculate cyclic correlation matrix of the mixtures corresponding to different cyclefrequencies and time lags, stack the cyclic correlation matrices with the same cyclefrequency and different time lags into the extended cyclic correlation matrix form byalgebraic method. Then estimate the signal subspaces and the noise subspaces by jointdiagonalize a set of extended cyclic correlation matrices with different cycle frequencies.Finally estimate the DOAs by the conventional subspace-like methods. The proposedDOA estimation algorithm does not require the source signals to be sparse in the timefrequency domain and can estimate the DOAs in the underdetermined case bygenerating a virtual of both the effective aperture and the number of sensors of theconsidered array through the algebraic method. Furthermore, it is insensitive to thespatially correlated noise and its estimation performance can be improved greatly byutilizing multiple extended cyclic autocorrelation matrices of source signals. After theestimation of DOAs, a new method for source separation based on ExpectationMaximization (EM) algorithm and optimum beamforming in the time frequency domainis proposed. The source signals in each time frequency neighborhood can be extractedby obtaining the corresponding optimum beamformers. The probability densityparameters of the sources and noise required in the calculation of the optimumbeamformers can be estimated by the expectation maximization method. Simulationresults confirm the validity and high performance of the proposed algorithm.
In chapter4, the problem of underdetermined BSS in the case that the receptionstructure of multiple channels is random is investigated. A novel underdeterminedseparation algorithm based on single source point detection and improved matrixdiagonalization is proposed in the case of that there should be some single source pointsfor each source and the number of active sources at any time frequency neighborhooddoes not exceed that of sensors. Firstly, calculate the time frequency ratio matrix of themixtures and detect single source point of each source signal by hist stat. of the real partand imag part of the time frequency ratio matrix, then estimate the number of the sourcesignals and the mixing matrix simultaneously by clustering the mixing vectors in thecorresponding single source point set by utilizing the cluster validation technique basedon k-means clustering algorithm. The proposed mixing matrix estimation algorithm hastwo major advantanges:1) relaxes the sparsity requirement of the source signals and canestimate the mixing matrix under the assumption that there exist disjointed single sourcepoints for each source signal.2) user-parameters in the estimation process of number ofsources are easy to set. After the mixing matrix has been estimated, the source signalscan be obtained by the improved matrix diagonalization algorithm. For the single sourceneighborhood, the corresponding mixing vector can be obtained by the subspaceprojection method, and for the multiple source neighborhood where there are more thanone active sources, the corresponding mixing matrix can be obtained by measuring thedifferences between the diagonal elements and non-diagonal elements of the covariancematrix. Finally, the source signals in each time frequency neighborhood can beestimated by calculating the peuside inverse of the corresponding mixing matrix. Theproposed algorithm improves the accuracy over the matrix diagonalization basedalgorithm via estimating the number of active sources at any time frequencyneighborhood. Simulation results confirm the validity and high performance of theproposed algorithm.
In chapter5, the problem of the specific signal extraction in theoverdetermined/determined case is investigated. The constrained independentcomponent analysis (CICA) framework under the linear instantaneous mixing model isgeneralized to the linear delayed mixing model, the types and the sources of theconstraints are summarized, and two novel solutions to the CICA framework areproposed. Based on the new CICA framework, two new CICA algorithms are proposedby utilizing different prior information of the communication signals. One is CICAalgorithm with cyclosationary constraint which exploits the cyclostationary property ofthe target signals as prior information. The convergence condition and the selectionrules of user parameters are analyzed. The other is CICA algorithm with spatialconstraint which exploits the spatial information corresponding to the Directions ofArrival (DOAs) of the SOIs as prior information. The convergence condition and theselection rules of user parameters are analyzed. The CICA algorithms incorporate the a priori information about the desired signal as the additional constraints into theconventional ICA learning process and means that only a single statisticallyindependent component will be extracted for the given constraint, which effectivelysolve the order ambiguities in conventional BSS problem. The correspondingexperiment results show the efficacy and accuracy of the proposed algorithms.
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