复杂电磁环境下的欠定盲源分离技术研究
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摘要
雷达、通信等各种电子设备的广泛使用,形成了时域高度密集、频谱严重混叠的复杂电磁环境。在复杂电磁环境下,接收到的混合信号在时域、频域都是相互交叠的。此外,由于潜在的源信号数目未知而阵元数目有限,混合信号中源的数目往往大于阵元数目。此时,直接对混合信号进行参数估计和信息提取是非常困难的,通常首先需要对混合信号进行分离。本文对复杂电磁环境下的欠定盲分离问题进行了深入研究,充分利用了源信号在时频域上的稀疏性,以及独立性、循环平稳性、周期性等其它统计特性,把欠定盲分离问题转化为适定或超定问题,完成源信号的分离。其主要工作概括如下:
第二章针对源信号在时频域上存在单源邻域,并且在任意时频点上同时存在的源信号数小于阵元数的情况,提出了基于单源检测和改进的子空间投影的欠定盲分离算法。首先利用特征值分解检测出信号在时频域上的单源邻域,然后通过系统聚类法对单源邻域对应的特征矢量进行聚类分析,从而完成混合矩阵的估计,算法不需要已知源信号的数目并且具有很好的鲁棒性。在估计出混合矩阵的条件下,通过准确地估计出任意时频点上同时存在的源信号数目,改进了基于子空间的源信号分离算法,克服了原有方法设定固定的源数目而导致分离性能降低的不足。仿真结果验证了算法的有效性。
第三章针对源信号是相互独立的,并且在任意时频邻域内同时存在的源信号数不大于阵元数的情况,提出了基于二阶循环相关和矩阵对角化的欠定盲分离算法。首先计算信号的循环相关矩阵,通过张量正则分解估计出混合矩阵,由于该方法充分利用了源信号的循环平稳特性,当源信号具有不同的循环频率时能够显著提高混合矩阵的估计精度。在估计出混合矩阵后,通过度量协方差矩阵的对角化程度来找出不为零的源信号对应的混合矩阵,从而估计出源信号,该方法充分利用了源信号的独立性,进一步放宽了信号在时频域上的稀疏性条件,只要在任意时频邻域内同时存在的源信号数不超过阵元数就可以完成源信号的分离。仿真结果表明本文算法能够很好地分离出源信号。
第四章针对源信号的自源时频点与互源时频点不混叠的情况,提出了基于空间时频分布的欠定盲分离算法。首先计算信号的空间时频分布矩阵,并把自源点对应的时频分布矩阵表示成三阶张量的形式,从而把欠定问题转化为超定问题,然后利用联合对角化或张量正则分解估计出混合矩阵和源信号。该算法不要求源信号在时域是稀疏的或相互独立的,仿真结果表明本文算法具有很好的源信号估计性能。
第五章在单通道条件下分别研究了同步和非同步长码DS-CDMA信号扩频序列的盲估计问题。对于同步的情况,提出了基于ICA和重叠分段的扩频序列盲估计算法,首先对信号进行载波和码片同步得到基带采样信号,然后用ICA方法分别估计出每个用户的扩频序列片段,并通过重叠部分的相关性解决扩频序列片段的次序置换和幅度模糊问题,从而估计出每个用户完整周期的扩频序列,最后推导了该算法的理论性能。对于非同步的情况,提出了基于Complex-ICA和重叠分段的扩频序列盲估计算法,首先通过Complex-ICA和重叠分段估计出每个用户存在频偏的基带扩频波形,然后对每个用户分别进行载波同步和码片同步,从而估计出每个用户的扩频序列。仿真结果验证了算法的有效性。
The extensive use of the radar, communication and other eletronic equipments makes the electromagnetic environment in the war field more and more complex, where large numbers of signals are overlapped in the frequency domain at any same time. In this circumstance the received signal is always non-disjointed in time frequency (TF) domain. Furthermore, in practical field the number of sources is larger than that of sensors sometimes as a result of unknowing the number of the potential sources beforehand and that the number of the sensors is finite. To estimate the parameters and extract the transmitted information from the each interceped signal, the original signals must be separated from the mixtures firstly. The problem of the underdetermined signal blind separation in the complex electromagnetic environment is investigated in this paper. The underdetermined problem is transformed into over or well determined problem by exploiting the sparsity of sources in the TF domain, independence, cyclostationarity, periodicity and other statistic property, and then separate all the original signals. The main contributions are detailed as follows:
In chapter 2, the underdertemined blind separation algorithm based on single source detection and subspace projection is proposed in the case of that there should be some single-source TF neighborhoods for each source and the number of active sources at any TF point is strictly less than the number of sensors. Fristly, detect the single source neighborhoods by eigenvalue decomposition and then estimate the mixing matrix via clustering the principal eigenvectors of the covariance matrixes corresponding to the single source neighborhoods without knowing the number of original sources. Extract the original signals by the modified subspace algorithm when the mixing matrix has been estimated. Because of the inequality between the assumed number and real number will lead to estimation performance degradation of source signals, to overcome the drawback this paper improve the based-subspace algorithm for extracting the original signals via estimating the number of active sources at any TF point. Simulation results verify the effectiveness of the proposed algorithm.
In chapter 3, the novel underdertemined blind separation algorithm based on second-order cyclic correlation and covariance matrix diagonalization is proposed in the case of that the sources are independent and the number of active sources in any TF neighborhood does not exceed that of sensors.Fristly, calculate cyclic correlation matrix of the mixtures and stack the cyclic correlation matrices corresponding to different cycle frequencies and time lags into a three order tensor, achieve the estimation of mixing matrix by canonical decomposition. To exploit the cyclostationarity of the sources sufficiently, the proposed method improves the estimation accuracy when the cyclic frequency of the signals are different. Separate the source by measuring the diagonalization degree of the covariance matrix after the mixing matrix has been estimated. This method considers the independence of the sources sufficiently and relaxes the sparsity condition of sources in TF domain further, which allows the number of the active sources in any TF neighborhood simultaneously equals to that of sensors. Simulation results demonstrate that the proposed algorithm performs well.
In chapter 4, the Underdetermined blind source separation algorithm based on TF distribution is proposed in the case of that the auto-source TF point and cross-source TF point is disjointed. Fristly calculate the spatial TF distribution matrix of the mixture and fold the TFD matrices into a third-order tensor corresponding to the auto-source TF points, then estimate the mixing matrix by tensor canonical decomposition or joint diagonalization. Secondly, transform the underdetermined problem into the over-determined case with knowing the mixing matrix. Finally we obtain the sources by calculating the pseudo-inverse matrix and TF synthesis techniques. It is not necessary that assume the sources are sparse in time domain or independent for the proposed algorithm. The simulations verify the capabilities of the proposed method.
In chapter 5, the spreading sequences estimation of the synchronous and non synchronous DS-CDMA signal in the case of the single channel is investigated. For synchronous DS-CDMA, the estimation algorithm based on ICA and overlapped segmentation is proposed. Firstly, the baseband samples are obtained with chip period by carrier frequency synchronization and chip timing, and then divide the intact spreading sequences into many overlapped short-time segments so as to recover them in a sequential procedure. Estimate the spreading sequences segments of each user respectively by ICA and then solve the order permutation and amplitude ambiguity by the correlation of the overlap. The intact spreading sequences are estimated by splicing the segments and the closed-form expression that characterizes the estimation performance of the proposed algorithm in theory is obtained. For non-synchronous DS-CDMA, the baseband spreading wave with frequency offset of each user is estimated by the method based on Complex-ICA and overlapped segmentation, and then extract the spreading sequences of each user by carrier frequency synchronization and chip timing. Simulation results verify the effectiveness of the proposed algorithms.
第二章针对源信号在时频域上存在单源邻域,并且在任意时频点上同时存在的源信号数小于阵元数的情况,提出了基于单源检测和改进的子空间投影的欠定盲分离算法。首先利用特征值分解检测出信号在时频域上的单源邻域,然后通过系统聚类法对单源邻域对应的特征矢量进行聚类分析,从而完成混合矩阵的估计,算法不需要已知源信号的数目并且具有很好的鲁棒性。在估计出混合矩阵的条件下,通过准确地估计出任意时频点上同时存在的源信号数目,改进了基于子空间的源信号分离算法,克服了原有方法设定固定的源数目而导致分离性能降低的不足。仿真结果验证了算法的有效性。
第三章针对源信号是相互独立的,并且在任意时频邻域内同时存在的源信号数不大于阵元数的情况,提出了基于二阶循环相关和矩阵对角化的欠定盲分离算法。首先计算信号的循环相关矩阵,通过张量正则分解估计出混合矩阵,由于该方法充分利用了源信号的循环平稳特性,当源信号具有不同的循环频率时能够显著提高混合矩阵的估计精度。在估计出混合矩阵后,通过度量协方差矩阵的对角化程度来找出不为零的源信号对应的混合矩阵,从而估计出源信号,该方法充分利用了源信号的独立性,进一步放宽了信号在时频域上的稀疏性条件,只要在任意时频邻域内同时存在的源信号数不超过阵元数就可以完成源信号的分离。仿真结果表明本文算法能够很好地分离出源信号。
第四章针对源信号的自源时频点与互源时频点不混叠的情况,提出了基于空间时频分布的欠定盲分离算法。首先计算信号的空间时频分布矩阵,并把自源点对应的时频分布矩阵表示成三阶张量的形式,从而把欠定问题转化为超定问题,然后利用联合对角化或张量正则分解估计出混合矩阵和源信号。该算法不要求源信号在时域是稀疏的或相互独立的,仿真结果表明本文算法具有很好的源信号估计性能。
第五章在单通道条件下分别研究了同步和非同步长码DS-CDMA信号扩频序列的盲估计问题。对于同步的情况,提出了基于ICA和重叠分段的扩频序列盲估计算法,首先对信号进行载波和码片同步得到基带采样信号,然后用ICA方法分别估计出每个用户的扩频序列片段,并通过重叠部分的相关性解决扩频序列片段的次序置换和幅度模糊问题,从而估计出每个用户完整周期的扩频序列,最后推导了该算法的理论性能。对于非同步的情况,提出了基于Complex-ICA和重叠分段的扩频序列盲估计算法,首先通过Complex-ICA和重叠分段估计出每个用户存在频偏的基带扩频波形,然后对每个用户分别进行载波同步和码片同步,从而估计出每个用户的扩频序列。仿真结果验证了算法的有效性。
The extensive use of the radar, communication and other eletronic equipments makes the electromagnetic environment in the war field more and more complex, where large numbers of signals are overlapped in the frequency domain at any same time. In this circumstance the received signal is always non-disjointed in time frequency (TF) domain. Furthermore, in practical field the number of sources is larger than that of sensors sometimes as a result of unknowing the number of the potential sources beforehand and that the number of the sensors is finite. To estimate the parameters and extract the transmitted information from the each interceped signal, the original signals must be separated from the mixtures firstly. The problem of the underdetermined signal blind separation in the complex electromagnetic environment is investigated in this paper. The underdetermined problem is transformed into over or well determined problem by exploiting the sparsity of sources in the TF domain, independence, cyclostationarity, periodicity and other statistic property, and then separate all the original signals. The main contributions are detailed as follows:
In chapter 2, the underdertemined blind separation algorithm based on single source detection and subspace projection is proposed in the case of that there should be some single-source TF neighborhoods for each source and the number of active sources at any TF point is strictly less than the number of sensors. Fristly, detect the single source neighborhoods by eigenvalue decomposition and then estimate the mixing matrix via clustering the principal eigenvectors of the covariance matrixes corresponding to the single source neighborhoods without knowing the number of original sources. Extract the original signals by the modified subspace algorithm when the mixing matrix has been estimated. Because of the inequality between the assumed number and real number will lead to estimation performance degradation of source signals, to overcome the drawback this paper improve the based-subspace algorithm for extracting the original signals via estimating the number of active sources at any TF point. Simulation results verify the effectiveness of the proposed algorithm.
In chapter 3, the novel underdertemined blind separation algorithm based on second-order cyclic correlation and covariance matrix diagonalization is proposed in the case of that the sources are independent and the number of active sources in any TF neighborhood does not exceed that of sensors.Fristly, calculate cyclic correlation matrix of the mixtures and stack the cyclic correlation matrices corresponding to different cycle frequencies and time lags into a three order tensor, achieve the estimation of mixing matrix by canonical decomposition. To exploit the cyclostationarity of the sources sufficiently, the proposed method improves the estimation accuracy when the cyclic frequency of the signals are different. Separate the source by measuring the diagonalization degree of the covariance matrix after the mixing matrix has been estimated. This method considers the independence of the sources sufficiently and relaxes the sparsity condition of sources in TF domain further, which allows the number of the active sources in any TF neighborhood simultaneously equals to that of sensors. Simulation results demonstrate that the proposed algorithm performs well.
In chapter 4, the Underdetermined blind source separation algorithm based on TF distribution is proposed in the case of that the auto-source TF point and cross-source TF point is disjointed. Fristly calculate the spatial TF distribution matrix of the mixture and fold the TFD matrices into a third-order tensor corresponding to the auto-source TF points, then estimate the mixing matrix by tensor canonical decomposition or joint diagonalization. Secondly, transform the underdetermined problem into the over-determined case with knowing the mixing matrix. Finally we obtain the sources by calculating the pseudo-inverse matrix and TF synthesis techniques. It is not necessary that assume the sources are sparse in time domain or independent for the proposed algorithm. The simulations verify the capabilities of the proposed method.
In chapter 5, the spreading sequences estimation of the synchronous and non synchronous DS-CDMA signal in the case of the single channel is investigated. For synchronous DS-CDMA, the estimation algorithm based on ICA and overlapped segmentation is proposed. Firstly, the baseband samples are obtained with chip period by carrier frequency synchronization and chip timing, and then divide the intact spreading sequences into many overlapped short-time segments so as to recover them in a sequential procedure. Estimate the spreading sequences segments of each user respectively by ICA and then solve the order permutation and amplitude ambiguity by the correlation of the overlap. The intact spreading sequences are estimated by splicing the segments and the closed-form expression that characterizes the estimation performance of the proposed algorithm in theory is obtained. For non-synchronous DS-CDMA, the baseband spreading wave with frequency offset of each user is estimated by the method based on Complex-ICA and overlapped segmentation, and then extract the spreading sequences of each user by carrier frequency synchronization and chip timing. Simulation results verify the effectiveness of the proposed algorithms.
引文
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