直扩信号参数估计的盲源分离方法研究
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摘要
直接序列扩频信号又称直扩信号，在军事和民用通信领域都有广泛的应用。在电子信息对抗中，如何在没有足够多的先验知识的条件下检测敌方发射的直扩信号，并且对信号相关参数进行准确估计是一个困难的问题。而在实际通信环境中，非协作接收方获得的信号往往是多个直扩信号的混合，这就使得多个信号的联合参数估计问题变得更加复杂。本文针对这一课题，提出将盲源分离的思想引入多个直扩信号的参数估计问题中，并将研究重点集中于接近实际的通信环境中，本文的创新及主要工作包括以下几个方面：
1、针对实际通信环境中需要检测的直扩信号的数目动态变化的情况，将具有快速收敛性的RLS算法与源数目估计技术相结合，提出一种基于动态源数目估计的改进RLS盲分离算法。通过在线估计观测信号均值和协方差矩阵，定义一个关于源信号数目的代价函数，然后最小化代价函数可得到源信号数目的估计。利用估计得到的源数目动态调整RLS算法中的分离矩阵及其它相关参数矩阵的维数，进而使得改进RLS盲分离算法能够有效的分离超定和数目动态变化的源信号。仿真实验表明，新的算法比现有算法具有更好的收敛性和分离性能。在直扩信号的参数估计仿真中，新算法能够有效地跟踪直扩信号源数目，并且准确估计出相关参数。
2、针对信噪比较低情况下多个直扩信号参数的联合估计问题，分析了一类基于非高斯性的代价函数，并将关于源信号估计的后验期望函数与一类非线性去噪函数等价，理论上证明了去噪与分离的等价性。在描述线性函数去噪的基础上，详细阐述了非线性函数的去噪原理。在没有噪声的协方差矩阵等先验知识的条件下，仿真实验表明其性能比现有的需要先验知识的算法具有更好的分离效果。而且在多个直扩信号的参数估计中也有好的结果，能够在信噪比小于0dB的条件下准确估计出相关参数。
3、针对多个直扩信号卷积混合的盲分离问题，首先通过矢量化方法将其变为矩阵联合分块对角化问题。然后基于两类代价函数，分别提出一种新的矩阵联合分块对角化算法。针对第一类代价函数，考虑到现有的迭代非正交联合分块对角化算法都存在不收敛的情况，利用分离矩阵的特殊结构确保其可逆性，使得算法的迭代过程稳定。依据代价函数的最小化等价于矩阵中每个分块的范数最小化，将整个分离矩阵的迭代更新转化成每个分块的迭代更新，利用最小化条件得到迭代算法。实数和复数两种情况下的算法都进行了推导。针对第二类代价函数，利用矩阵矢量化算子将问题转化为一个多参数的最小二乘问题，通过构造正交投影算子的逐元素微分矩阵，推导出一种实现简单的迭代联合分块对角化算法。仿真实验首先验证了两种新算法在不同条件下的性能，然后对三个基带直扩信号的卷积混合进行盲分离，实验结果表明新算法能够成功地将多个直扩信号分离出来。
4、针对强噪声条件下多个直接序列扩频信号在多径信道传输后的卷积盲分离问题，在无线通信中增加接收天线数目可以获得分集增益的原理启发下，通过放宽接收端数目的条件，提出了一个基于特征函数和矩阵代数的卷积盲分离方法。首先利用多接收端的条件，构建接收信号模型，且证明此模型符合独立子空间分析的基本条件；接着通过引入独立子空间分析的定义，证明直扩信号源的特征函数的Hessian矩阵满足块对角化性质；然后利用矩阵代数中矩阵分解的方法，将多个矩阵的联合块对角化问题转化为求取某个矩阵代数的可交换代数的一般性矩阵问题。当这个一般性矩阵被对角化时，卷积盲分离问题求解简化为求取一组齐次线性方程组的一个随机解。理论分析还表明，当噪声信号为高斯噪声且具有相同的能量时，算法对于噪声具有非常强的鲁棒性。最后通过计算机仿真和与现有算法的比较，验证了新算法的有效性和可靠性，且具有更好的分离性能和相对更少的约束条件。
Direct sequence spread spectrum signals which are also called DSSS signals are widelyused in military and civilian communications. Especially in situation of electronic war,it’s difficult to detect and estimate parameters of enemy’s signals without enough priorinformation. And in the real environment of communication,the problem becomes morecomplex. Because that received signals are almost the mixture of multiple DSSS signals.To deal with this situation, we introduce the theory of Blind Source Separation into thejoint parameters estimation problem,and mainly consider the models which are closed toreal communication environment. Our innovations and main work is composed of theseparts:
1. Consider that the number of DSSS signals which is needed to detect is unknown and changes with time in the real environment, a novel improved RLS algorithm combing with an online source number estimation method is proposed. First using the estimation of mean value and covariance matrix of observed signals to define a cost function.Then the function is minimized to achieve the estimation of source number. The dimensions of separated matrix and other related parameter matrices can be dynamic modified according to the estimated source number, which makes the RLS-like algorithm can separate the source signals efficiently in the super-condition and dynamic source numbers environments. Computer simulations show that the proposed algorithm is better than the existing algorithms with faster convergence and lower error index. In the application of parameters estimation of DSSS signals, the proposed algorithms can also trace the change of source number and estimate the parameters accurately.
2. To solve the problem of joint parameters estimation of multiple DSSS signals in the low signal-to-noise ratio environment, the Expectation Maximum algorithm is usedto alternately estimate the mixing matrix and original signals. Then a denosingsource separation framework is proposed, using the equvalence of nonlineardenosing function and posterior expectation function of source estimation, manynonlinear Independent Component Analysis based algorithms is included in thisframework. The denosing principle of nonlinear function is expounded based on thedescription of the linear denosing function. And the unitary of separating anddenosing is also explained. In the condition of none prior knowledge of noisecovariance martrix, simulations result show that proposed denosing sourceseparation algorithm has better performance than the exsiting algorithm. And in theapplication of DSSS signals parameters estimation, results show that proposedmethod can also work well in the environment of high level of noise.
3. Two new joint block diagonalization algorithms are proposed to solve the blindconvolutive separation of DSSS signals. The convolutive mixture is rewritten as aninstantaneous one which satisfied the joint block diagonalization model. In theminimization problem of the first cost function, considering that the exsiting iterativealgorithms may not converge to the correct solution, a special structured separationmatrix which is always invertible is proposed to aviod the divergence of thealgorithm. The whole matrix iteration is transformed to update of the each blocksub-matrix as that the minimization of the cost function is equivalent to theminimization of Frobenius norm of each block. The iterative algorithm is deducedboth in the situation of real and complex model. Then in the optimization of thesecond cost function,with the help of matrix-vector operator, the original peoblem istransfromed to a multivariant least squares model. A simple iterative joint blockdiagonalization algorithm is deduced using the differential matrix of orthogonalprojection operator. Computer simulation demonstrate the good performance of two algorithms in the different condition, and the base band DSSS signals can also beseparated successfully in the application of blind convolutive separation.
4. A method based on characteristic function and matrxi-*algebraic is proposed to solvethe convolutive blind separation of DSSS signals in the high noise level environment.The main idea is from the knowledge of wireless communication that increasing thenumbers of receivers to improve the signal to noise ratio. First,the signals modelunder the condition of multiple sensors is built and proved to be consistent with thebasis of the Independent subspace analysis. Then the concept of independentsubspace analysis is introduced,also the Hessian of Characteristic functions of theDSSS signals are proved to be block diagonal.Finally the matrix decompositiontheory of matrix-*algebraic is used to transform the joint block diagonalization ofmultiple matries into the problem of finding a generic matrix of the commutantalgebra, which is correspond to the matrix-*algebraic formed by the Hessian ofCharacteristic functions of the observed signals. And the diagonalization of thegeneric matrix is proved to be equivalent with the Joint block diagnolization of somematrix-*algebraic. Then the original problem comes down to finding a randomsolution of a homogeneous linear equations. The theory analyze implies that theproposed algorithm is very robust if the sensor noise is gaussian and shares the samevariance,whenever the noise is white or color. Computer simulation shows thevalidity and reliability of the algorithm in the condition of three DSSS signals. Theresult also demonstrates that the proposed algorithm has better performance and lessconstraints comparing with the exsiting algorithms.
1、针对实际通信环境中需要检测的直扩信号的数目动态变化的情况，将具有快速收敛性的RLS算法与源数目估计技术相结合，提出一种基于动态源数目估计的改进RLS盲分离算法。通过在线估计观测信号均值和协方差矩阵，定义一个关于源信号数目的代价函数，然后最小化代价函数可得到源信号数目的估计。利用估计得到的源数目动态调整RLS算法中的分离矩阵及其它相关参数矩阵的维数，进而使得改进RLS盲分离算法能够有效的分离超定和数目动态变化的源信号。仿真实验表明，新的算法比现有算法具有更好的收敛性和分离性能。在直扩信号的参数估计仿真中，新算法能够有效地跟踪直扩信号源数目，并且准确估计出相关参数。
2、针对信噪比较低情况下多个直扩信号参数的联合估计问题，分析了一类基于非高斯性的代价函数，并将关于源信号估计的后验期望函数与一类非线性去噪函数等价，理论上证明了去噪与分离的等价性。在描述线性函数去噪的基础上，详细阐述了非线性函数的去噪原理。在没有噪声的协方差矩阵等先验知识的条件下，仿真实验表明其性能比现有的需要先验知识的算法具有更好的分离效果。而且在多个直扩信号的参数估计中也有好的结果，能够在信噪比小于0dB的条件下准确估计出相关参数。
3、针对多个直扩信号卷积混合的盲分离问题，首先通过矢量化方法将其变为矩阵联合分块对角化问题。然后基于两类代价函数，分别提出一种新的矩阵联合分块对角化算法。针对第一类代价函数，考虑到现有的迭代非正交联合分块对角化算法都存在不收敛的情况，利用分离矩阵的特殊结构确保其可逆性，使得算法的迭代过程稳定。依据代价函数的最小化等价于矩阵中每个分块的范数最小化，将整个分离矩阵的迭代更新转化成每个分块的迭代更新，利用最小化条件得到迭代算法。实数和复数两种情况下的算法都进行了推导。针对第二类代价函数，利用矩阵矢量化算子将问题转化为一个多参数的最小二乘问题，通过构造正交投影算子的逐元素微分矩阵，推导出一种实现简单的迭代联合分块对角化算法。仿真实验首先验证了两种新算法在不同条件下的性能，然后对三个基带直扩信号的卷积混合进行盲分离，实验结果表明新算法能够成功地将多个直扩信号分离出来。
4、针对强噪声条件下多个直接序列扩频信号在多径信道传输后的卷积盲分离问题，在无线通信中增加接收天线数目可以获得分集增益的原理启发下，通过放宽接收端数目的条件，提出了一个基于特征函数和矩阵代数的卷积盲分离方法。首先利用多接收端的条件，构建接收信号模型，且证明此模型符合独立子空间分析的基本条件；接着通过引入独立子空间分析的定义，证明直扩信号源的特征函数的Hessian矩阵满足块对角化性质；然后利用矩阵代数中矩阵分解的方法，将多个矩阵的联合块对角化问题转化为求取某个矩阵代数的可交换代数的一般性矩阵问题。当这个一般性矩阵被对角化时，卷积盲分离问题求解简化为求取一组齐次线性方程组的一个随机解。理论分析还表明，当噪声信号为高斯噪声且具有相同的能量时，算法对于噪声具有非常强的鲁棒性。最后通过计算机仿真和与现有算法的比较，验证了新算法的有效性和可靠性，且具有更好的分离性能和相对更少的约束条件。
Direct sequence spread spectrum signals which are also called DSSS signals are widelyused in military and civilian communications. Especially in situation of electronic war,it’s difficult to detect and estimate parameters of enemy’s signals without enough priorinformation. And in the real environment of communication,the problem becomes morecomplex. Because that received signals are almost the mixture of multiple DSSS signals.To deal with this situation, we introduce the theory of Blind Source Separation into thejoint parameters estimation problem,and mainly consider the models which are closed toreal communication environment. Our innovations and main work is composed of theseparts:
1. Consider that the number of DSSS signals which is needed to detect is unknown and changes with time in the real environment, a novel improved RLS algorithm combing with an online source number estimation method is proposed. First using the estimation of mean value and covariance matrix of observed signals to define a cost function.Then the function is minimized to achieve the estimation of source number. The dimensions of separated matrix and other related parameter matrices can be dynamic modified according to the estimated source number, which makes the RLS-like algorithm can separate the source signals efficiently in the super-condition and dynamic source numbers environments. Computer simulations show that the proposed algorithm is better than the existing algorithms with faster convergence and lower error index. In the application of parameters estimation of DSSS signals, the proposed algorithms can also trace the change of source number and estimate the parameters accurately.
2. To solve the problem of joint parameters estimation of multiple DSSS signals in the low signal-to-noise ratio environment, the Expectation Maximum algorithm is usedto alternately estimate the mixing matrix and original signals. Then a denosingsource separation framework is proposed, using the equvalence of nonlineardenosing function and posterior expectation function of source estimation, manynonlinear Independent Component Analysis based algorithms is included in thisframework. The denosing principle of nonlinear function is expounded based on thedescription of the linear denosing function. And the unitary of separating anddenosing is also explained. In the condition of none prior knowledge of noisecovariance martrix, simulations result show that proposed denosing sourceseparation algorithm has better performance than the exsiting algorithm. And in theapplication of DSSS signals parameters estimation, results show that proposedmethod can also work well in the environment of high level of noise.
3. Two new joint block diagonalization algorithms are proposed to solve the blindconvolutive separation of DSSS signals. The convolutive mixture is rewritten as aninstantaneous one which satisfied the joint block diagonalization model. In theminimization problem of the first cost function, considering that the exsiting iterativealgorithms may not converge to the correct solution, a special structured separationmatrix which is always invertible is proposed to aviod the divergence of thealgorithm. The whole matrix iteration is transformed to update of the each blocksub-matrix as that the minimization of the cost function is equivalent to theminimization of Frobenius norm of each block. The iterative algorithm is deducedboth in the situation of real and complex model. Then in the optimization of thesecond cost function,with the help of matrix-vector operator, the original peoblem istransfromed to a multivariant least squares model. A simple iterative joint blockdiagonalization algorithm is deduced using the differential matrix of orthogonalprojection operator. Computer simulation demonstrate the good performance of two algorithms in the different condition, and the base band DSSS signals can also beseparated successfully in the application of blind convolutive separation.
4. A method based on characteristic function and matrxi-*algebraic is proposed to solvethe convolutive blind separation of DSSS signals in the high noise level environment.The main idea is from the knowledge of wireless communication that increasing thenumbers of receivers to improve the signal to noise ratio. First,the signals modelunder the condition of multiple sensors is built and proved to be consistent with thebasis of the Independent subspace analysis. Then the concept of independentsubspace analysis is introduced,also the Hessian of Characteristic functions of theDSSS signals are proved to be block diagonal.Finally the matrix decompositiontheory of matrix-*algebraic is used to transform the joint block diagonalization ofmultiple matries into the problem of finding a generic matrix of the commutantalgebra, which is correspond to the matrix-*algebraic formed by the Hessian ofCharacteristic functions of the observed signals. And the diagonalization of thegeneric matrix is proved to be equivalent with the Joint block diagnolization of somematrix-*algebraic. Then the original problem comes down to finding a randomsolution of a homogeneous linear equations. The theory analyze implies that theproposed algorithm is very robust if the sensor noise is gaussian and shares the samevariance,whenever the noise is white or color. Computer simulation shows thevalidity and reliability of the algorithm in the condition of three DSSS signals. Theresult also demonstrates that the proposed algorithm has better performance and lessconstraints comparing with the exsiting algorithms.
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