多分量信号分离与参数估计研究
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摘要
在当今信息时代,信号环境复杂多变。对于接收设备而言,接收到的信号通常为多个分量信号的混合。对多分量信号进行分离,以提取出有用信号中蕴涵的信息,成为在理论上和实践上均具有重要意义的研究课题。与传统单分量信号的处理不同,多分量信号处理难度和计算复杂度更大。本文针对这一问题,首先按照通道数目与分量信号数目大小关系进行了分类,对于不同类型,明确了解决问题的不同前提条件和思路。其次,对于单通道这一特殊情况,阐明了多分量信号分离与参数估计的一致性。在此基础上,本文对于单通道多分量信号分离与参数估计,提出了一系列算法。同时,在正定条件下,对传统的独立分量分析方法进行了改进。主要成果如下:
1.在单通道条件下,提出了一种基于累积量方程组的角度调制信号混合矢量估计算法。算法通过对角度调制信号等价概率密度函数的推导和各统计量的计算,建立累积量方程组,并通过方程组的求解得到混合矢量的估计。该算法对多分量角度调制信号混合矢量进行估计时,并不需要分量信号的具体调制类型的先验信息,只需要它们属于角度调制信号即可,使其具有较为广泛的应用范围。
2.在单通道条件下,针对各分量信号具有相同信号形式的情况,提出了一种基于重要性采样的联合参数估计算法,并针对多分量多项式相位信号和多分量正弦调频信号,分别推导了重要性采样估计器。算法采用了两次解耦的思想,首先是对最大似然估计中与数据呈线性关系的参数和与数据呈非线性关系的参数的解耦,其次是通过重要性采样,对多分量信号的解耦。作为一种非迭代算法,该算法避免了常规迭代算法中初值选择不当而陷于局部极值的不利影响;同时,相对于直接针对多分量信号的全局最优算法的联合搜索,该算法通过对多分量信号的解耦,减少了搜索维数。
3.在单通道条件下,针对各分量信号为脉冲串形式的情况,分别提出了基于信号模型和基于奇异值分解的单通道多分量脉冲串信号分离算法。基于信号模型的算法利用脉冲串信号特点,将信号与混合系统建模为线性方程组的形式,通过对方程组的求解,恢复各分量信号。在这一算法中,针对分量脉冲串信号固定脉冲重复间隔和变化脉冲重复间隔的情况,分别进行了讨论。此外,基于奇异值分解的算法利用固定脉冲重复间隔的脉冲串信号的周期性,将单通道混合信号重排为矩阵形式,并通过奇异值分解实现多分量信号分离。在这些算法中,对于不同分量信号的脉内信息不作具体要求。
4.在正定条件下,提出了一种基于相关熵的盲源分离算法,作为对独立分量分析方法的改进。与传统独立分量分析方法利用四阶统计量或时间结构的盲源分离不同,算法从信息理论学习中的相关熵概念出发,利用相关熵中蕴涵的各偶数阶统计信息,通过参数化中心相关熵与独立性测度的关系,建立代价函数,并通过优化算法对其进行寻优,从而得到解混矩阵并分离出源信号。
In modern information age, the signal environment is complicated and varying. The receiver always receives the mixture of many multicomponent signals. Separating these signals in order to extract the information implied in the useful signal, becomes a research task with significance both in theory and in practice. However, unlike the processing technologies specified for the monocomponent signal, the ones for the multicomponent signals are more difficult, and have heavier computational complexity. Aiming at this multicomponent case, this paper sorts the separation problem into different categories according to the relationship between the number of channels and the number of components. Further, the coherence of separation and parameter estimation of multicomponent signals in single channel case is illustrated. On this basis, this paper proposes a series of algorithms for the multicomponent signal separation and parameter estimation in a single channel. Besides, for the determined separation problem, this paper improves the traditional independent component analysis method. The main contributions of this paper are as follows:
1. For the single channel case, a mixing vector estimation algorithm of multicomponent angle modulated signals based on cumulant system of equations is proposed. This algorithm derives the equivalent probability density function of the angle modulated signals, computes the corresponding statistics, and establishes the cumulant system of equations. Then the mixing vector estimation is achieved through the solution of the system of equations. This algorithm does not require specific information about the modulation types of these angle modulated signals, and can be used in a wide range of applications.
2. For the single channel case, a joint parameter estimation algorithm based on importance sampling is proposed, where each component signal has the same expression. The importance sampling estimators for the multicomponent polynomial phase signals and for the multicomponent sinusoidal frequency modulated signals, respectively, are derived. This algorithm has two decoupling operations. The first one is to decouple the parameters linearly related to the data and those nonlinearly related to the data in maximum likelihood estimation, while the other one is to decouple multicomponent signals using importance sampling. As a non-iterative algorithm, this algorithm avoids getting the local maxima from an inappropriate choice of the initial value. Besides, as opposed to the global optimization algorithm where the joint grid search is directly applied on the multicomponent signals, this algorithm decreases the searching dimension via the decoupling of the multicomponent signals.
3. For the single channel case, the multicomponent pulse train signal separation algorithm based on the signal model and the one based on singular value decomposition are proposed, respectively. The algorithm based on the signal model uses characteristics of the pulse train signal to model the signal and the mixing system as the form of the linear system of equations. Subsequently, the component signals are recovered via the solution of the system of equations. This algorithm has two versions, one is for the fixed pulse repetition interval signals, and the other is for the varying pulse repetition interval signals. Besides, the algorithm based on singular value decomposition uses the periodicity of the fixed pulse repetition interval signal to reconstruct the mixing signal to a matrix form. Subsequently, the multicomponent signal separation is achieved based on singular value decomposition. These algorithms do not have the specific request for the intra-pulse information.
4. For the determined case, a blind source separation algorithm is presented, as an improvement for the traditional independent component analysis. As opposed to the blind source separation based on the fourth statistics or the temporal structure, this algorithm is from the concept of correntropy in information theoretic learning. Using the information of even order statistics implied in correntropy, the cost function is established based on the relationship between the parameterized center correntropy and the test of independence. Subsequently, the demixing matrix and the recovered sources are obtained by using the optimization algorithm.
1.在单通道条件下,提出了一种基于累积量方程组的角度调制信号混合矢量估计算法。算法通过对角度调制信号等价概率密度函数的推导和各统计量的计算,建立累积量方程组,并通过方程组的求解得到混合矢量的估计。该算法对多分量角度调制信号混合矢量进行估计时,并不需要分量信号的具体调制类型的先验信息,只需要它们属于角度调制信号即可,使其具有较为广泛的应用范围。
2.在单通道条件下,针对各分量信号具有相同信号形式的情况,提出了一种基于重要性采样的联合参数估计算法,并针对多分量多项式相位信号和多分量正弦调频信号,分别推导了重要性采样估计器。算法采用了两次解耦的思想,首先是对最大似然估计中与数据呈线性关系的参数和与数据呈非线性关系的参数的解耦,其次是通过重要性采样,对多分量信号的解耦。作为一种非迭代算法,该算法避免了常规迭代算法中初值选择不当而陷于局部极值的不利影响;同时,相对于直接针对多分量信号的全局最优算法的联合搜索,该算法通过对多分量信号的解耦,减少了搜索维数。
3.在单通道条件下,针对各分量信号为脉冲串形式的情况,分别提出了基于信号模型和基于奇异值分解的单通道多分量脉冲串信号分离算法。基于信号模型的算法利用脉冲串信号特点,将信号与混合系统建模为线性方程组的形式,通过对方程组的求解,恢复各分量信号。在这一算法中,针对分量脉冲串信号固定脉冲重复间隔和变化脉冲重复间隔的情况,分别进行了讨论。此外,基于奇异值分解的算法利用固定脉冲重复间隔的脉冲串信号的周期性,将单通道混合信号重排为矩阵形式,并通过奇异值分解实现多分量信号分离。在这些算法中,对于不同分量信号的脉内信息不作具体要求。
4.在正定条件下,提出了一种基于相关熵的盲源分离算法,作为对独立分量分析方法的改进。与传统独立分量分析方法利用四阶统计量或时间结构的盲源分离不同,算法从信息理论学习中的相关熵概念出发,利用相关熵中蕴涵的各偶数阶统计信息,通过参数化中心相关熵与独立性测度的关系,建立代价函数,并通过优化算法对其进行寻优,从而得到解混矩阵并分离出源信号。
In modern information age, the signal environment is complicated and varying. The receiver always receives the mixture of many multicomponent signals. Separating these signals in order to extract the information implied in the useful signal, becomes a research task with significance both in theory and in practice. However, unlike the processing technologies specified for the monocomponent signal, the ones for the multicomponent signals are more difficult, and have heavier computational complexity. Aiming at this multicomponent case, this paper sorts the separation problem into different categories according to the relationship between the number of channels and the number of components. Further, the coherence of separation and parameter estimation of multicomponent signals in single channel case is illustrated. On this basis, this paper proposes a series of algorithms for the multicomponent signal separation and parameter estimation in a single channel. Besides, for the determined separation problem, this paper improves the traditional independent component analysis method. The main contributions of this paper are as follows:
1. For the single channel case, a mixing vector estimation algorithm of multicomponent angle modulated signals based on cumulant system of equations is proposed. This algorithm derives the equivalent probability density function of the angle modulated signals, computes the corresponding statistics, and establishes the cumulant system of equations. Then the mixing vector estimation is achieved through the solution of the system of equations. This algorithm does not require specific information about the modulation types of these angle modulated signals, and can be used in a wide range of applications.
2. For the single channel case, a joint parameter estimation algorithm based on importance sampling is proposed, where each component signal has the same expression. The importance sampling estimators for the multicomponent polynomial phase signals and for the multicomponent sinusoidal frequency modulated signals, respectively, are derived. This algorithm has two decoupling operations. The first one is to decouple the parameters linearly related to the data and those nonlinearly related to the data in maximum likelihood estimation, while the other one is to decouple multicomponent signals using importance sampling. As a non-iterative algorithm, this algorithm avoids getting the local maxima from an inappropriate choice of the initial value. Besides, as opposed to the global optimization algorithm where the joint grid search is directly applied on the multicomponent signals, this algorithm decreases the searching dimension via the decoupling of the multicomponent signals.
3. For the single channel case, the multicomponent pulse train signal separation algorithm based on the signal model and the one based on singular value decomposition are proposed, respectively. The algorithm based on the signal model uses characteristics of the pulse train signal to model the signal and the mixing system as the form of the linear system of equations. Subsequently, the component signals are recovered via the solution of the system of equations. This algorithm has two versions, one is for the fixed pulse repetition interval signals, and the other is for the varying pulse repetition interval signals. Besides, the algorithm based on singular value decomposition uses the periodicity of the fixed pulse repetition interval signal to reconstruct the mixing signal to a matrix form. Subsequently, the multicomponent signal separation is achieved based on singular value decomposition. These algorithms do not have the specific request for the intra-pulse information.
4. For the determined case, a blind source separation algorithm is presented, as an improvement for the traditional independent component analysis. As opposed to the blind source separation based on the fourth statistics or the temporal structure, this algorithm is from the concept of correntropy in information theoretic learning. Using the information of even order statistics implied in correntropy, the cost function is established based on the relationship between the parameterized center correntropy and the test of independence. Subsequently, the demixing matrix and the recovered sources are obtained by using the optimization algorithm.
引文
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