核自适应滤波算法及其在噪声对消与信道均衡中应用

发布时间：2018-11-07 19:41

【摘要】：线性自适应滤波算法解决一些问题时有一定优越性,但是,实际中所研究的问题涉及的往往是一些非线性问题。线性算法在处理非线性问题时,表现出的性能效果并不令人满意,例如,在噪声对消及信道均衡等应用场合。核方法(Kernel Methods)随着支持向量机的研究而被引入到非线性领域。核方法为研究非线性问题提供了一种技术路径,通过在合适的高维特征空间中用线性算法来处理原空间中的非线性关系。核方法已广泛应用在模式识别和图像处理等问题中。当前,存在众多的线性自适应滤波算法,如何利用这些已有成果,借助核方法研究出更多的、有效的非线性滤波算法具有重要的理论意义和价值。核方法是一种由线性算法诱导出非线性算法的有效技术。针对最小均方(LMS)算法在处理非线性问题时性能不理想的缺陷,本文利用模式识别中的核方法思想研究了两种新颖的非线性自适应滤波算法,分别是归一化最小均方(NLMS)算法和四阶误差信号最小化(LMF)算法的非线性版本,称为KNLMS算法和KLMF算法。本文的主要研究工作总结如下:(1)利用核方法原理,研究了两种核自适应滤波算法:核归一化最小均方(KNLMS)算法及核四阶误差信号最小化(KLMF)算法。提供了这两种算法的数值实验结果。(2)讨论了所研究KLMF算法在噪声对消中的应用。对比仿真实验说明了算法的可用性与有效性。(3)讨论了所研究的KLMF算法在非线性信道均衡中的应用。对比仿真实验结果说明了算法的可用性与优势,同时分析了不同参数对算法性能的影响。
[Abstract]:The linear adaptive filtering algorithm has some advantages in solving some problems, but the problems studied in practice are often related to some nonlinear problems. The performance of the linear algorithm in dealing with nonlinear problems is not satisfactory, for example, in the applications of noise cancellation and channel equalization. The kernel method (Kernel Methods) is introduced into the nonlinear field with the research of support vector machine (SVM). The kernel method provides a technical path for the study of nonlinear problems. The linear algorithm is used to deal with the nonlinear relations in the original space in a suitable high dimensional feature space. Kernel method has been widely used in pattern recognition and image processing. At present, there are many linear adaptive filtering algorithms. It is of great theoretical significance and value to study more and more effective nonlinear filtering algorithms with the help of kernel method. Kernel method is an effective technique to induce nonlinear algorithm by linear algorithm. Aiming at the shortcoming of the least mean square (LMS) algorithm in dealing with nonlinear problems, two novel nonlinear adaptive filtering algorithms are studied by using the kernel method in pattern recognition. The nonlinear versions of normalized minimum mean square (NLMS) algorithm and fourth-order error signal minimization (LMF) algorithm are called KNLMS algorithm and KLMF algorithm respectively. The main work of this paper is summarized as follows: (1) two kernel adaptive filtering algorithms, kernel normalized least mean square (KNLMS) algorithm and kernel fourth-order error signal minimization (KLMF) algorithm, are studied by using the kernel method principle. Numerical results of the two algorithms are presented. (2) the application of the proposed KLMF algorithm in noise cancellation is discussed. The simulation results show the availability and effectiveness of the proposed algorithm. (3) the application of the proposed KLMF algorithm in nonlinear channel equalization is discussed. The simulation results show the availability and advantage of the algorithm, and analyze the influence of different parameters on the performance of the algorithm.
【学位授予单位】：西华大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TN713;TN911.5

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