基于符号函数的自适应滤波器的稳态性能研究

发布时间：2018-03-17 05:03

本文选题：自适应滤波器　切入点：稳态均方误差　出处：《大连海事大学》2017年硕士论文　论文类型：学位论文

【摘要】：随着移动通信网络的迅速发展,数字信号处理技术已经得到了前所未有的发展机会,而自适应滤波器作为信号处理技术的重要组成部分,也使得自适应滤波器的发展进入了一个全新的时代。自适应滤波器已经成为许多现代通信和控制系统的关键部分,可用于系统识别、回波消除、波束形成、自适应均衡等方面。常用的自适应滤波算法有很多,其中最小均方(Least Mean Square,LMS)算法是目前最流行的自适应滤波算法,由于其简单性和鲁棒性而被广泛的应用。近些年来,相关文献已经提出了 LMS的多个改进算法,通过将估计误差函数从线性改变为非线性来克服LMS算法的一些限制,例如归一化LMS(Normalized LMS,NLMS)算法、最小混合范数(Least Mean Mixed Norm,LMMN)算法、仿射投影(Affine Projection,AP)算法等等,但是对于估计误差信号含有符号函数的这类算法,相关文献涉及的不是很多,因此,对此类算法进行详细的研究是很有必要的。本文的主要工作从以下几个方面进行:(1)对自适应滤波器的历史进行简要的分析和回顾,接下来再对LMS算法、NLMS算法以及AP算法进行详细的分析,以便对其进行更进一步的研究。(2)对含有估计误差信号f(e)=g(e)sgn(e)的自适应滤波器的稳态均方误差(Mean Square Error,MSE)和稳态跟踪超量均方误差(Tracking Excess MSE,TEMSE)进行了详细的分析,包括实数和复数两种情况,其推导过程是基于泰勒级数展开以及Price理论,推导出了适用于实值情况和复值情况下的稳态MSE和稳态TEMSE的表达式,最后对其理论值和仿真值进行大量的仿真。(3)将含有符号函数sgn(e)的非线性估计误差信号应用到NLMS算法以及AP算法中,推导出了其权矢量的更新表达式,并且对这两种新算法的MSE进行理论推导,仿真结果表明理论值与仿真值具有很好的吻合度。
[Abstract]:With the rapid development of mobile communication network, digital signal processing technology has been unprecedented development opportunities, and adaptive filter as an important part of signal processing technology, The development of adaptive filter has entered a new era. Adaptive filter has become a key part of many modern communication and control systems, which can be used for system identification, echo cancellation, beamforming, There are many kinds of adaptive filtering algorithms, among which the least mean square least Mean squared algorithm is the most popular adaptive filtering algorithm, which is widely used in recent years because of its simplicity and robustness. Several improved LMS algorithms have been proposed to overcome the limitations of the LMS algorithm by changing the estimation error function from linear to nonlinear, such as the normalized LMS(Normalized LMS-NLMS algorithm and the least mixed norm least Mean Mixed NormMMMN algorithm. Affine projection (affine projection) algorithms and so on, but for the estimation of error signals with symbolic functions, the literature is not much involved, so, It is necessary to study this kind of algorithm in detail. The main work of this paper is to analyze and review the history of adaptive filter from the following aspects: 1. Then the LMS algorithm and AP algorithm are analyzed in detail. In order to further study it, the steady-state mean square error (mean Square error) and tracking Excess mean square error (Tracking Excess MSE) of adaptive filters with estimated error signals are analyzed in detail, including real number and complex number. Based on Taylor series expansion and Price theory, the expressions of steady-state MSE and steady-state TEMSE for real and complex cases are derived. Finally, a large number of theoretical and simulation values are simulated. The nonlinear estimation error signal with sign function sgne) is applied to the NLMS algorithm and AP algorithm, and the updating expression of its weight vector is derived. The MSE of these two new algorithms is deduced theoretically, and the simulation results show that the theoretical value is in good agreement with the simulation value.
【学位授予单位】：大连海事大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TN713

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