A general class of nonlinear normalized adaptive filteringalgorithms

The normalized least mean square (NLMS) algorithm is an important variant of the classical LMS algorithm for adaptive linear filtering. It possesses many advantages over the LMS algorithm, including having a faster convergence and providing for an automatic time-varying choice of the LMS stepsize parameter that affects the stability, steady-state mean square error (MSE), and convergence speed of the algorithm. An auxiliary fixed step-size that is often introduced in the NLMS algorithm has the advantage that its stability region (step-size range for algorithm stability) is independent of the signal statistics. In this paper, we generalize the NLMS algorithm by deriving a class of nonlinear normalized LMS-type (NLMS-type) algorithms that are applicable to a wide variety of nonlinear filter structures. We obtain a general nonlinear NLMS-type algorithm by choosing an optimal time-varying step-size that minimizes the next-step MSE at each iteration of the general nonlinear LMS-type algorithm. As in the linear case, we introduce a dimensionless auxiliary step-size whose stability range is independent of the signal statistics. The stability region could therefore be determined empirically for any given nonlinear filter type. We present computer simulations of these algorithms for two specific nonlinear filter structures: Volterra filters and the previously proposed class of Myriad filters. These simulations indicate that the NLMS-type algorithms, in general, converge faster than their LMS-type counterparts     

A robust variable step-size LMS-type algorithm: analysis andsimulations

A number of time-varying step-size algorithms have been proposed to enhance the performance of the conventional LMS algorithm. Experimentation with these algorithms indicates that their performance is highly sensitive to the noise disturbance. This paper presents a robust variable step-size LMS-type algorithm providing fast convergence at early stages of adaptation while ensuring small final misadjustment. The performance of the algorithm is not affected by existing uncorrelated noise disturbances. An approximate analysis of convergence and steady-state performance for zero-mean stationary Gaussian inputs and for nonstationary optimal weight vector is provided. Simulation results comparing the proposed algorithm to current variable step-size algorithms clearly indicate its superior performance for cases of stationary environments. For nonstationary environments, our algorithm performs as well as other variable step-size algorithms in providing performance equivalent to that of the regular LMS algorithm     

自适应算法在干扰抵消器应用中的比较研究

文中介绍了自适应滤波算法的原理和干扰抵消器工作原理，并将LMS算法、NLMS算法和变步长LMS算法分别应用在了干扰抵消器中进行了仿真。仿真的结果表明，三种自适应算法运用到了干扰抵消器中，都可以很好地滤除干扰，提取有用信号。其中运用了变步长LMS算法的干扰抵消器无论在收敛速度和滤波性能上，都要强于其他两种算法。     

一种新的变步长LMS算法

在对基本LMS算法分析的基础上,通过构造步长因子μ与误差信号e（n）之间的非线性函数,提出一种新的变步长最小均方误差（LMS）算法,并且分析了参数的取值对算法性能的影响。该算法通过调整步长参数,使权向量达到最优,有效改善了收敛速度与稳态误差的性能。理论分析和仿真结果表明,与基本LMS算法以及部分同类变步长LMS算法相比,该算法具有更快的收敛速度和更小的稳态误差,进一步验证了新算法优于这里所述其他算法。     

一种新的变步长变换域自适应滤波算法

变换域LMS算法能通过正交变换有效降低输入信号自相关矩阵特征值的分散程度,可提高算法的收敛速度;变步长LMS算法可以克服固定步长因子所导致的算法在较快收敛速度和较小稳态误差之间存在的矛盾,从而获得较快的收敛速度和较好的收敛结果。将二者相结合,提出了一种新的变步长变换域自适应滤波算法。计算机仿真结果表明该算法具有更快的收敛速度和更小的稳态误差,并且运算量较少,具有良好的实用性能。     

基于小波变换的变步长LMS自适应滤波算法

变步长LMS自适应滤波算法通过构造合适的步长因子有效的解决了传统LMS算法收敛速度和稳态误差相矛盾的问题.变换域LMS自适应滤波算法通过正交变换降低了输入信号矩阵的相关性,提高了算法的收敛速度.将这两种算法相结合,提出了一种新的基于小波变换的变步长LMS自适应滤波算法.仿真结果表明,该算法无论是收敛速度还是稳态误差都有了很大的提高.     

基于NLMS的CDMA盲自适应多用户检测算法研究

多用户检测是抑制DS-CDMA系统多址干扰最有效的技术之一。由于所需的先验知识仪有期望用户的地址码,盲多用户检测技术的研究尤受重视。最小输出能量(MOE)准则被广泛用于盲线性多用户检测。目前已提出的该类检测器多采用LMS或RLS算法。本文则研究基于NLMS算法的盲自适应检测技术,并进一步提出盲自适应变步长NLMS检测器和参数可变的盲自适应变步长NLMS检测器。它们具备很好的收敛速度和跟踪能力,以及较高的输出信干比,同时计算复杂度仅为O(3N)或O(4N),非常适合硬件实现。     

A two-stage affine projection algorithm with mean-square-error-matching step-sizes

This paper proposes a two-stage affine projection algorithm (APA) with different projection orders and step-sizes. The proposed algorithm has a high projection order and a fixed step-size to achieve fast convergence rate at the first stage and a low projection order and a variable step-size to achieve small steady-state estimation errors at the second stage. The stage transition moment from the first to the second stage is determined by examining, from a stochastic point of view, whether the current error reaches the steady-state value. Moreover, in order to prevent the sudden drop of convergence rate on switching from a high projection order to a low projection order, a matching step-size method has been introduced to determine the initial step-size of the second stage by matching the mean-square errors (MSEs) before and after the transition moment. In order to continuously reduce steady-state estimation errors, the proposed algorithm adjusts the step-size of the second stage by employing a simple algorithm. Because of the reduced projection orders and variable step-size in the steady-state, the algorithm achieves improved performance as well as extremely low computational complexity as compared to the existing APAs with selective input vectors and APAs with variable step-size.     

On the convergence behavior of the LMS and the normalized LMSalgorithms

It is shown that the normalized least mean square (NLMS) algorithm is a potentially faster converging algorithm compared to the LMS algorithm where the design of the adaptive filter is based on the usually quite limited knowledge of its input signal statistics. A very simple model for the input signal vectors that greatly simplifies analysis of the convergence behavior of the LMS and NLMS algorithms is proposed. Using this model, answers can be obtained to questions for which no answers are currently available using other (perhaps more realistic) models. Examples are given to illustrate that even quantitatively, the answers obtained can be good approximations. It is emphasized that the convergence of the NLMS algorithm can be speeded up significantly by employing a time-varying step size. The optimal step-size sequence can be specified a priori for the case of a white input signal with arbitrary distribution     

依据迭代系数状态因子分段的变步长NLMS算法

针对固定步长的归一化LMS算法（NLMS）存在不能同时兼顾收敛速度与稳态误差的问题,本文提出一种依据迭代系数状态因子进行分段的变步长NLMS算法。该变步长NLMS算法采用迭代系数状态因子作为表征迭代系数与实际系数的逼近状态的指标。当迭代系数状态因子值大于1,则说明迭代系数有偏离真实系数的趋势,此时采用步长因子较大的变步长方案;反之,说明迭代系数有逼近真实系数的趋势,应该采样步长因子较小的变步长方案。这样的自适应选择措施使得算法具有较强的收敛能力。理论分析和实验表明:在同样实验条件下,本文算法能够获得比其他文献更快的收敛速度和更小的稳态误差。      

Variable step-size Griffiths’ algorithm for improved performance of feedforward/feedback active noise control

A new robust computationally efficient variable step-size LMS algorithm is proposed and it is applied for secondary path (SP) identification of feedforward and feedback active noise control (ANC) systems. The proposed variable step-size Griffiths’ LMS (VGLMS) algorithm not only uses a step-size, but also the gradient itself, based on the cross-correlation between input and the desired signal. This makes the algorithm robust to both stationary and non-stationary observation noise and the additional computational load involved for this is marginal. Further, in terms of convergence speed and error, it is better than those by the Normalized LMS (NLMS) and the Zhang’s method (Zhang in EURASIP J. Adv. Signal Process. 2008(529480):1–9, 2008). The convergence rate of the feedforward and feedback ANC systems with the VGLMS algorithm for SP identification is faster (by a factor of 2 and 3, respectively) compared with that using NLMS algorithm. For feedforward ANC, its convergence rate is faster (3 times) compared with Akhtar’s algorithm (Akhtar in IEEE Trans Audio Speech Lang Process 14(2), 2006). Also, for higher main path lengths compared with SP, the proposed algorithm is computationally efficient compared with Akhtar’s algorithm.     

变步长NLMS算法在CDMA窄带干扰抑制中的应用

CDMA窄带干扰可以通过自适应线性预测器(ALP)来抑制。而自适应算法的稳态均方误差(MSE)与收敛速度是决定其性能的关键。在正规最小均方误差算法(NLMS)的基础上引入变步长NLMS算法(VSS-NLMS)，并对其进行了稳态性能分析。通过计算机仿真模拟，证实此算法的稳态MSE和收敛速度都明显优于NLMS算法，因而改善了对CDMA窄带干扰的抑制能力。     

平方根变步长lp范数LMS算法的稀疏系统辨识

针对稀疏未知系统的辨识问题,提出了一种基于lp(0相似文献   

Convergence and performance analysis of the normalized LMSalgorithm with uncorrelated Gaussian data

It is demonstrated that the normalized least mean square (NLMS) algorithm can be viewed as a modification of the widely used LMS algorithm. The NLMS is shown to have an important advantage over the LMS, which is that its convergence is independent of environmental changes. In addition, the authors present a comprehensive study of the first and second-order behavior in the NLMS algorithm. They show that the NLMS algorithm exhibits significant improvement over the LMS algorithm in convergence rate, while its steady-state performance is considerably worse     

一种改进的可变步长LMS算法及性能分析

为解决自适应算法的收敛速度和稳态误差两者间的矛盾,对归一化的最小均方(NLMS)算法、变步长算法及可变步长NVSS算法进行了研究,并结合变步长的思想,提出了一种新的可变步长算法。新的算法中引入合适的遗忘因子与修正参数来建立与步长因子间的函数关系,加快了算法收敛速度的同时,也能在非平稳的环境中有好的跟踪能力。最后把不同的算法应用到系统辨识系统中,通过MATLAB进行实验仿真,结果证实了新提出的算法有快的收敛速度和跟踪时变系统的能力。     

一种改进的NLMS算法在声回波抵消中的应用

收敛速度和残余均方误差是衡量最小均方算法性能的重要指标。在声回波抵消算法中,为了寻求收敛速度快和计算量小的自适应算法,在归一化最小均方误差算法基础上,把当前时刻以前的误差引入归一化收敛因子中得到一种新算法,可以减小信号样本波动对权重带来的影响。该算法比传统的归一化最小均方算法收敛性能更好,稳态失调也比其小。计算机仿真结果表明,新算法在自适应回波抵消中的综合性能要优于传统的归一化最小均方误差算法。     

一种约束稳定性最小均方噪声对消算法

研究了最小均方误差(LMS)算法、归一化的最小均方(NLMS)算法及变步长NLMS算法在自适应噪声干扰抵消器中的应用,针对目前这些算法在噪声对消器应用中的缺点,将约束稳定性最小均方(CS-LMS)算法应用到噪声处理中,并进一步结合变步长的思想提出来一种新的变步长CS-LMS算法。通过MATLAB进行仿真分析,结果证实提出的算法与其他算法相比,能很好地滤除掉噪声从而得到期望信号,明显的降低了稳态误差,并拥有好的收敛速度。     

The stability of variable step-size LMS algorithms

Variable step-site LMS (VSLMS) algorithms are a popular approach to adaptive filtering, which can provide improved performance while maintaining the simplicity and robustness of conventional fixed step-size LMS. Here, we examine the stability of VSLMS with uncorrelated stationary Gaussian data. Most VSLMS described in the literature use a data-dependent step-size, where the step-size either depends on the data before the current time (prior step-size rule) or through the current time (posterior step-size rule). It has often been assumed that VSLMS algorithms are stable (in the sense of mean-square bounded weights), provided that the step-size is constrained to lie within the corresponding stability region for the LMS algorithm. For a single tap fitter, we find exact expressions for the stability region of VSLMS over the classes of prior and posterior step-sizes and show that the stability region for prior step size coincides with that of fixed step-size, but the region for posterior step-size is strictly smaller than for fixed step-size. For the multiple tap case, we obtain bounds on the stability regions with similar properties. The approach taken here is a generalization of the classical method of analyzing, the exponential stability of the weight covariance equation for LMS. Although it is not possible to derive a weight covariance equation for general data-dependent VSLMS, the weight variances can be upper bounded by the solution of a linear time-invariant difference equation, after appropriately dealing with certain nonlinear terms. For prior step-size (like fixed step-size), the state matrix is symmetric, whereas for posterior step-size, the symmetry is lost, requiring a more detailed analysis. The results are verified by computer simulations     

LMS和归一化LMS算法收敛门限与步长的确定

从LMS算法失调量的准确表达式出发,根据输入信号特征值分布重新研究了LMS,归一化LMS(Normalized LMS,NLMS)算法收敛的必要条件,推导出LMS和NLMS 算法收敛的步长门限,并分析了输入信号特征值分布、滤波器阶数对算法收敛步长门限的影响,推导出满足性能失调下步长的自适应计算公式,减小了应用 LMS,NLMS算法时步长选取的盲目性,与已有的算法相比,具有计算简单、实用、自适应性能强,同时可获得满意失调量的特点,计算机模拟结果表明该方法的正确性。     

集成多种自适应滤波算法的回声消除器

如何选择自适应算法的步长,从而有效解决收敛速度和稳态失调之间的矛盾是回声消除中的一个重要问题。论文提出一种集成多种自适应滤波算法的回声消除框架,以挖掘不同自适应滤波算法以及不同步长选择之间的互补性,来获得稳定的消除效果。所提算法可以分析同一时刻不同算法的误差,并始终选择一种最好的算法。通过对LMS、NLMS、PNLMS和IPNLMS这四种自适应算法的结合实验,显示了该算法可以集合各种算法以及步长选择的优点,具有更快的收敛速度和良好的稳态特性。