Zero‐attracting variable‐step‐size least mean square algorithms for adaptive sparse channel estimation

Recently, sparsity‐aware least mean square (LMS) algorithms have been proposed to improve the performance of the standard LMS algorithm for various sparse signals, such as the well‐known zero‐attracting LMS (ZA‐LMS) algorithm and its reweighted ZA‐LMS (RZA‐LMS) algorithm. To utilize the sparsity of the channels in wireless communication and one of the inherent advantages of the RZA‐LMS algorithm, we propose an adaptive reweighted zero‐attracting sigmoid functioned variable‐step‐size LMS (ARZA‐SVSS‐LMS) algorithm by the use of variable‐step‐size techniques and parameter adjustment method. As a result, the proposed ARZA‐SVSS‐LMS algorithm can achieve faster convergence speed and better steady‐state performance, which are verified in a sparse channel and compared with those of other popular LMS algorithms. The simulation results show that the proposed ARZA‐SVSS‐LMS algorithm outperforms the standard LMS algorithm and the previously proposed sparsity‐aware algorithms for dealing with sparse signals. Copyright © 2015 John Wiley & Sons, Ltd.     

A simple variable step size LMS adaptive algorithm

A new LMS based variable step size adaptive algorithm is presented. The step size is incremented or decremented by a small positive value, whenever the instantaneous error is positive or negative, respectively. The algorithm is simple, robust and efficient. It is characterized by fast convergence and low steady state mean squared error. The performance of the algorithm is analysed for a stationary zero‐mean white‐Gaussian input. MC simulations are provided to demonstrate its improved performance over the conventional LMS (Proc. IEEE 1976; 64 :1151–1162) and some other variable step size adaptive algorithms (IEEE Trans. Signal Process. 1992; 40 :1633–1642; IEEE Trans. Signal Process. 1997; 45 :631–639) within a range of statistical environments. For a non‐stationary input, the proposed algorithm behaves similar to these algorithms. A modified version of the algorithm is presented to perform in the presence of abrupt changes. Copyright © 2004 John Wiley & Sons, Ltd.     

基于自适应变步长最小均方的谐波检测算法的研究

从数字信号处理中的自适应噪声对消原理出发,介绍了一种改进的变步长最小均方(LMS)算法,该算法根据基波电流和谐波电流的不相关性,利用误差信号和参考输入的互相关估计来控制迭代步长,使得步长的更新不受谐波电流的影响。该算法原理简单,运算量小,易于实现,仿真结果表明了该谐波电流检测算法的有效性。     

一种改进的变步长LMS自适应算法

为了得到一种抗干扰性能强、收敛速度快、稳态误差小的变步长LMS算法,本文分析了传统LMS算法、变步长LMS算法及其改进算法,并对现有变步长LMS算法进行分类归纳,在列出几种具有代表性算法的基础上,提出了一种改进的变步长LMS算法.新方法引入修正系数,通过当前和过去估计误差以及误差的时域均值来调节自适应算法的步长,具有收敛速度快,稳态误差小的优点,并且提高了LMS算法的抗干扰性能.文中最后给出了仿真结果,仿真结果与理论分析一致.     

一种模糊变步长自适应谐波检测算法

电力有源滤波器的成功应用依赖于精确的谐波电流检测技术。基于自适应干扰对消理论,提出一种基于模糊变步长推理的最小均方差（LMS）自适应谐波检测算法。通过分析影响LMS自适应谐波算法性能的不利因素,选取均方误差变化量和输入输出信号相关函数作为参量,建立模糊推理系统,自适应地调节算法的步长,实现谐波检测过程中,既能保证较快的动态响应速度和对噪声干扰的抑制,又能保持较高的检测精度,并通过计算机仿真及物理实验验证了该算法的有效性和可行性。     

Improvement of a Fourier coefficient estimation method using an adaptive algorithm and its performance analysis

There are many applications where it is necessary to estimate accurately the amplitude and phase of signals when the information regarding the frequencies is obtained in advance. This paper presents a new algorithm for estimating more accurately Fourier coefficients of a signal contaminated by additive noise where sinusoidal frequencies of interest are not distributed uniformly. In the proposed method, Fourier coefficients are adaptive parameters. It uses averaged gradient signals and has almost the same acquisition time as the conventional LMS algorithm with more accurate estimation. The performance analysis of the proposed method is presented and its validity and limits are verified under various conditions by computer simulations. It is shown that the proposed method has especially better performance than the LMS algorithm when both the number of frequencies and the step size parameter, µ, are large. © 2004 Wiley Periodicals, Inc. Electr Eng Jpn, 149(1): 52–60, 2004; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/eej.10362     

改进变步长LMS算法在软起动谐波检测中的应用

针对现有自适应变步长最小均方(LMS)谐波电流检测算法在低信噪比环境中易受干扰影响,提出一种改进自适应变步长LMS算法。该算法将误差信号与前一工频周期误差信号的差值作为反馈量,结合箕舌线函数构造出随动的动态因子,将此动态因子也作为调节权值的动量因子,利用自相干估计误差控制步长。该算法折中考虑收敛速度和稳态精度,并有效降低噪声信号的干扰。通过对电机软起动器工作过程中产生的周期重复性谐波进行检测和分析,证明了该谐波电流检测算法的可行性。     

Development and convergence analysis of new least‐mean‐square‐based algorithm equipped with exponential‐decay step size and disturbance compensation for active noise control

In real‐world active noise control (ANC) applications, disturbance can be picked up by error sensors and significantly degrade the steady‐state ANC performance. This study proposes two techniques in combination with a least‐mean‐square (LMS) based ANC algorithm, named normalized filtered‐x LMS/commutation error (NFxLMS/CE) algorithm, to deal with the disturbance that is independent of a reference signal. A new stochastic method to analyze convergence properties of the NFxLMS/CE algorithm under influence of the disturbance is first established. Given that the reference signal is persistently exciting of sufficient order, exponential convergence of the algorithm is derived with a step‐size condition. An exponential‐decay step size (EDSS) is then proposed to obtain a new ANC algorithm referred to as EDSS‐NFxLMS/CE algorithm. In addition, a disturbance‐compensation (DC) technique is developed for the EDSS‐NFxLMS/CE algorithm to obtain an EDSS‐NFxLMS/CE_DC algorithm such that the influence of the disturbance can be reduced. It is shown that the EDSS‐NFxLMS/CE_DC algorithm is exponentially convergent. Moreover, computer simulations show that the EDSS‐NFxLMS/CE_DC algorithm can achieve a better ANC performance in terms of convergence rate and level of noise reduction as compared with that using the EDSS‐NFxLMS/CE algorithm without DC and that using NFxLMS/CE_DC algorithm of constant step sizes. These results support the effectiveness of the proposed techniques and EDSS‐NFxLMS/CE_DC algorithm. Copyright © 2012 John Wiley & Sons, Ltd.     

二进小波变换结合自适应滤波用于局放检测

在局部放电在线监测和实时信号处理中,干扰较大时单纯依靠传统的硬件滤波较难准确提取有用信号,而在软件抗干扰中,传统多抽头自适应滤波器的参数设置也较难,有时会导致收敛很缓慢甚至不稳定。为此,提出了一种将二进小波变换与自适应滤波结合的局放信号检测算法,先对信号作简单的单抽头自适应LMS算法滤波,然后对滤波结果进行基于āTrous算法的二进小波变换来提取有用信号。通过对仿真白噪、窄带周期干扰及现场实测数据处理表明,该算法有很好的去噪性能,稳定性和实时性优于传统的自适应滤波,满足大部分工程要求,为工程实际应用提供了有效的去噪手段。     

Transient analysis of diffusion least‐mean squares adaptive networks with noisy channels

In this paper, we study the effect of noisy channels on the transient performance of diffusion adaptive network with least‐mean squares (LMS) learning rule. We first drive the update equation of diffusion LMS which incorporates the effects of noisy channels. Then, using the framework of fundamental weighted energy conservation relation, we derive closed‐form expressions for learning curves in terms of mean‐square deviation and excess mean‐square error. We also find the mean and mean‐square stability bounds of step‐size for diffusion LMS with noisy channels. We show that although noisy channels affect the performance of the diffusion LMS network, the stability bounds of the step‐size are the same form as in the ideal channels case. The derived closed‐form expressions are shown to provide a good match with values found by simulation. Copyright © 2011 John Wiley & Sons, Ltd.     

横向时延滤波和IQ正交滤波的滤波效果仿真

由于横向时延滤波和IQ正交滤波在稳定性、收敛速度和误差率等方面的性能差异对于最小均方算法(LMS,Least Mean Squares)在工程上的实际应用具有参考意义,采用数值仿真的方法模拟了两者实现自适应最小均方算法的具体过程,并对比分析了它们的滤波性能。仿真结果显示IQ正交滤波具有更高的稳定性、更快的收敛速度、更小的误差率,其滤波性能优于横向时延滤波。IQ正交滤波器的阶数为2阶,而横向时延滤波器的阶数通常>10,滤波器阶数越多引入的权噪声也会相对增加,对于稳定性、收敛速度和误差率都是不利的,因此实际应用中优先选择阶数较少的IQ正交滤波器。     

An adaptive recursive filter for autoregressive inputs

A novel off-line procedure for IIR system identification problems has been recently proposed and analysed under the assumption of a white input signal. The method happens to have a single, unbiased stationary point under this condition. This approach is based in interpolation theory and tries to overcome the drawbacks of equation- and output-error strategies. Here it is shown that the unicity of the stationary point is still preserved for a wider class of input signals, namely autoregressive processes of a certain order. With coloured input signals, an SPR condition arises for the convergence of the original on-line algorithm. A modification is proposed that eliminates this SPR condition, while leaving the stationary point untouched. Two different structures that implement the on-line algorithm are presented; the use of a lattice structure for the implementation of the recursive part of the filter is considered as well. © 1998 John Wiley & Sons, Ltd.     

Stability and linearization: discrete‐time systems

A theorem by Hadamard gives a two‐part condition under which a map from one Banach space to another is a homeomorphism. The theorem, while often very useful, is incomplete in the sense that it does not explicitly specify the family of maps for which the condition is met. Recently, under a typically weak additional assumption on the map, it was shown that Hadamard's condition is met if and only if the map is a homeomorphism with a Lipschitz continuous inverse. Here an application is given concerning the relation between the stability of a discrete‐time non‐linear system and the stability of related linear systems. Copyright © 2002 John Wiley & Sons, Ltd.     

Chaotic synchronization‐based communications using constant envelope pulse

We propose use of a constant‐envelope pulse for the purpose of improving noise‐rejection property in chaotic synchronization‐based communication systems. In a conventional system where discrete‐time chaotic signals are transmitted through the pulse amplitude modulation, the correlator output variance increases as the spreading factor decreases, while the synchronization error increases as the spreading factor increases. Therefore, it is difficult to control the bit error rate only by adjusting the spreading factor. In the proposed system, use of pulse width modulation keeps the envelope of transmitted signals constant, which leads to the correlator output with zero variance. The synchronization error is kept small because the spreading factor can be set to be one without increasing the correlator output variance. We have a result of computer simulation showing that the proposed system achieves a bit error performance better than the conventional system. In addition, a new blind adaptive algorithm is proposed which suppresses intersymbol interference. © 2008 Wiley Periodicals, Inc. Electr Eng Jpn, 163(3): 47– 56, 2008; Published online in Wiley InterScience ( www. interscience.wiley.com ). DOI 10.1002/eej.20318     

一种新的变步长LMS自适应算法及其应用

传统的固定步长的LMS算法难于同时获取较快的收敛速度与较小的稳态误差,基于这一矛盾,本文在分析基本LMS算法的基础上,提出了一种新的变步长LMS算法,该算法具有较快的收敛速度和较小的稳态误差。理论分析和计算机仿真结果表明该算法在收敛速度与稳态误差的性能上均优于基本LMS算法。尤其是在低估噪比的情况下,其性能的优越性更为突出。与传统的LMS算法相比较,新算法更适合于应用到回波消除等实时性要求高的场合。     

基于双DSP的模糊变步长自适应谐波检测的研究

对谐波检测算法进行了研究,着重研究了自适应LMS算法,利用模糊控制与自适应滤波相结合,提出一种模糊变步长谐波检测算法.利用MATLAB软件对此算法及另一种性能优越的变步长LMS算法进行比较,验证本文算法的可行性及优越性.基于以上理论研究,设计并制作电路采集板及基于双DSP的开发平台,进行了软硬件设计.最后通过实验验证了...     

Adaptive least mean squares block Volterra filters

Adaptive filtering has found many applications in situations where the underlying signals are changing or unknown. While linear filters are simple from implementation and conceptual points of view, many signals are non‐linear in nature. Non‐linear filters based on truncated Volterra expansions can effectively model a large number of systems. Unfortunately, the resulting input auto‐moment matrix is ill conditioned, which results in a slow convergence rate. This paper proposes a class of block adaptive Volterra filters in which the input sequences are Hadamard transformed to improve the condition number of the input auto‐moment matrix and consequently improve the convergence rate. This is achieved by the decorrelation effect produced by the orthogonality of the transform. Since Hadamard transformation employs only ±1's, the additional required computational and implementation burdens are few. The effect of additive white Gaussian noise is introduced. Simulation experiments are given to illustrate the improved performance of the proposed method over the conventional Volterra LMS method. Copyright © 2001 John Wiley & Sons, Ltd.     

一种改进的步长控制连续性潮流计算方法

提出了一种改进的步长控制连续性潮流计算方法.在传统连续性方法的基础上,根据预测环节中得到的信息,自动选取合适的步长,从而确保系统内的各控制元件能够按照实际的顺序进行调节,在保证计算结果正确性的基础上,又能兼顾到计算速度.对568母线系统的计算表明该算法能够有效地控制步长,在保证计算结果准确性的前提下具有较高的计算效率.     

快速收敛变换域自适应滤波算法

为了提高LMS算法均衡相关信号时的收敛性能,提出了一种新的快速收敛变换域自适应滤波算法（VS-DCTLMS）。该算法融合了归一化离散余弦变换LMS算法和变步长离散余弦变换LMS算法的优点,具有结构简单,收敛速度快,稳态误差小的特点。仿真结果表明,该算法计算量和变步长归一化LMS（VS-NLMS）算法、解相关LMS（DescorrLMS）等算法相当,但在收敛速度上具有很大优势;收敛性能和最小二乘回归算法（RLS）接近,却克服了RLS计算量大、不利于硬件实现的实际问题,是一种性能优良的可实现方法。     

一种改进的自适应谐波检测方法及其应用

提出了一种改进的变步长自适应算法,将其运用于有源电力滤波器中的谐波电流检测中,取得了很好的效果。在常见的变步长自适应算法中,步长与误差或者输入信号有关,而在自适应的调节过程中,步长存在较大的波动,影响谐波电流检测的准确性。改进的自适应算法首先对误差信号加绝对值,接着对其求均值并以该均值来控制步长的变化,从而克服了步长波动的不足。该算法不但具有较快的动态响应,而且提高了谐波检测的精度。通过MATLAB仿真验证了该算法的可行性和有效性。