A variable step size LMS algorithm

A least-mean-square (LMS) adaptive filter with a variable step size is introduced. The step size increases or decreases as the mean-square error increases or decreases, allowing the adaptive filter to track changes in the system as well as produce a small steady state error. The convergence and steady-state behavior of the algorithm are analyzed. The results reduce to well-known results when specialized to the constant-step-size case. Simulation results are presented to support the analysis and to compare the performance of the algorithm with the usual LMS algorithm and another variable-step-size algorithm. They show that its performance compares favorably with these existing algorithms     

Energy constrained frequency-domain normalized LMS algorithm for blind channel identification

This paper deals with the blind adaptive identification of single-input multi-output (SIMO) finite impulse response acoustic channels from noise-corrupted observations. The normalized multichannel frequency-domain least-mean-squares (NMCFLMS) algorithm [1] is known to be a very effective and efficient technique for identification of such channels when noise effects can be ignored. It, however, misconverges in presence of noise [2]. In this paper, we present an analysis of noise effects on the NMCFLMS algorithm and propose a novel technique for ameliorating such misconvergence characteristics of the NMCFLMS algorithm for blind channel identification (BCI) with noise by attaching a spectral constraint in the adaptation rule. Experimental results demonstrate that the robustness of the NMCFLMS algorithm for BCI can be significantly improved using such a constraint.     

Designing a fuzzy step size LMS algorithm

A new approach in adjusting the step size of the least mean square (LMS) using the fuzzy logic technique is presented. It extends the earlier work of Gan (see Signal Process., vol.49, no.2, p.145-49, 1996) by giving a complete design methodology and guidelines for developing a reliable and robust fuzzy step size LMS (FSS LMS) algorithm. It also presents a computational study and simulation results of this newly proposed algorithm compared to other conventional variable step size LMS algorithms     

改进的变步长变换域最小均方算法

变换域是一种在强相关信号输入时加快自适应算法收敛的方法,但仍然存在收敛速度的要求与稳态失调的要求相矛盾的问题。本文在变换域最小均方误差算法（transform domain LMS, TDLMS）的基础上提出了一种改进的变步长方案,其变步长因子受到误差自相关的控制,消除了不相关的观测噪声的影响。本文分别在平稳和非平稳状态下,对算法的收敛和稳态性能进行理论分析,并给出了最佳的算法参数。仿真设置相同的稳态误差,结果表明本文算法在平稳状态下比固定步长的算法提前1300点收敛,在非平稳状态下提前1400点收敛,且与文献中其它变步长的算法相比收敛速度均有提升。      

一种新的可变步长LMS算法及其性能分析

为了解决基本LMS（Least Mean Square）算法中收敛速度和稳态误差之间的矛盾，提出了一种新的可变步长LMS算法（λNVSS）。该算法通过引入修正系数β和遗忘因子λ，利用当前和过去共M（滤波器阶数）个误差信息来决定下一步的迭代步长。仿真结果显示，λNVSS算法对于平稳过程中的滤波器，能获得较NVSS更快的收敛速度和更小的稳态误差。同时，λNVSS算法还有较好的跟踪跃变系统的能力。     

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     

变步长LMS盲多用户检测算法改进研究

针对CDMA系统中存在多址干扰的问题,提出了一种变步长LMS盲多用户检测算法。根据瞬时输出能量作为平均输出能量的这一准则,将步长因子μ定义为输入函数,灵活地更新检测器的权值,使步长自调整,前期μ较大值,方便算法收敛,待稳定后再减小μ的取值,以减少迭代误差,提高算法精度。该算法在继承了传统算法计算复杂度低的优点的前提下,性能有较大的提高。计算机仿真表明,该算法达到了加快收敛速率,提高抗干扰能力,减小稳态误差的效果。     

Median LMS algorithm

A median least-mean-square (MLMS) algorithm is described. This filter operates by replacing the instantaneous gradient estimate, used by the well known LMS algorithm, by the short-term median of this quantity. The filter is applied to signals corrupted by impulsive interferences.<>     

Bursting in the LMS algorithm

The least mean square (LMS) algorithm is known to converge in the mean and in the mean square. However, during short time periods, the error sequence can blow up and cause severe disturbances, especially for non-Gaussian processes. The paper discusses potential short time unstable behavior of the LMS algorithm for spherically invariant random processes (SIRP) like Gaussian, Laplacian, and K₀. The result of this investigation is that the probability for bursting decreases with the step size. However, since a smaller step size also causes a slower convergence rate, one has to choose a tradeoff between convergence speed and the frequence of bursting     

Stability of the quantized LMS algorithm

The least mean square (LMS) algorithm is investigated for stability when implemented with two's complement quantization. The study is restricted to algorithms with periodically varying inputs. Such inputs are common in a variety of applications, and for system identification, they can always be generated as shown with an example. It is shown that the quantized LMS algorithm is just a special case of a quantized periodically shift-varying (PSV) filter. Two different sufficient conditions are obtained for the bounded input bounded output (BIBO) stability of the PSV filter. When the filter is BIBO stable, two different bounds on the filter output are also derived. These conditions and bounds are then applied to the quantized LMS algorithm. The results are illustrated with examples.     

自适应LMS算法的收敛特性

本文首先指出了Widrow给出的自适应最小均方(LMS)算法权收敛规律的缺陷,进而通过对LMS算法的非统计分析,首次指出了影响收敛速度的因素是信号样本相关阵的本征值的范围。     

LMS算法收敛步长的精确求解

本文提出了用步长阀值上下限的算术平均值去计算收敛步长的新方法,通过LMS算法失调量的精确分析,寻出了计算步长的公式.计算机模拟结果证实了本文方法及其步长计算公式的准确性.     

Robust design of the LMS algorithm

A method to optimize the step size of the LMS algorithm when it is used to identify a time-varying system is proposed. The formulation allows uncertain specifications of the input excitation and the plant variation. The method is robust in that it minimizes the mean square error for the worst-case data of these variables     

Leaky delayed LMS algorithm: stochastic analysis for Gaussian data and delay modeling error

This paper presents a stochastic analysis of the delayed least-mean-square (DLMS) adaptive algorithm with leakage. This analysis is obtained taking into account that mismatches between the system delay and its estimate may occur. Such an approach is not considered in previous models. In addition, it is shown that the introduction of a leakage factor into the adaptive algorithm keeps the adaptive algorithm stable under an imperfect delay estimate condition. Recursive difference equations for the first and second moments of the adaptive filter weights are derived. An expression for the critical value of the step size is also determined. Results of Monte Carlo simulations present excellent agreement with the proposed model for both white and colored Gaussian inputs.     

Complex fuzzy adaptive filter with LMS algorithm

A fuzzy adaptive filter is constructed from a set of fuzzy IF-THEN rules that change adaptively to minimize some criterion function as new information becomes available. This paper generalizes the fuzzy adaptive filter based on least mean squares (LMS) to include complex parameters and complex signals. The fuzzy filter as adaptive equalizer is applied to quadrature amplitude modulation (QAM) digital communication with linear complex channel characteristics     

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     

The complex LMS algorithm

A least-mean-square (LMS) adaptive algorithm for complex signals is derived. The original Widrow-Hoff LMS algorithm is Wj+l= Wj+ 2µεjXj. The complex form is shown to be Wj+1= Wj+ 2µεjX^-j, where the boldfaced terms represent complex (phasor) signals and the bar above Xjdesignates complex conjugate.     

Constrained LMS adaptive algorithm

A new least-mean-squares (LMS) adaptive algorithm is developed in the letter. This new algorithm solves a specific variance problem that occurs in LMS algorithms in the presence of high noise levels and when the input signal is bandlimited. Quantitative results in terms of an accuracy measure of a finite impulse response (FIR) system identification are presented.     

A Novel Convergence Accelerator for the LMS Adaptive Filter

Due to its ease of implementation, the least mean square (LMS) algorithm is one of the most well-known algorithms for mobile communication systems. However, the main limitation of this approach is its relatively slow convergence rate. This paper proposes a booster using the Markov chain concept to speed up the convergence rate of LMS algorithms. The nature of Markov chains makes it possible to exploit past information in the updating process. According to the central limit theorem, the transition matrix has a smaller variance than that of the weight itself. As a result, the weight transition matrix converges faster than the weight itself. Therefore, the proposed Markov-chain based booster is able to track variations in signal characteristics and simultaneously accelerate the rate of convergence for LMS algorithms. Simulation results show that the Markov-chain based booster allows an LMS algorithm to effectively increase the convergence rate and further approach the Wiener solution. This approach also markedly reduces the mean square error while improving the convergence rate.     

基于小波变换变步长LMS自适应信道均衡的新方法

结合变换域最小均方(LMS)和变步长LMS算法的优势,提出了一种基于小波变换的变步长LMS自适应均衡方法。该方法中步长调整函数采用了改进的Sigmoid函数,该函数具有简单且误差信号接近零时变化缓慢的特点。并且,在训练模式、判决引导模式以及混合模式下,将提出方法和传统均衡方法进行了仿真比较。结果表明,所提出的方法比传统的线性LMS算法、变步长LMS以及小波变换LMS收敛更快、性能更优。