Hybrid filtered error LMS algorithm: another alternative to filtered-x LMS

The filtered-error LMS (FELMS) algorithms are widely used in multi-input and multi-output control (MIMO) active noise control (ANC) systems as an alternative to the filtered-x LMS (FXLMS) algorithms to reduce the computational complexity and memory requirements. However, the available FELMS algorithms introduce significant delays in updating the adaptive filter coefficients that slow the convergence rate. In this paper, we introduce a novel algorithm called the hybrid filtered-error LMS algorithm (HFELMS) which, while still a form of the FELMS algorithm, allows users to have some freedom to construct the error filter that guarantees its convergence with a sufficiently small step size. Without increasing the computational complexity, the proposed algorithm can improve the control system performance in one of several ways: 1) increasing the convergence rate without extra computation cost; 2) reducing the remaining noise mean square error (MSE); or 3) shaping the excess noise power. Simulation results show the effectiveness of the proposed method.     

A frequency-weighted block LMS algorithm and its application to speech processing

In this letter, we propose a frequency-weighted block LMS (FWBLMS) algorithm that is based on minimization of the frequency-weighted block mean-squared error. The FWBLMS algorithm has an important advantage over the time-domain LMS algorithm in that it can be designed with different frequency weighting on error signal depending on the relative significance of various frequency bands. Application of the FWBLMS algorithm in adaptive linear prediction of speech is discussed.     

Analysis of the frequency-domain block LMS algorithm

We present a new analysis of the frequency-domain block least-mean-square (FBLMS) algorithm. An earlier analysis uses a mapping of the frequency-domain information to the time-domain before proceeding with the analysis of the algorithm. We present a direct analysis of the FBLMS algorithm in the frequency domain. As compared with the previous analysis, the new analysis is easier to follow. It is also more rigorous than the previous works and gives a better insight to the effect of various processing components in the algorithm structure on its convergence behavior. In particular, we show how the transformation of input samples to the frequency domain, combined with the effect of the involved windowing matrices, and step-normalization affect the convergence behavior of both constrained and unconstrained versions of the FBLMS algorithm. We also report a procedure for derivation of misadjustment equations of various versions of the FBLMS algorithm     

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.     

A trigonometric formulation of the LMS algorithm for realization on pipelined CORDIC

This paper presents an alternate formulation of the least mean square (LMS) algorithm by using a set of angle variables monotonically related to the filter coefficients. The algorithm updates the angles directly instead of the filter coefficients and relies on quantities that can be realized by simple CORDIC rotations. Two architectures based on pipelined CORDIC unit are proposed which achieve efficiency either in time or in area. Further simplifications result from extending the approach to the sign-sign LMS algorithm. An approximate convergence analysis of the proposed algorithm, along with simulation results showing its convergence characteristics are presented.     

A computationally efficient frequency-domain LMS algorithm withconstraints on the adaptive filter

The frequency domain implementation of the LMS algorithm is attractive due to both the reduced computational complexity and the potential of faster convergence compared with the time domain implementation. Another advantage is the potential of using frequency-domain constraints on the adaptive filter, such as limiting its magnitude response or limiting the power of its output signal. This paper presents a computationally efficient algorithm that allows the incorporation of various frequency domain constraints into the LMS algorithm. A penalty function formulation is used with a steepest descent search to adapt the filter so that it converges to the new constrained minimum. The formulation of the algorithm is derived first, after which the use of some practical constraints with this algorithm and a simulation example for adaptive blind equalization are described     

基于激光传感器的统计特征提取和误差分析

近年来, 激光测量系统(LMS)在各个研究领域中的应用日益增多。基于激光的距离测量技术具有较高的精度和速度,方向性好,能够以较高的频率提供分辨率高、准确性好的距离信息。常用的二维脉冲式激光传感器,测量到的有限长数据序列是一个关于环境的扫描平面。其测量数据的获取质量受到诸多环境因素影响。文中基于LMS 221激光传感器的应用,对不同材质物体的测量进行了误差分析,总结了由于物体表面特性、漂移和距离等因素对测量精度造成的影响。通过分析不同材质的测量数据,可有效地对测量物体进行大致分类,并对检测的误差进行补偿以提高测量精度。     

基于频域块LMS算法的实时虚拟暗室测试方法

针对电磁辐射现场测试被测设备信号和干扰未知的情况,提出了一种基于频域块最小均方算法的实时虚拟暗室测试方法。该方法采用双通道接收机,根据测试通道和背景通道中干扰信号的相关性设计自适应滤波器,在频域对背景通道信号滤波以趋近测试通道中的干扰分量,采用瞬时双通道信号迭代更新滤波器系数,滤波器系数收敛后系统输出中只有被测设备信号。仿真与分析表明,该方法在背景通道有无被测设备信号泄露的情况下都能有效抑制干扰,与基于时域最小均方算法的方法相比,在滤波器长度相同的情况下其计算复杂度更低,适用于实时现场测试。     

Postsmoothing for the LMS algorithm and a fixed point roundofferror analysis

The effect of post-algorithm smoothing on digital implementations of the least mean square (LMS) algorithm is studied. An expression is derived for the mean square error (MSE) with post-algorithm (PA) smoothing but without finite wordlength effects. It is shown that the MSE can be reduced from that of LMS without PA smoothing. PA smoothing results in reduced convergence speed. The effect of fixed-point finite precision on PA smoothing is studied. An expression for the MSE is derived. Monte Carlo simulation results that support the result that digital LMS with PA smoothing performs better than digital LMS without PA smoothing are presented     

Analysis of the partitioned frequency-domain block LMS (PFBLMS)algorithm

In this paper, we present a new analysis of the partitioned frequency-domain block least-mean-square (PFBLMS) algorithm. We analyze the matrices that control the convergence rates of the various forms of the PFBLMS algorithm and evaluate their eigenvalues for both white and colored input processes. Because of the complexity of the problem, the detailed analyses are only given for the case where the filter input is a first-order autoregressive process (AR-1). However, the results are then generalized to arbitrary processes in a heuristic way by looking into a set of numerical examples. An interesting finding (that is consistent with earlier publications) is that the unconstrained PFBLMS algorithm suffers from slow modes of convergence, which the FBLMS algorithm does not. Fortunately, however, these modes are not present in the constrained PFBLMS algorithm, A simplified version of the constrained PFBLMS algorithm, which is known as the schedule-constrained PFBLMS algorithm, is also discussed, and the reason for its similar behavior to that of its fully constrained version is explained     

Separate/joint optimization of error feedback and realization for roundoff noise minimization in a class of 2-D state-space digital filters

Techniques for the separate/joint optimization of error-feedback and realization are developed to minimize the roundoff noise subject to l ₂-norm dynamic-range scaling constraints for a class of 2-D state-space digital filters. In the joint optimization, the problem at hand is converted into an unconstrained optimization problem by using linear-algebraic techniques. The unconstrained problem obtained is then solved by applying an efficient quasi-Newton algorithm. A numerical example is presented to illustrate the utility of the proposed techniques.     

A floating-point arithmetic error analysis of direct and indirectcoefficient updating techniques for adaptive lattice filters

The ways in which finite precision arithmetic effects can deleteriously manifest themselves in both the stochastic gradient and the recursive least squares adaptive lattice filters are discussed. closed form expressions are derived for the steady-state variance of the accumulated arithmetic error in a single adaptive lattice coefficient using a floating-point stochastic arithmetic error analysis. The analytical results show that the performance of adaptive lattice filters using a direct updating computational form is less sensitive to finite precision effects than that of adaptive lattice filters using an indirect updating computational form. In addition, a method for reducing the self-generated noise is presented. Experimental results obtained on a 32-b floating-point hardware implementation of the adaptive lattice filters and with computer simulations are included to verify the analytical results describing the effects of finite precision on adaptive lattice filters     

Leaky LMS algorithm: MSE analysis for Gaussian data

Despite the widespread usage of the leaky LMS algorithm, there has been no detailed study of its performance. This paper presents an analytical treatment of the mean-square error (MSE) performance for the leaky LMS adaptive algorithm for Gaussian input data. The common independence assumption regarding W(n) and X(n) is also used. Exact expressions that completely characterize the second moment of the coefficient vector and algorithm steady-state excess MSE are developed. Rigorous conditions for MSE convergence are also established. Analytical results are compared with simulation and are shown to agree well     

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。     

部分更新块LMS均衡算法分析及应用

采用部分更新最小均方(LMS)算法和重叠保留的块信号频域处理结构,针对现场可编程门阵列(FPGA)的硬件实现平台,提出了时频混合部分更新块LMS和周期性块部分更新LMS均衡算法结构。2种新结构均能有效降低均衡算法的实现复杂度。步长收敛条件分析和数值仿真结果表明,新结构能够在适当调整更新步长的情况下,有效跟踪缓变信道的变化,实现与完整块LMS算法相当的性能,能够有效解决高速数据传输中的均衡复杂度过高的问题。     

Mean-square deviation analysis of the zero-attracting variable step-size LMS algorithm

The well-known variable step-size least-mean-square (VSSLMS) algorithm provides faster convergence rate while maintaining lower mean-square error than the conventional LMS algorithm. The performance of the VSSLMS algorithm can be improved further in a channel estimation problem if the impulse response of the channel is sparse. Recently, a zero-attracting (ZA)-VSSLMS algorithm was proposed to exploit the sparsity of a channel. This was done by imposing an \(\ell _1\)-norm penalty to the original cost function of the VSSLMS algorithm which utilizes the sparsity in the filter taps during the adaptation process. In this paper, we present the mean-square deviation (MSD) analysis of the ZA-VSSLMS algorithm. A steady-state MSD expression for the ZA-VSSLMS algorithm is derived. An upper bound of the zero-attractor controller (\(\rho \)) that provides the minimum MSD is also provided. Moreover, the effect of the noise distribution on the MSD performance is shown theoretically. It is shown that the theoretical and simulation results of the algorithm are in good agreement with a wide range of parameters, different channel, input signal, and noise types.     

Stochastic analysis of the LMS algorithm with a saturationnonlinearity following the adaptive filter output

This paper presents a statistical analysis of the least mean square (LMS) algorithm with a zero-memory scaled error function nonlinearity following the adaptive filter output. This structure models saturation effects in active noise and active vibration control systems when the acoustic transducers are driven by large amplitude signals. The problem is first defined as a nonlinear signal estimation problem and the mean-square error (MSE) performance surface is studied. Analytical expressions are obtained for the optimum weight vector and the minimum achievable MSE as functions of the saturation. These results are useful for adaptive algorithm design and evaluation. The LMS algorithm behavior with saturation is analyzed for Gaussian inputs and slow adaptation. Deterministic nonlinear recursions are obtained for the time-varying mean weight and MSE behavior. Simplified results are derived for white inputs and small step sizes. Monte Carlo simulations display excellent agreement with the theoretical predictions, even for relatively large step sizes. The new analytical results accurately predict the effect of saturation on the LMS adaptive filter behavior     

Error bound method and its application to the LMS algorithm

A method to determine a bound on the error performance of an adaptive filter due to roundoff effects is described. The method converts the analysis of a recursive algorithm into two much simpler sub-problems: convergence and momentary error. To apply the method, the input data has to be bounded. By classifying convergence into different categories according to their rates, it is observed that adaptive filtering algorithms that belong to a particular class share similar behavior due to roundoff error or other perturbation effects. The merit of the method is its simplicity and general applicability. Based on this method, a sufficient condition for the numerical stability of an adaptive filter is derived. Application of the method to the least mean square (LMS) algorithm is described. The analysis may also be generalized to include other perturbation effects     

A simple and efficient block motion estimation algorithm based on full-search array architecture

This paper first presents an array structure using ±1 full-search (FS) architecture as the search engine of block motion estimation which takes advantage of the design regularity of FS. An efficient algorithm named modified gradient-descent search (MGDS) is then introduced based on the proposed architecture. MGDS utilizes an adaptive computation distribution mechanism to efficiently allocate computation of the employed ±1 FS array to blocks or frames of video sequences. Experimental results indicate that MGDS uniformly achieves a higher quality than FS by an amount that is dependent on motion activities of sequences.     

基于LMS算法与RLS算法自适应滤波及仿真分析

自适应滤波器在随机信号处理当中得到了广泛应用.文讲述了LMS算法和RLS算法的基本原理,基于两种算法的推导过程较为繁琐,不便理解,本文以两种算法的主要计算环节为突破口,选取合适的迭代公式,对两种算法进行公式推导,方便读者理解.同时,本文通过原理推导、软件仿真的试验方法,设置输入信号、噪声信号,通过输出信号的图像走势对两种算法的优缺点进行对比分析,使读者对两种算法及滤波器的设计具有直观的认识,有一定的参考意义.