Use of adaptive RLS, LMS, and NLMS algorithms for nonlinearity modeling in a modified laser interferometer

Laser heterodyne interferometer is one kind of nano-metrology systems which has been widely used in industry for high-accuracy displacement measurements. The accuracy of the nano-metrology systems based on the laser heterodyne interferometers can be effectively limited by the periodic nonlinearity. In this paper, we present the nonlinearity modeling of the nano-metrology interferometric system using some adaptive filters. The adaptive algorithms consist of the least mean squares (LMS), normalized least mean squares (NLMS), and recursive least squares (RLS). It is shown that the RLS algorithm can obtain optimal modeling parameters of nonlinearity.     

Partial-update NLMS algorithms with data-selective updating

In this paper, we present mean-squared convergence analysis for the partial-update normalized least-mean square (PU-NLMS) algorithm with closed-form expressions for the case of white input signals. The formulae presented here are more accurate than the ones found in the literature for the PU-NLMS algorithm. Thereafter, the ideas of the partial-update NLMS-type algorithms found in the literature are incorporated in the framework of set-membership filtering, from which data-selective NLMS-type algorithms with partial-update are derived. The new algorithms, referred to herein as the set-membership partial-update normalized least-mean square (SM-PU-NLMS) algorithms, combine the data-selective updating from set-membership filtering with the reduced computational complexity from partial updating. A thorough discussion of the SM-PU-NLMS algorithms follows, whereby we propose different update strategies and provide stability analysis and closed-form formulae for excess mean-squared error (MSE). Simulation results verify the analysis for the PU-NLMS algorithm and the good performance of the SM-PU-NLMS algorithms in terms of convergence speed, final misadjustment, and computational complexity.     

Delta Levinson and Schur-type RLS algorithms for adaptive signalprocessing

In this paper, we develop delta operator based Levinson and Schur type on-line RLS algorithms. Such algorithms have the potential of improved numerical behavior for ill-conditioned input data. These new algorithms are obtained by a unified transformation on the existing q operator based ones. We first show that the conventional lattice structure can be naturally derived when the backward delta operator is used. With this operator, Levinson and Schur algorithms for the stationary stochastic model in q-domain can easily be transformed into the delta domain. Then, same transformation, will be applied to the q-domain on-line Levinson and Schur type RLS algorithms to obtain the delta-domain counterparts. Their normalized versions as well as a systolic array architecture implementing the new delta Schur RLS algorithm are proposed. Extension to the equal length multichannel case is also given. Computer simulations show the expected numerical advantages of the delta-based algorithms for fast-sampled data in real time, over the q-domain ones under finite precision implementation     

基于LMS及RLS的自适应均衡算法仿真分析

在通信系统中采用均衡技术是改善信道特性行之有效的方法,为此从时域均衡原理出发,讨论了基于LMS和基于RLS的自适应均衡算法,并利用Matlab对两类算法进行了仿真,从均衡前后信号的星座图、算法收敛特性以及均衡前后系统的误码特性这三个方面对两类算法的性能进行了比较.     

The behavior of LMS and NLMS algorithms in the presence ofspherically invariant processes

The behavior of least-mean-square (LMS) and normalized least-mean-square (NLMS) algorithms with spherically invariant random processes (SIRPs) as excitations is shown. Many random processes fall into this category, and SIRPs closely resemble speech signals. The most pertinent properties of these random processes are summarized. The LMS algorithm is introduced, and the first- and second-order moments of the weight-error vector between the Wiener solution and the estimated solution are shown. The behavior of the NLMS algorithm is obtained, and the first- and second-order moments of the weight-error vector are calculated. The results are verified by comparison with known results when a white noise process and a colored Gaussian process are used as input sequences. Some simulation results for a K₀-process are then shown     

Rotation-based RLS algorithms: unified derivations, numericalproperties, and parallel implementations

This work presents a unified derivation of four rotation-based recursive least squares (RLS) algorithms. They solve the adaptive least squares problems of the linear combiner, the linear combiner without a desired signal, the single channel, and the multichannel linear prediction and transversal filtering. Compared to other approaches, the authors' derivation is simpler and unified, and may be useful to readers for better understanding the algorithms and their relationships. Moreover, it enables improvements of some algorithms in the literature in both the computational and the numerical issues. All algorithms derived in this work are based on Givens rotations. They offer superior numerical properties as shown by computer simulations. They are computationally efficient and highly concurrent. Aspects of parallel implementation and parameter identification are discussed     

Comparison of RLS, LMS, and sign algorithms for tracking randomlytime-varying channels

The performance of adaptive FIR filters governed by the recursive least-squares (RLS) algorithm, the least mean square (LMS) algorithm, and the sign algorithm (SA), are compared when the optimal filtering vector is randomly time-varying. The comparison is done in terms of the steady-state excess mean-square estimation error ξ and the steady-state mean-square weight deviation, η. It is shown that ξ does not depend on the spread of eigenvalues of the input covariance matrix, R, in the cases of the LMS algorithm and the SA, while it does in the case of the RLS algorithm. In the three algorithms, η is found to be increasing with the eigenvalue spread. The value of the adaptation parameter that minimizes ξ is different from the one that minimizes η. It is shown that the minimum values of ξ and η attained by the RLS algorithm are equal to the ones attained by the LMS algorithm in any one of the three following cases: (1) if R has equal eigenvalues, (2) if the fluctuations of the individual elements of the optimal vector are mutually uncorrelated and have the same mean-square value, or (3) if R is diagonal and the fluctuations of the individual elements of the optimal vector have the same mean-square value. Conditions that make the values of ξ and η of the LMS algorithm smaller (or greater) than the ones of the RLS algorithm are derived. For Gaussian input data, the minimum values of ξ and η attained by the SA are found to exceed the ones attained by the LMS algorithm by 1 dB independently of R and the mutual correlation between the elements of the optimal vector     

Comparative tracking performance of the LMS and RLS algorithms forchirped narrowband signal recovery

This paper studies the comparative tracking performance of the recursive least squares (RLS) and least mean square (LMS) algorithms for time-varying inputs, specifically for linearly chirped narrowband input signals in additive white Gaussian noise. It is shown that the structural differences in the implementation of the LMS and RLS weight updates produce regions where the LMS performance exceeds that of the RLS and other regions where the converse occurs. These regions are shown to be a function of the signal bandwidth and signal-to-noise ratio (SNR). LMS is shown to place a notch in the signal band of the mean lag filter, thus reducing the lag error and improving the tracking performance. For the chirped signal, it is shown that this produces smaller tracking error for small SNR. For high SNR, there is a region of signal bandwidth for which RLS will provide lower error than LMS, but even for these high SNR inputs, LMS always provides superior performance for very narrowband signals     

Analysis of LMS and NLMS algorithms with delayed coefficient updateunder the presence of spherically invariant processes

Certain conditions require a delay in the coefficient update of the least mean square (LMS) and normalized least mean square (NLMS) algorithms. This paper presents an in-depth analysis of these modificated versions for the important case of spherically invariant random processes (SIRPs), which are known as an excellent model for speech signals. Some derived bounds and the predicted dynamic behavior of the algorithms are found to correspond very well to simulation results and a real time implementation on a fixed-point signal processor. A modification of the algorithm is proposed to assure the well known properties of the LMS and NLMS algorithms     

Systolic block Householder transformation for RLS algorithm withtwo-level pipelined implementation

The authors propose a systolic block Householder transformation (SBHT) approach to implement the HT on a systolic array and also propose its application to the RLS (recursive least squares) algorithm. Since the data are fetched in a block manner, vector operations are in general required for the vectorized array. However, a modified HT algorithm permits a two-level pipelined implementation of the SBHT systolic array at both the vector and word levels. The throughput rate can be as fast as that of the Givens rotation method. The present approach makes the HT amenable for VLSI implementation as well as applicable to real-time high-throughput applications of modern signal processing. The constrained RLS problem using the SBHT RLS systolic array is also considered     

A New Robust Variable Step-Size NLMS Algorithm

A new framework for designing robust adaptive filters is introduced. It is based on the optimization of a certain cost function subject to a time-dependent constraint on the norm of the filter update. Particularly, we present a robust variable step-size NLMS algorithm which optimizes the square of the a posteriori error. We also show the link between the proposed algorithm and another one derived using a robust statistics approach. In addition, a theoretical model for predicting the transient and steady-state behavior and a proof of almost sure filter convergence are provided. The algorithm is then tested in different environments for system identification and acoustic echo cancelation applications.     

一种新的变步长NLMS自适应算法

文章根据最优步长理论提出一个向量因子来控制步长的变化，其长度及形式与权向量相同，并且由输入数据相关性大的部分决定两个向量中每次应更新的部分，从而使权向量异步更新达到最佳。计算机仿真结果表明，在输入数据相关性很强时，该算法与传统的变步长LMS及NLMS算法相比不仅具有更决的收敛速度，更小的稳态误差及更平稳的收敛过程，同时计算量也有一定的减少。     

A generic post-deblocking filter for block based image compression algorithms

In this paper we propose a new post-processing deblocking technique that is independent of the compression method used to encode the image. The development of this filter was motivated by the use of Multidimensional Multiscale Parser (MMP) algorithm, a generic lossy and lossless compression method. Since it employs an adaptive block size, it presents some impairments when using the deblocking techniques presented in the literature. This led us to the development of a new and more generic deblocking method, based on total variation and adaptive bilateral filtering.The proposed method was evaluated not only for still images, but also for video sequences, encoded using pattern matching and transform based compression methods. For all cases, both the objective and subjective quality of the reconstructed images were improved, showing the versatility of the proposed technique.     

Implementing block ciphering algorithms in hardware

Many ciphering algorithms map efficiently into hardware, giving encryption with very high throughput. Hardware designs are presented for two secretkey block ciphers, Blowfish and REDOC III. Pipelined systems using arrays of programmable logic and RAM offer encryption rates of 1032 Mbit/s and 1640 Mbit/s, respectively.     

块迭代码片均衡算法

为了增强码片均衡器的性能,降低运算量,提出了一种 LMMSE 的改进新算法—BILMMSE 算法。理论分析与计算机模拟结果表明 BILMMSE 码片均衡器性能优于传统的 Rake,以及 Griffith 与 MRLS 码片均衡器,与LMMSE 码片均衡器性能基本保持一致,而运算量却大大降低,非常有利于 FPGA 与 DSP 实现。     

A Modular Analog NLMS Structure for Adaptive Filtering

This paper proposes a modular Analog Adaptive filter (AAF) algorithm, in which the coefficient adaptation is carried out by using a time varying step size analog normalized LMS (NLMS) algorithm, which is implemented as an external analog structure. The proposed time varying step size is estimated by using the first element of the crosscorrelation vector between the output error and reference signal, and the first element of the crosscorrelation vector between the output error and the adaptive filter output signal, respectively. Proposed algorithm reduces distortion when additive noise power increases or DC offsets are present, without significatively decreasing the convergence rate nor increasing the complexity of the conventional NLMS algorithms. Simulation results show that proposed algorithm improves the performance of AAF when DC offsets are present. The proposed VLSI structure for the time varying step size normalized NLMS algorithm has, potentially, a very small size and faster convergence rates than its digital counterparts. It is suitable for general purpose applications or oriented filtering solution such as echo cancellation and equalization in cellular telephony in which high performance, low power consumption, fast convergence rates and small size adaptive digital filters (ADF) are required. The convergence performance of analog adaptive filters using integrators like first order low pass filter is analyzed.     

LFM信号的自适应校正应用研究

在提出用自适应滤波方法对接收机通道之间的不平衡性进行校正的基础上,重点分析了NLMS(NormalizedLeastMeanSquare),即归一化最小均方算法对雷达中的线性调频信号(LFM)的校正。通过仿真,对影响LFM信号校正精度的因素做了探讨。     

基于累积量的递归最小二乘算法研究

从基于累积量的均方误差（ＣＭＳＥ）准则,本文推导了一种基于累积量的递归最小二乘（ＣＲＬＳ）算法．并从信号检验和估计的角度对三阶ＣＲＩＳ算法中出现的加权求和系数给出的一种物理解释,以说明其抗高斯噪声的机理．本文提出应根据三种不同条件下信号的最优估计来确定最佳窗口函数的原则,并进一步证明了在极大似（ＭＬ）和线性均方（ＬＭＳ）估计意义下的最佳窗口都是矩形窗而非Ｄｅｌｏｐｏｕｌｏｓ和Ｇｉａｎｎａｋｉｓ建议的Ｈａｍｍｉｎｇ窗~［３］。仿真实验证实：ＣＲＬＳ算法采用矩形窗确定比采用Ｈａｍｍｉｎｇ窗具有更上的结果偏差。     

Adaptive combined Chase-GMD algorithms for block codes

This work proposes a new adaptive approach to the soft decision decoding of the so-called combined Chase-GMD class of algorithms (CGA). A reliability threshold is used to match the decoding performance to the channel conditions. As a result, a significant reduction in decoding complexity can be achieved by reducing the number of required algebraic decodings. The proposed adaptive application can achieve the upper performance limit of the CGA with significant complexity reduction.     

基于改进NLMS算法的通道校正技术研究

在电子侦察中,由于数字接收机通道中的放大器、混频器中的本振以及低通滤波器等器件的非理想性,造 成了接收机通道之间的幅相不平衡现象,极大地影响了无源测向的精度。本文在自适应滤波理论的基础上,提出了一种基 于改进NLMS算法的自适应通道校正方法。改进的算法在无法得到信号先验信息的情况下,也能获得较快的收敛速度和较 小的失调量,完成通道校正过程。基于该算法的通道校正方法不需要参考信号,直接利用天线接收到的雷达信号完成自校 正过程。仿真结果表明,该方法能有效提高通道的幅相一致性,是一种较好的通道校正方法。