Robust M-estimate adaptive filtering

An M-estimate adaptive filter for robust adaptive filtering in impulse noise is proposed. Instead of using the conventional least-square cost function, a new cost function based on an M-estimator is used to suppress the effect of impulse noise on the filter weights. The resulting optimal weight vector is governed by an M-estimate normal equation. A recursive least M-estimate (RLM) adaptive algorithm and a robust threshold estimation method are derived for solving this equation. The mean convergence performance of the proposed algorithm is also analysed using the modified Huber (1981) function (a simple but good approximation to the Hampel's three-parts-redescending M-estimate function) and the contaminated Gaussian noise model. Simulation results show that the proposed RLM algorithm has better performance than other recursive least squares (RLS) like algorithms under either a contaminated Gaussian or alpha-stable noise environment. The initial convergence, steady-state error, robustness to system change and computational complexity are also found to be comparable to the conventional RLS algorithm under Gaussian noise alone     

A New Sequential Block Partial Update Normalized Least Mean M-Estimate Algorithm and its Convergence Performance Analysis

This paper proposes a new sequential block partial update normalized least mean square (SBP-NLMS) algorithm and its nonlinear extension, the SBP-normalized least mean M-estimate (SBP–NLMM) algorithm, for adaptive filtering. These algorithms both utilize the sequential partial update strategy as in the sequential least mean square (S–LMS) algorithm to reduce the computational complexity. Particularly, the SBP–NLMM algorithm minimizes the M-estimate function for improved robustness to impulsive outliers over the SBP–NLMS algorithm. The convergence behaviors of these two algorithms under Gaussian inputs and Gaussian and contaminated Gaussian (CG) noises are analyzed and new analytical expressions describing the mean and mean square convergence behaviors are derived. The robustness of the proposed SBP–NLMM algorithm to impulsive noise and the accuracy of the performance analysis are verified by computer simulations.     

On the Performance Analysis of a Class of Transform-domain NLMS Algorithms with Gaussian Inputs and Mixture Gaussian Additive Noise Environment

This paper studies the convergence performance of the transform domain normalized least mean square (TDNLMS) algorithm with general nonlinearity and the transform domain normalized least mean M-estimate (TDNLMM) algorithm in Gaussian inputs and additive Gaussian and impulsive noise environment. The TDNLMM algorithm, which is derived from robust M-estimation, has the advantage of improved performance over the conventional TDNLMS algorithm in combating impulsive noises. Using Price’s theorem and its extension, the above algorithms can be treated in a single framework respectively for Gaussian and impulsive noise environments. Further, by introducing new special integral functions, related expectations can be evaluated so as to obtain decoupled difference equations which describe the mean and mean square behaviors of the TDNLMS and TDNLMM algorithms. These analytical results reveal the advantages of the TDNLMM algorithm in impulsive noise environment, and are in good agreement with computer simulation results.     

A robust past algorithm for subspace tracking in impulsive noise

The PAST algorithm is an effective and low complexity method for adaptive subspace tracking. However, due to the use of the recursive least squares (RLS) algorithm in estimating the conventional correlation matrix, like other RLS algorithms, it is very sensitive to impulsive noise and the performance can be degraded substantially. To overcome this problem, a new robust correlation matrix estimate, based on robust statistics concept, is proposed in this paper. It is derived from the maximum-likelihood (ML) estimate of a multivariate Gaussian process in contaminated Gaussian noise (CG) similar to the M-estimates in robust statistics. This new estimator is incorporated into the PAST algorithm for robust subspace tracking in impulsive noise. Furthermore, a new restoring mechanism is proposed to combat the hostile effect of long burst of impulses, which sporadically occur in communications systems. The convergence of this new algorithm is analyzed by extending a previous ordinary differential equation (ODE)-based method for PAST. Both theoretical and simulation results show that the proposed algorithm offers improved robustness against impulsive noise over the PAST algorithm. The performance of the new algorithm in nominal Gaussian noise is very close to that of the PAST algorithm.     

自适应滤波算法在微弱振动测量中的应用

将递归最小二乘自适应滤波算法应用于激光多普勒测振技术中,搭建了相应的微弱振动测量装置。模拟仿真与实验中,通过与设计的切比雪夫低通滤波算法对比,结果表明:该递归最小二乘自适应滤波算法能够有效抑制随机高斯白噪声,还原出原始信号;能够对简谐振动信号实现有效滤波,并且可以还原出淹没在噪声中的低频20 Hz信号;文中算法可以去除语音噪声,使声音更加纯净,增强语音信号,以此验证了该算法在外差振动测量中的可行性。该算法简单易用、收敛性强、速度快,尤其对于随机噪声的去除比普通的低通滤波器更加有效。     

A Stabilized Multichannel Fast RLS Algorithm for Adaptive Transmultiplexer Receivers

The transmultiplexer (TMUX) system has been studied for its application to multicarrier communications. The channel impairments including noise, interference, and distortion draw the need for adaptive reconstruction at the TMUX receiver. Among possible adaptive methods, the recursive least squares (RLS) algorithm is appealing for its good convergence rate and steady state performance. However, higher computational complexity due to the matrix operation is the drawback of utilizing RLS. A fast RLS algorithm used for adaptive signal reconstruction in the TMUX system is developed in this paper. By using the polyphase decomposition method, the adaptive receiver in the TMUX system can be formulated as a multichannel filtering problem, and the fast algorithm is obtained through the block Toeplitz matrix structure of received signals. In addition to the reduction of complexity, simulation results show that the adaptive TMUX receiver has a convergence rate close to that of the standard RLS algorithm and the performance approaches the minimum mean square error solution.     

On the Performance Analysis of the Least Mean M-Estimate and Normalized Least Mean M-Estimate Algorithms with Gaussian Inputs and Additive Gaussian and Contaminated Gaussian Noises

This paper studies the convergence analysis of the least mean M-estimate (LMM) and normalized least mean M-estimate (NLMM) algorithms with Gaussian inputs and additive Gaussian and contaminated Gaussian noises. These algorithms are based on the M-estimate cost function and employ error nonlinearity to achieve improved robustness in impulsive noise environment over their conventional LMS and NLMS counterparts. Using the Price’s theorem and an extension of the method proposed in Bershad (IEEE Transactions on Acoustics, Speech, and Signal Processing, ASSP-34(4), 793–806, 1986; IEEE Transactions on Acoustics, Speech, and Signal Processing, 35(5), 636–644, 1987), we first derive new expressions of the decoupled difference equations which describe the mean and mean square convergence behaviors of these algorithms for Gaussian inputs and additive Gaussian noise. These new expressions, which are expressed in terms of the generalized Abelian integral functions, closely resemble those for the LMS algorithm and allow us to interpret the convergence performance and determine the step size stability bound of the studied algorithms. Next, using an extension of the Price’s theorem for Gaussian mixture, similar results are obtained for additive contaminated Gaussian noise case. The theoretical analysis and the practical advantages of the LMM/NLMM algorithms are verified through computer simulations.     

Low Complexity Linear Channel Estimation for MIMO Communication Systems

Channel estimation is employed to get the current knowledge of channel states for an optimum detection in fading environments. In this paper, a new recursive multiple input multiple output (MIMO) channel estimation is proposed which is based on the recursive least square solution. The proposed recursive algorithm utilizes short training sequence on one hand and requires low computational complexity on the other hand. The algorithm is evaluated on a MIMO communication system through simulations. It is realized that the proposed algorithm provides fast convergence as compared to recursive least square (RLS) and robust variable forgetting factor RLS (RVFF-RLS) adaptive algorithms while utilizing lesser computational cost and provides independency on forgetting factor.     

The multi-user detection under fading channel

This paper proposes a method of blind multi-user detection algorithm based on signal sub-space estimation under the fading channels in the present of impulse noise. This algorithm adapts recursive least square (RLS) filter that can estimate the coefficients using only the signature waveform. In addition, to strengthen the ability of resisting the impulse noise, a new suppressive factor is induced, which can suppress the amplitude of the impulse, and improve the ability of convergence speed. Simulation results show that new RLS algorithm is more robust against consecutive impulse noise and have better convergence ability than conventional RLS. In addition, Compared to the least mean square (LMS) detector, the new robust RLS sub-space based method has better multi-address-inference (MAI) suppressing performance, especially, when channel degrades.     

用于自适应数字波束形成的稳健子阵异步RLS算法

提出了一种修正的递归最小二乘自适应算法--稳健子阵异步递推最小二乘算法(MSARLS)--用于自适应数字波束形成.该算法综合运用稳健估计和子阵异步递推技术.改进后的算法,不但大大减少了运算量,而且增强了算法抗突发强干扰的性能.另还给出了计算的理论分析和计算机仿真结果.     

采用归一化最小均方误差准则的LM-BP算法

传统神经网络通常以最小均方误差(LMS)或最小二乘（RLS）为收敛准则,而在自适应均衡等一些应用中,使用归一化最小均方误差（NLMS）准则可以使神经网络性能更加优越。本文在NLMS准则基础上,提出了一种以Levenberg-Marquardt（LM）训练的神经网络收敛算法。通过将神经网络的误差函数归一化,然后采用LM算法作为训练算法,实现了神经网络的快速收敛。理论分析和实验仿真表明,与采用最速下降法的NLMS准则和采用LM算法的LMS准则相比,本文算法收敛速度快,归一化均方误差更小,应用于神经网络水印系统中实现了水印信息的盲提取,能更好的抵抗噪声、低通滤波和重量化等攻击,性能平均提高了4%。      

Optimization of Recursive Least Square-Based Adaptive Linear Equalizer for ZigBee Transceiver

An efficient technique to compensate for the channel detrimental effects in ZigBee systems is introduced in this paper. The proposed methodology relies on adding a recursive least square (RLS) based adaptive linear equalizer (ALE) to the physical layer of the receiver side. The performance of the RLS based ALE is investigated inside the ZigBee system under different multipath fading situations: Rician and Rayleigh. Moreover, the paper proposes a methodology for deciding the RLS based ALE’s design parameters. The design procedure depends on solving multiple objectives optimizing function based on genetic algorithms (GAs). The ALE’s parameters are chosen, such that the system experiences minimum bit error rate (BER) with fast convergence response. For design verification purposes, the ZigBee transceiver is modeled in MATLAB Simulink and tested under different fading and signal to noise ratios. In addition, the performance of the RLS adaptation algorithm is compared with the least mean square (LMS) one. The results show that the RLS based ALE provides better ZigBee performance with less BER and fast adaptation response.     

Adaptive joint beamforming and B‐MMSE detection for CDMA signal reception under multipath interference

The combination of antenna array beamforming with multiuser detection can effectively improve the detection efficiency of a wireless system under multipath interference, especially in a fast‐fading channel. This paper studies the performance of an adaptive beamformer incorporated with a block‐wise minimum mean square error(B‐MMSE) detector, which works on a unique signal frame characterized by training sequence preamble and data blocks segmented by zero‐bits. Both beam‐former weights updating and B‐MMSE detection are carried out by either least mean square (LMS) or recursive least square (RLS) algorithm. The comparison of the two adaptive algorithms applied to both beamformer and B‐MMSE detector will be made in terms of convergence behaviour and estimation mean square error. Various multipath patterns are considered to test the receiver's responding rapidity to changing multipath interference. The performance of the adaptive B‐MMSE detector is also compared with that of non‐adaptive version (i.e. through direct matrix inversion). The final performance in error probability simulation reveals that the RLS/B‐MMSE scheme outperforms non‐adaptive B‐MMSE by 1–5 dB, depending on the multipath channel delay profiles of concern. The obtained results also suggest that adaptive beamformer should use RLS algorithm for its fast and robust convergence property; while the B‐MMSE filter can choose either LMS or RLS algorithm depending on antenna array size, multipath severity and implementation complexity. Copyright © 2004 John Wiley & Sons, Ltd.     

基于RLS的二次加权相关时延估计算法

针对测向定位中时延估计的问题,提出了一种基于递推最小二乘（Recursive Least Squares,RLS）算法的二次加权相关时延估计方法。该方法在二次相关算法基础上,一方面引入RLS算法,在二次相关前进行自适应滤波,提高系统抗噪能力,且具有较快的收敛速度;另一方面借鉴广义互相关的思路,引入加权函数,并且采用二次加权方式,提高时延估计的性能。仿真结果表明,在低信噪比环境下,基于RLS的二次加权相关时延估计法使谱峰更加尖锐,抑制了噪声的影响,提高了估计的精度。     

Bias-remedy least mean square equation error algorithm for IIRparameter recursive estimation

In the area of infinite impulse response (IIR) system identification and adaptive filtering the equation error algorithms used for recursive estimation of the plant parameters are well known for their good convergence properties. However, these algorithms give biased parameter estimates in the presence of measurement noise. A new algorithm is proposed on the basis of the least mean square equation error (LMSEE) algorithm, which manages to remedy the bias while retaining the parameter stability. The so-called bias-remedy least mean square equation error (BRLE) algorithm has a simple form. The compatibility of the concept of bias remedy with the stability requirement for the convergence procedure is supported by a practically meaningful theorem. The behavior of the BRLE has been examined extensively in a series of computer simulations     

Adaptive H∞ channel equalization for wirelesspersonal communications

In this paper, a new adaptive H_∞ filtering algorithm is developed to recursively update the tap-coefficient vector of a decision feedback equalizer (DFE) in order to adaptively equalize the time-variant dispersive fading channel of a high-rate indoor wireless personal communication system. Different from conventional L ₂ (such as the recursive least squares (RLS)) filtering algorithms which minimize the squared equalization error, the adaptive H _∞ filtering algorithm is a worst case optimization. It minimizes the effect of the worst disturbances (including input noise and modeling error) on the equalization error. Hence, the DFE with the adaptive H_∞ filtering algorithm is more robust to the disturbances than that with the RLS algorithm. Computer simulation demonstrates that better transmission performance can be achieved using the adaptive H_∞ algorithm when the received signal-to-noise ratio (SNR) is larger than 20 dB     

Image restoration using a conjugate gradient-based adaptive filtering algorithm

A new two-dimensional (2D) sample-based conjugate gradient (SCG) algorithm is developed for adaptive filtering. This algorithm is based on the conjugate gradient method of optimization and therefore has a fast convergence characteristic. The SCG is computationally simpler than the recursive least squares (RLS) algorithm. The SCG algorithm with the equation-error and output-error methods is investigated for application in image restoration. Simulation results show that the new algorithm significantly outperforms existing algorithms in the restoration of noisy images.This work was supported in part by a grant from the Colorado Advanced Software Institute.     

Adaptive Filtering Techniques using Cyclic Prefix in OFDM Systems for Multipath Fading Channel Prediction

This paper presents adaptive channel prediction techniques for wireless orthogonal frequency division multiplexing (OFDM) systems using cyclic prefix (CP). The CP not only combats intersymbol interference, but also precludes requirement of additional training symbols. The proposed adaptive algorithms exploit the channel state information contained in CP of received OFDM symbol, under the time-invariant and time-variant wireless multipath Rayleigh fading channels. For channel prediction, the convergence and tracking characteristics of conventional recursive least squares (RLS) algorithm, numeric variable forgetting factor RLS (NVFF-RLS) algorithm, Kalman filtering (KF) algorithm and reduced Kalman least mean squares (RK-LMS) algorithm are compared. The simulation results are presented to demonstrate that KF algorithm is the best available technique as compared to RK-LMS, RLS and NVFF-RLS algorithms by providing low mean square channel prediction error. But RK-LMS and NVFF-RLS algorithms exhibit lower computational complexity than KF algorithm. Under typical conditions, the tracking performance of RK-LMS is comparable to RLS algorithm. However, RK-LMS algorithm fails to perform well in convergence mode. For time-variant multipath fading channel prediction, the presented NVFF-RLS algorithm supersedes RLS algorithm in the channel tracking mode under moderately high fade rate conditions. However, under appropriate parameter setting in \(2\times 1\) space–time block-coded OFDM system, NVFF-RLS algorithm bestows enhanced channel tracking performance than RLS algorithm under static as well as dynamic environment, which leads to significant reduction in symbol error rate.     

基于压缩感知的分布式协同估计算法

为了降低分布式协同估计算法的计算量并改善其收敛性能,提出了基于压缩感知(CS)和递归最小二乘(RLS)的分布式协同估计算法.该算法在传统RLS分布式协同估计算法的基础上引入压缩感知技术,首先在压缩域中进行递归最小二乘运算,然后利用压缩感知重构算法得到未知参数向量的估计值.提出的算法能够在增量式策略和两种模式的扩散式策略下实现对未知向量的有效估计.理论分析和仿真结果表明,该算法一方面降低了RLS分布式协同估计算法的计算量,另一方面保持较快的收敛速度与良好的均方误差性能.     

鲁棒总体均方最小自适应滤波:算法与分析

本文研究了在输入输出观测数据均含有噪声的情况下如何有效地进行鲁棒自适应滤波的问题.以总体均方误差(TMSE)最小为准则,基于最速下降原理,通过对总体均方误差梯度进行修正,提出了一种鲁棒的总体均方最小自适应滤波算法.通过与已有算法的对比分析表明,该算法能够有效地降低权向量的每步调整量对噪声的敏感程度.仿真实验的结果进一步表明,该算法的鲁棒抗噪性能和稳态收敛精度明显地高于其它同类方法,而且可以使用较大的学习因子,在高噪声环境下仍然保持良好的收敛性.