Sparse LMS/F algorithms with application to adaptive system identification

Standard least mean square/fourth (LMS/F) is a classical adaptive algorithm that combined the advantages of both least mean square (LMS) and least mean fourth (LMF). The advantage of LMS is fast convergence speed while its shortcoming is suboptimal solution in low signal‐to‐noise ratio (SNR) environment. On the contrary, the advantage of LMF algorithm is robust in low SNR while its drawback is slow convergence speed in high SNR case. Many finite impulse response systems are modeled as sparse rather than traditionally dense. To take advantage of system sparsity, different sparse LMS algorithms with l_p‐LMS and l₀‐LMS have been proposed to improve adaptive identification performance. However, sparse LMS algorithms have the same drawback as standard LMS. Different from LMS filter, standard LMS/F filter can achieve better performance. Hence, the aim of this paper is to introduce sparse penalties to the LMS/F algorithm so that it can further improve identification performance. We propose two sparse LMS/F algorithms using two sparse constraints to improve adaptive identification performance. Two experiments are performed to show the effectiveness of the proposed algorithms by computer simulation. In the first experiment, the number of nonzero coefficients is changing, and the proposed algorithms can achieve better mean square deviation performance than sparse LMS algorithms. In the second experiment, the number of nonzero coefficient is fixed, and mean square deviation performance of sparse LMS/F algorithms is still better than that of sparse LMS algorithms. Copyright © 2013 John Wiley & Sons, Ltd.     

Sparse least mean fourth algorithm for adaptive channel estimation in low signal‐to‐noise ratio region

Both least mean square (LMS) and least mean fourth (LMF) are popular adaptive algorithms with application to adaptive channel estimation. Because the wireless channel vector is often sparse, sparse LMS‐based approaches have been proposed with different sparse penalties, for example, zero‐attracting LMS and L_p‐norm LMS. However, these proposed methods lead to suboptimal solutions in low signal‐to‐noise ratio (SNR) region, and the suboptimal solutions are caused by LMS‐based algorithms that are sensitive to the scaling of input signal and strong noise. Comparatively, LMF can achieve better solution in low SNR region. However, LMF cannot exploit the sparse information because the algorithm depends only on its adaptive updating error but neglects the inherent sparse channel structure. In this paper, we propose several sparse LMF algorithms with different sparse penalties to achieve better solution in low SNR region and take the advantage of channel sparsity at the same time. The contribution of this paper is briefly summarized as follows: (1) construct the cost functions of the LMF algorithm with different sparse penalties; (2) derive their lower bounds; and (3) provide experiment results to show the performance advantage of the propose method in low SNR region. Copyright © 2013 John Wiley & Sons, Ltd.     

Adaptive sparse system identification using normalized least mean fourth algorithm

Normalized least mean square (NLMS) was considered as one of the classical adaptive system identification algorithms. Because most of systems are often modeled as sparse, sparse NLMS algorithm was also applied to improve identification performance by taking the advantage of system sparsity. However, identification performances of NLMS type algorithms cannot achieve high‐identification performance, especially in low signal‐to‐noise ratio regime. It was well known that least mean fourth (LMF) can achieve high‐identification performance by utilizing fourth‐order identification error updating rather than second‐order. However, the main drawback of LMF is its instability and it cannot be applied to adaptive sparse system identifications. In this paper, we propose a stable sparse normalized LMF algorithm to exploit the sparse structure information to improve identification performance. Its stability is shown to be equivalent to sparse NLMS type algorithm. Simulation results show that the proposed normalized LMF algorithm can achieve better identification performance than sparse NLMS one. Copyright © 2013 John Wiley & Sons, Ltd.     

A novel variable step size adjustment method based on channel output autocorrelation for the LMS training algorithm

The least mean squares (LMS) algorithm, the most commonly used channel estimation and equalization technique, converges very slowly. The convergence rate of the LMS algorithm is quite sensitive to the adjustment of the step‐size parameter used in the update equation. Therefore, many studies have concentrated on adjusting the step‐size parameter in order to improve the training speed and accuracy of the LMS algorithm. A novel approach in adjusting the step size of the LMS algorithm using the channel output autocorrelation (COA) has been proposed for application to unknown channel estimation or equalization in low‐SNR in this paper. Computer simulations have been performed to illustrate the performance of the proposed method in frequency selective Rayleigh fading channels. The obtained simulation results using HIPERLAN/1 standard have demonstrated that the proposed variable step size LMS (VSS‐LMS) algorithm has considerably better performance than conventional LMS, recursive least squares (RLS), normalized LMS (N‐LMS) and the other VSS‐LMS algorithms. Copyright © 2011 John Wiley & Sons, Ltd.     

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     

Combined LMS/F algorithm

A new adaptive filter algorithm has been developed that combines the benefits of the least mean square (LMS) and least mean fourth (LMF) methods. This algorithm, called LMS/F, outperforms the standard LMS algorithm judging either constant convergence rate or constant misadjustment. While LMF outperforms LMS for certain noise profiles, its stability cannot be guaranteed for known input signals even For very small step sizes. However, both LMS and LMS/F have good stability properties and LMS/F only adds a few more computations per iteration compared to LMS. Simulations of a non-stationary system identification problem demonstrate the performance benefits of the LMS/F algorithm     

Block sequential least squares decision feedback equalizationalgorithm with application to terrestrial HDTV transmission

Due to the very high symbol rate of terrestrial HDTV systems, up to now there exist no equalization solutions with sufficiently low hardware complexity and satisfactory performance for commercial applications. We present a block sequential least squares decision feedback equalization algorithm with application to over-the-air HDTV channels. The proposed adaptive algorithm is derived on the basis of minimization of the least squares criterion, thereby achieving faster convergent and tracking rate relative to the recommended LMS algorithm. Meanwhile, good numerical stability is guaranteed because it successfully eliminates time updates of the filtering coefficients, which is the main cause of instability of FTF-like algorithms. Also of great significance is its drastic reduction in computational complexity by means of block operation, taking advantage of the slowly time-varying nature of terrestrial broadcasting channels. Simulation results show that the equalizer achieves an almost 3.5 dB SNR improvement at a bit error rate of 3×10^-6 without significant increase in computational complexity, as compared to the conventional LMS decision feedback equalizer (DFE) when applied to the equalization of over-the-air HDTV channels     

一种改进的变步长频域批处理LMS自适应算法

从基本的经典LMS自适应算法开始,简要介绍了频域批处理LMS算法的推导、实现原理及优势,并在频域批处理LMS算法基础上提出了一种由当前时刻输入信号能量和前一时刻均方误差曲面梯度估计量联合控制的变步长改进算法,改进算法在减小计算量的同时,不仅消除了经典LMS算法收敛性能对输入信号功率敏感的缺陷,而且较好地协调了高速收敛与小稳态误差之间的矛盾.     

Adaptive echo cancellation using least mean mixed-norm algorithm

A novel algorithm for echo cancellation is presented in this work. The algorithm consists of simultaneously applying the least mean square (LMS) algorithm to the near-end section of the echo canceller and the least mean fourth (LMF) algorithm to the far-end section. This new scheme results in a substantial performance improvement over the LMS algorithm and other algorithms     

VLSI implementation of a new LMS-based algorithm for noise removal in ECG signal

Least mean square (LMS)-based adaptive filters are widely deployed for removing artefacts in electrocardiogram (ECG) due to less number of computations. But they posses high mean square error (MSE) under noisy environment. The transform domain variable step-size LMS algorithm reduces the MSE at the cost of computational complexity. In this paper, a variable step-size delayed LMS adaptive filter is used to remove the artefacts from the ECG signal for improved feature extraction. The dedicated digital Signal processors provide fast processing, but they are not flexible. By using field programmable gate arrays, the pipelined architectures can be used to enhance the system performance. The pipelined architecture can enhance the operation efficiency of the adaptive filter and save the power consumption. This technique provides high signal-to-noise ratio and low MSE with reduced computational complexity; hence, it is a useful method for monitoring patients with heart-related problem.     

基于LMK准则的盲自适应多用户检测器

 本文提出了一种加性高斯白噪声(AWGN)信道下,同步直扩码分多址(DS/CDMA)系统的基于LMK(最小平均峰度,Least Mean Kurtosis)准则的线性盲自适应多用户检测器.这种检测器的算法是一种具有较低计算量的基于高阶统计量的算法.分析证明了这种检测器的算法的收敛性和可以实现多用户信号的盲解相关.并对基于该准则的线性盲自适应检测器和基于LMS(最小均方,Least Mean Square)准则的检测器的收敛性能进行了仿真比较.     

Efficient sign based normalized adaptive filtering techniques for cancelation of artifacts in ECG signals: Application to wireless biotelemetry

In this paper, several simple and efficient sign based normalized adaptive filters, which are computationally superior having multiplier free weight update loops are used for cancelation of noise in electrocardiographic (ECG) signals. The proposed implementation is suitable for applications such as biotelemetry, where large signal to noise ratios with less computational complexity are required. These schemes mostly employ simple addition, shift operations and achieve considerable speed up over the other least mean square (LMS) based realizations. Simulation studies shows that the proposed realization gives better performance compared to existing realizations in terms of signal to noise ratio and computational complexity.     

Non-stationary signal analysis by least mean fourth (LMF) adaptive algorithm

A modified least mean fourth (LMF) adaptive algorithm applicable to non-stationary signals is presented. The performance of the proposed algorithm is studied by simulation for non-stationarities in bandwidth, centre frequency and gain of a stochastic signal. These non-stationarities are in the form of linear, sinusoidal and jump variations of the parameters. The proposed LMF adaptation is found to have better parameter tracking capability than the LMS adaptation for the same speed of convergence.     

一种改进的变步长LMS自适应算法

传统的最小均方误差(LMS)算法难以同时获取较快的收敛速度和较小的稳态误差,而变步长LMS算法可获得二者之间的平衡。对已有的一些变步长LMS算法进行了分析,在变系数步长(VFSS)算法的基础上,引入输入信号因子,并建立步长因子与误差信号之间新的非线性函数关系,提出一种改进的变步长LMS算法,该算法不仅继承了VFSS算法在低信噪比环境下抗噪声性能好的特点,而且能够快速跟踪系统的变化,仿真结果表明改进算法的性能优于现有算法。     

一种改进的变步长自适应滤波器LMS算法

本文提出一种改进的LMS算法(即MS-LMS)，并建立了步长因子μ与误差信号e(n)之间另一种新的非线性函数关系。该关系不仅具有原有算法在误差e(n)接近零处缓慢变化的优点，而且低信噪比环境下比原有算法具有更好的收敛性能。理论分析和计算机仿真结果表明，在低信噪比的环境下，改进算法的收敛速度和稳态误差的性能指标都有较大的提高，并对系统发生的突变表现出较强的鲁棒性。     

基于子带分解的自适应滤波

本文对基于子带分解的自适应滤波做了研究，给出子带分解下的包含子带间滤波的最优维纳解和ＬＭＳ算法，并分析了其收敛性能和计算复杂度，与传统的ＬＭＳ算法相比，基于子带分解的自适应滤波具有更好的性能，计算机模拟结果也体现了这一点。     

LMS算法的二次稳定性及鲁棒LMS算法

本文在时域内研究LMS算法(least mean square algorithm)的稳定性及鲁棒LMS算法的构造.首先将LMS算法表达式转化为标准的离散时间系统状态方程形式,之后运用线性矩阵不等式(LMI)技术对其二次稳定性进行了分析.针对滤波过程中会出现的输入和测量噪声干扰,本文提出了一种兼顾收敛性、鲁棒稳定性以及鲁棒性能的鲁棒LMS算法,最后给出了仿真算例,通过和一般的LMS算法的比较,体现了这种鲁棒LMS算法的优越性.     

一种用于水声相干通信系统的自适应均衡算法

多通道判决反馈均衡器(MC-DFE)是水声相干通信克服信道多径效应、消除码间干扰(ISI)的主要手段。为了减少多通道数据处理的复杂性、优化算法、提高算法精度,该文提出了自适应自最优预合并多通道判决反馈均衡算法。该算法将快速自优化LMS分集合并(FOLMSDC)算法、快速自优化LMS(FOLMS)算法和快速自优化LMS相位补偿(FOLMSPC)算法有机地结合在一起,使用统一的误差信号,按照最小化均方误差(MMSE)准则调节各部分的系数,从而实现均衡器性能的全局最优。仿真试验和湖上试验对该算法的性能进行了分析。实验结果表明,该文提出的算法可以进一步减少运算量,提高通信系统的接收性能,算法性能优于已有算法。     

Fuzzy stochastic gradient decision feedback equalizer for VSBterrestrial HDTV broadcasting

We present a fuzzy stochastic gradient (FSG) decision feedback equalizer (DFE) for VSB terrestrial HDTV broadcasting. This equalizer employs a well-designed fuzzy Takagi-Sugeno (1985) model to automatically regulate the step size of the descent gradient vector, combining a fast convergence rate and a low excess mean square error (MSE). The only penalty paid is a slight increase in the computational complexity compared with the LMS algorithm. Simulation results show that this equalizer provides 3.5 dB signal-to-noise ratio (SNR) improvement at a BER of 3.0×10^-6 with respect to the conventional LMS DFE recommended by the Grand Alliance     

Adaptive power techniques for blind channel estimation in CDMA systems

The problem of blind adaptive channel estimation in code-division multiple access (CDMA) systems is considered. Motivated by the iterative power method, which is used in numerical analysis for estimating singular values and singular vectors, we develop recursive least squares (RLS) and least mean squares (LMS) subspace-based adaptive algorithms in order to identify the impulse response of the multipath channel. The schemes proposed in this paper use only the spreading code of the user of interest and the received data and are therefore blind. Both versions (RLS and LMS) exhibit rapid convergence combined with low computational complexity. With the help of simulations, we demonstrate the improved performance of our methods as compared with the already-existing techniques in the literature.