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.     

Sparse least mean mixed‐norm adaptive filtering algorithms for sparse channel estimation applications

Sparse least‐mean mixed‐norm (LMMN) algorithms are developed to improve the estimation performance for sparse channel estimation applications. Both the benefits of the least mean fourth and least mean square algorithms are utilized to exploit a type of sparse LMMN algorithms. The proposed sparse‐aware LMMN algorithms are implemented by integrating an l ₁‐norm or log‐sum function into the cost function of traditional LMMN algorithm so that they can exploit the sparse properties of the broadband multi‐path channel and achieve better channel estimation performance. The proposed sparse LMMN algorithms are equal to adding an amazing zero‐attractor in the update equation of the traditional LMMN algorithm, which aim to speed up the convergence. The channel estimation performance of the proposed sparse LMMN algorithms are evaluated over a sparse broadband multi‐path channel to verify their effectiveness. Simulation results depict that the sparse LMMN algorithms are superior to the previously reported sparse‐aware least mean square/fourth, least mean fourth and least mean square and their corresponding sparse‐aware algorithms in terms of both the convergence and steady‐state behavior when the broadband multi‐path channel is sparse. Copyright © 2016 John Wiley & Sons, Ltd.     

A bias‐compensated proportionate NLMS algorithm with noisy input signals

This paper proposes a novel proportionate normalized least‐mean‐squares (PNLMS) algorithm that is robust to input noises. Through compensating for biases due to input noise added at the filter input, the proposed PNLMS algorithm avoids performance deterioration owing to the noisy input signals. Moreover, since the proposed PNLMS algorithm uses a new gain‐distribution matrix, it has a fast convergence rate compared with the existing PNLMS algorithms, even when there is no input noise. The experimental results verify that the proposed PNLMS algorithm enhances the filter performance for sparse system identification in the presence of input noises.     

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.     

平方根变步长lp范数LMS算法的稀疏系统辨识

针对稀疏未知系统的辨识问题,提出了一种基于lp(0相似文献   

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%。      

Recursive least square–based fast sparse multipath channel estimation

In the next‐generation wireless communication systems, the broadband signal transmission over wireless channel often incurs the frequency‐selective channel fading behavior and also results in the channel sparse structure, which is supported only by few large coefficients. For the stable wireless propagation to be ensured, linear adaptive channel estimation algorithms, eg, recursive least square and least mean square, have been developed. However, these traditional algorithms are unable to exploit the channel sparsity. Actually, channel estimation performance can be further improved by taking advantage of the sparsity. In this paper, 2 recursive least square–based fast adaptive sparse channel estimation algorithm is proposed by introducing sparse constraints, L1‐norm and L0‐norm, respectively. To improve the flexibility of the proposed algorithms, this paper introduces a regularization parameter selection method to adaptively exploit the channel sparsity. Finally, Monte Carlo–based computer simulations are conducted to validate the effectiveness of the proposed algorithms.     

基于自适应系统辨识的收发隔离技术研究

收发隔离是机载干扰机不可避免的难题。如果收发隔离问题解决不好,轻则削弱干扰机效率,重则造成自发自收,形成自激励。固定步长的归一化最小均方误差(NLMS)算法在解决基于自适应系统辨识的收发隔离的问题时,由于精度不够,隔离效果很不理想。针对此问题提出一种基于先验误差的变步长NLMS算法,该算法依据相邻时刻先验误差的相关系数改变步长因子,改变后的步长因子能够在算法收敛过程中削弱噪声的影响,提高算法精度。理论分析和仿真结果证明:基于文中的变步长NLMS算法的收发隔离方案与基于其他最小均方误差算法的隔离方案相比,隔离性能有较大的改善。     

Adaptive system identification using robust LMS/F algorithm

Adaptive system identification (ASI) problems have attracted both academic and industrial attentions for a long time. As one of the classical approaches for ASI, performance of least mean square (LMS) is unstable in low signal‐to‐noise ratio (SNR) region. On the contrary, least mean fourth (LMF) algorithm is difficult to implement in practical system because of its high computational complexity in high SNR region, and hence it is usually neglected by researchers. In this paper, we propose an effective approach to identify unknown system adaptively by using combined LMS and LMF algorithms in different SNR regions. Experiment‐based parameter selection is established to optimize the performance as well as to keep the low computational complexity. Copyright © 2013 John Wiley & Sons, Ltd.     

A Normalized Least Mean Square Algorithm Based on the Arctangent Cost Function Robust Against Impulsive Interference

In this paper, a normalized least mean square (NLMS) adaptive filtering algorithm based on the arctangent cost function that improves the robustness against impulsive interference is proposed. Owing to the excellent characteristics of the arctangent cost function, the adaptive update of the weight vector stops automatically in the presence of impulsive interference. Thus, this eliminates the likelihood of updating the weight vector based on wrong information resulting from the impulsive interference. When the priori error is small, the NLMS algorithm based on the arctangent cost function operates as the conventional NLMS algorithm. Simulation results show that the proposed algorithm can achieve better performance than the traditional NLMS algorithm, the normalized least logarithmic absolute difference algorithm and the normalized sign algorithm in system identification experiments that include impulsive interference and abrupt changes.     

A Low Power Algorithm for Sparse System Identification using Cross-Correlation

In this paper we present a low power system identification algorithm suitable for echo and crosstalk cancellation in data communications. Crosstalk and echo channels tend to be sparse systems i.e. many taps are negligible with just a few taps significant or active. The proposed adaptive algorithm, called the sparse cross-correlation (SCC) algorithm is designed to exploit the sparsity of crosstalk and echo channels in order to lower the power consumption in the circuit implementation when compared to the normalized least mean squares (NLMS) algorithm.Mathematical analysis of the mean square error suggests that zeroing insignificant taps has a relatively small impact on the algorithm performance. This motivates the SCC algorithm, which uses a cross-correlation to identify the active taps in an unknown system and control circuitry to allocate cancellation hardware at these active tap lags. In the case of sparse systems and signal to noise ratios (SNR) of 10 dB or less, we found that the SCC algorithm can do up to 2 dB better than the NLMS algorithm in terms of the achievable mean square error floor.A detailed hardware implementation of this algorithm is also presented and compared to the benchmark NLMS algorithm in terms of area, critical path and power consumption. Results indicate that a power saving of up to 40% can be achieved at a realistic canceller length of 64 taps while maintaining algorithm performance.Finbarr ORegan was born in Cork, Ireland in 1970, and received the B.E. degree in elctronic engineering from University College Cork in 1993, and the masters degree in electronic engineering from Dublin City University in 1998. He worked with Silicon and Software Systems for several years subsequent to graduation, in the area of IC digital design. His professional activity also includes extensive experience in development and delivery of training courses in the areas of Hardware Design Languages, Low-Power Digital Design, and DSP for Communciations (in collaboration with Esperan and NLight10 Technologies). His research interests include adaptive algorithms for sparse systems, low-power digital design, and signal processing for digital communications. He has recently submitted his Ph.D. thesis at University College Dublin on the topic of adaptive algorithms for sparse systems, with an anticipated award date of Spring 2005.Conor Heneghan was born in Dublin, Ireland, in 1968 and received the B.E. degree in electronic engineering from University College Dublin in 1990, and the Ph.D. degree in electrical engineering from Columbia University, New York, NY, in 1995. He is currently a Senior Lecturer in the Department of Electronic and Electrical Engineering at University College Dublin. His research interests are in the areas of digital signal processing for communications, and for biomedical applications. He is a member of the IEEE Signal Processing Society, Communications Society, and Engineering in Medicine and Biology Society, as well as being a memeber of the Institution of Electrical Engineers (IEE). He is a also a co-founder and director of BiancaMed Ltd., a company specialising in smart signal processing for medical applications.     

一种适用于稀疏多径信道的自适应均衡算法

针对传统的自适应均衡算法在稀疏多径信道下性能表现不佳的问题,提出了一种基于基追踪降噪的自适应均衡算法。该算法利用稀疏多径信道下均衡器权值的稀疏性,将自适应均衡器的训练过程看作压缩感知理论中稀疏信号对字典的加权求和,并利用重构算法直接对稀疏权值进行求解,解决了迭代参数设置和收敛慢的问题。采用基追踪降噪作为重构算法并选用变量分离近似稀疏重构对该最优化问题进行求解,既提高了权值的重构精度又降低了计算的复杂度。仿真结果表明,所提算法能够以较低的计算量和较少的训练序列达到更优性能,这对提升系统的通信性能具有参考价值。     

Real-Time Implementation of Parallel Architecture Based Noise Minimization from Speech Signals on FPGA

In recent years, the real time hardware implementation of LMS based adaptive noise cancellation on FPGA is becoming popular. There are several works reported in this area in the literature. However, NLMS based implementation of adaptive noise cancellation on FPGA using Xilinx System Generator (XSG) is not reported. This paper explores the various forms of parallel architecture based on NLMS algorithm and its hardware implementation on FPGA using XSG for noise minimization from speech signals. In total, the direct form, binary tree direct form and transposed form of parallel architecture of normalized least mean square (NLMS), delayed normalized least mean square and retimed delayed normalized least mean square algorithms are implemented on FPGA using hardware co-simulation model. The performance parameters (SNR and MSE) of these algorithms are analyzed for the adaptive noise cancellation system and the comparison is made with parallel architectures of least mean square (LMS), delayed least mean square, and retimed delayed least mean square algorithms respectively. The hardware utilization of all the said algorithms are also analyzed and compared. The result shows that NLMS based implementations outperform than that of LMS for all forms of parallel architecture for the given parameters with negligence increase in device utility. The binary tree direct form of retimed delayed NLMS achieves the maximum SNR improvement (39.83 dB) in comparison to other NLMS variants at the cost of optimum resource utilization.     

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     

一种改进的数字同频直放站自适应反馈干扰抑制算法

基于数字地面电视广播(Digital Terrestrial Television Broadcasting,DTTB)同频直放站的回波干扰抑制,提出了一种变步长块LMS(Variable Step- size Block Normalized Least Mean Square,VSSBNLMS)自适应算法.此算法的目的是为了提高传统回波干扰抑制的自适应算法的收敛速度和降低计算复杂度.其将输入信号分为长度相等的块,在每一个数据块内,权值向量只更新一次,有效地降低了计算复杂度.另外,该算法通过输出误差控制更新步长的变化,与传统的归一化LMS(NLMS)和块LMS(BLMS)算法相比,提高了收敛速度.仿真结果表明,该算法具有良好的收敛速度和回波干扰抑制性能.     

一种基于约束最小四阶矩的盲自适应多用户检测方法

基于约束最小四阶矩(Least Mean Fourth,LMF)准则,提出了一种新的高阶统计类型的盲多用户检测方法.通过理论分析和证明,采用此准则的盲多用户检测算法能够收敛于全局最小值,且该极值点符合多用户信号迫零解相关的要求.利用最速下降梯度方法,文中给出了盲自适应LMF接收机形式.该多用户接收机具有运算复杂度低,收敛性能好的特点.在AWGN信道和多用户环境中的仿真结果进一步验证了理论分析的结论.     

抗冲激干扰的稀疏惩罚约束遗漏最小均方算法

当被识别系统是稀疏系统时,传统的遗漏最小均方( LLMS )自适应算法收敛性能较差,特别在非高斯噪声环境中,该算法性能进一步恶化甚至算法不平稳收敛。为了解决因信道的稀疏性使算法收敛变慢的问题,对LLMS算法的代价函数分别利用加权詛1-norm和加权零吸引两种稀疏惩罚项进行改进;为了优化算法的抗冲激干扰的性能,利用符号函数对已改进的算法迭代式作进一步改进。同时,将提出的两个算法运用于非高斯噪声环境下的稀疏系统识别,仿真结果显示提出的算法性能优于现存的同类稀疏算法。     

基于子带分解和比例归一化算法的回声消除器设计与仿真

针对稀疏信道条件下的网络回声抵消问题。提出了一种比例归一化子带自适应滤波算法。该算法基于子带分解结构,并利用网络中回声路径的稀疏特性,使得各个系数的步长与该系数的绝对值成比例,加快了活动系数的收敛速度,从而改善了子带分解算法在稀疏信道条件下的性能。仿真结果表明：将所提算法应用于网络回声消除器,能够获得很快的收敛速度和很低的稳态失调。     

一种约束稳定性最小均方噪声对消算法

研究了最小均方误差(LMS)算法、归一化的最小均方(NLMS)算法及变步长NLMS算法在自适应噪声干扰抵消器中的应用,针对目前这些算法在噪声对消器应用中的缺点,将约束稳定性最小均方(CS-LMS)算法应用到噪声处理中,并进一步结合变步长的思想提出来一种新的变步长CS-LMS算法。通过MATLAB进行仿真分析,结果证实提出的算法与其他算法相比,能很好地滤除掉噪声从而得到期望信号,明显的降低了稳态误差,并拥有好的收敛速度。