一种约束稳定性最小均方波束形成算法

针对归一化最小均方（NLMS）算法步长调整精度不高的问题,将约束稳定性最小均方（CS-LMS）算法应用于智能天线的波束形成问题。通过引入后验误差的稳定性约束条件,构建适合波束形成问题的优化目标,并给出了其解的计算复杂度、收敛速度和稳态误差的理论分析。计算机仿真结果证实,CS-LMS波束形成算法比NLMS算法具有更加优良的抗干扰性能,较快的收敛速度,良好的系统跟踪能力和较小的稳态误差,尤其是当输入信号发生中断或突变时,算法依然工作得很好。     

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。     

一种改进的变步长ELMS算法

在简单讨论基本最小均方(LMS)算法的基础上,引入了扩展的最小均方(ELMS)算法,并分析说明了该算法能达到更小的稳态MSE。改进的变步长ELMS算法是在对有用信号的预测中采用了自适应为归一化的的最小均方(NLMS)预测估计器,步长的迭代中引入遗忘因子i,利用其与误差信号的加权和来产生新的步长参与迭代。理论分析与计算机仿真结果表明,该算法有较好的收敛性能和较小的稳态失调。     

变步长NLMS算法在CDMA窄带干扰抑制中的应用

CDMA窄带干扰可以通过自适应线性预测器(ALP)来抑制。而自适应算法的稳态均方误差(MSE)与收敛速度是决定其性能的关键。在正规最小均方误差算法(NLMS)的基础上引入变步长NLMS算法(VSS-NLMS)，并对其进行了稳态性能分析。通过计算机仿真模拟，证实此算法的稳态MSE和收敛速度都明显优于NLMS算法，因而改善了对CDMA窄带干扰的抑制能力。     

等效凹槽滤波器及其在无源相关定位雷达中的应用(英文)

归一化最小均方误差(NLMS)算法被广泛应用于无源相干定位(PCL)雷达系统的直达波和多径干扰对消。该文提出NLMS干扰对消器与雷达模糊函数结合可以等效为凹槽滤波器,该滤波器在雷达模糊函数平面中的零多普勒处产生一个凹槽。分析显示凹槽的宽度和深度与NLMS算法的步长密切相关。文章分析了凹槽对PCL雷达目标检测的影响,结果显示宽的凹槽会使PCL雷达系统的目标检测性能恶化。文章进一步提出了非均匀归一化最小均方误差(Non-uniform NLMS, NNLMS)算法,该算法能有效抑制具有多普勒频率的杂波,并且能有效降低雷达模糊函数的底噪。该算法引进了步长矩阵,利用该矩阵可以实现在不同的距离单元产生不同宽度的凹槽,每个距离门的凹槽宽度取决于杂波干扰的能量和多普勒频率。与传统NLMS相比,NNLMS算法可以实现更快的收敛速度,试验结果验证了该算法的有效性及优越性。      

一种新的可变步长LMS自适应滤波算法及其算法分析

在讨论基本LMS．变步长NLMS和LMS／F组合自适应滤波算法的基础上提出一种新的可变步长LMS自适应滤波算法,新算法引入修正系数和遗忘因子．并利用和来产生新的步长参与迭代。计算机仿真结果表明,与基本LMS算法或变步长NLMS、LMS／F组合算法相比,新算法在保持算法简单这一特点的同时进一步加快了收敛速度,并能够收敛到更小且稳定的均方误差(MSE)。     

一种改进的可变步长LMS算法及性能分析

为解决自适应算法的收敛速度和稳态误差两者间的矛盾,对归一化的最小均方(NLMS)算法、变步长算法及可变步长NVSS算法进行了研究,并结合变步长的思想,提出了一种新的可变步长算法。新的算法中引入合适的遗忘因子与修正参数来建立与步长因子间的函数关系,加快了算法收敛速度的同时,也能在非平稳的环境中有好的跟踪能力。最后把不同的算法应用到系统辨识系统中,通过MATLAB进行实验仿真,结果证实了新提出的算法有快的收敛速度和跟踪时变系统的能力。     

一种新的可变步长LMS自适应滤波算法

在简单讨论基本LMS，变步长NLMS和LMS／F组合自适应滤波算法的基础上提出一种新的可变步长LMS自适应滤波算法，新算法引入修正系数ρ和遗忘因子λi=exp(-i)，并利用ρ和λi来产生新的步长参与迭代，计算机仿真结果表明，与基本LMS算法或变步长NLMS、LMS／F组合算法相比，新算法在保持算法简单这一特点的同时进一步加快了收敛速度，并能够收敛到更小且稳定的均方误差(MSE)。     

基于相控阵自适应零陷的大规模NGSO星座间干扰规避策略研究

针对大规模非静止轨道（Non-Geo Stationary Orbit,NGSO）通信星座系统间同频干扰的实时性和突发性问题,将自适应波束成形技术的变步长LMS(Least Mean Square,最小均方误差)算法应用于NGSO间干扰场景。分析自适应波束成形技术的适用场景,选取OneWeb星座系统与Starlink星座系统的馈线链路间下行干扰场景进行仿真。通过对现有算法进行系统收敛速度、稳健性的性能比较,当NLMS(Normalization Least Mean Square,归一化最小均方误差)算法的参数μ0=0.6时,算法具有较快的收敛速度以及较小的稳态误差,因此运算量小、易于星上硬件实现。分别利用固定步长LMS算法、ENLMS(Error Normalization Least Mean Square,误差归一化最小均方误差)算法以及μ0=0.6的NLMS算法计算最优权向量,并应用于干扰仿真场景。结果表明,μ0=0.6的NLMS算法最能有效规避NGSO通信星座系统间的同频干扰,ENLMS算法次之,固定LMS算法的干扰规避效果最差。     

一种改进的变步长NLMS算法

针对传统NLMS使用固定步长而出现的收敛速度和稳态误差的矛盾,提出一种改进的变步长NLMS算法。该算法建立了步长与误差的函数关系,使步长随着输出误差和噪声误差的变化而动态更新,从而降低稳态误差。理论分析和仿真结果表明,与现有NLMS算法相比,改进的算法具有更快的收敛速度和更低的稳态误差。     

Block-based fuzzy step size nlms algorithms for subband adaptive channel equalisation

Judicious selection of the step size parameter is crucial for adaptive algorithms to strike a good balance between convergence speed and misadjustment. The fuzzy step size (FSS) technique has been shown to improve the performance of the classical fixed step size and variable step size (VSS) normalised least mean square (NLMS) algorithms. The performance of the FSS technique in the context of subband adaptive equalisation is analysed and two novel block-based fuzzy step size (BFSS) strategies for the NLMS algorithm, namely fixed block fuzzy step size (FBFSS) and adaptive block fuzzy step size (ABFSS) are proposed. By exploiting the nature of gradient noise inherent in stochastic gradient algorithms, these strategies are shown to substantially reduce the computational complexity of the conventional FSS technique without sacrificing the convergence speed and steady-state performance. Instead of updating the step size at every iteration, the proposed techniques adjust the step size based on the instantaneous squared error once over a block length. Design methodology and guidelines that lead to good performance for the algorithms are given.     

Convergence Behavior of NLMS Algorithm for Gaussian Inputs: Solutions Using Generalized Abelian Integral Functions and Step Size Selection

This paper studies the mean and mean square convergence behaviors of the normalized least mean square (NLMS) algorithm with Gaussian inputs and additive white Gaussian noise. Using the Price’s theorem and the framework proposed by Bershad in IEEE Transactions on Acoustics, Speech, and Signal Processing (1986, 1987), new expressions for the excess mean square error, stability bound and decoupled difference equations describing the mean and mean square convergence behaviors of the NLMS algorithm using the generalized Abelian integral functions are derived. These new expressions which closely resemble those of the LMS algorithm allow us to interpret the convergence performance of the NLMS algorithm in Gaussian environment. The theoretical analysis is in good agreement with the computer simulation results and it also gives new insight into step size selection.     

一种基于误差相关函数的改进变步长LMS算法

最小均方算法的收敛速度和稳态误差之间存在矛盾,为此人们提出了各种变步长LMS算法,其中E-LMS算法是将步长与瞬时误差平方相关联,R-LMS算法是将步长与误差的相关函数相关联。E-LMS算法的抗噪性能较差,在低信噪比条件下性能明显变差,R-LMS算法对突变系统的跟踪能力较差。为此文中给出了一种改进的,基于误差相关函数的VSS-LMS算法,该方法利用E-LMS算法的控制步长策略提高算法的跟踪能力。计算机仿真结果显示,该算法能够同时满足抗噪和跟踪两种要求。     

基于DFP的二阶Volterra模型及其对Rössler混沌序列的预测

为克服最小二乘法或归一化最小二乘法在二阶Volterra建模时参数选择不当引起的问题,在最小二乘法基础上,应用一种基于后验误差假设的可变收敛因子技术,构建了一种基于Davidon-Fletcher-Powell算法的二阶Volterra模型（DFPSOVF）.给出参数估计中自相关逆矩阵估计的递归更新公式,并对其正定性、有界性和τ（n）的作用进行了研究.将DFPSOVF模型应用于Rössler混沌序列的单步预测,仿真结果表明其能够保证算法的稳定性和收敛性,不存在最小二乘法和归一化最小二乘法的发散问题.     

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.     

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.     

Robust Regularization for Normalized LMS Algorithms

We present a novel normalized least mean square (NLMS) algorithm with robust regularization. The proposed algorithm dynamically updates the regularization parameter that is fixed in the conventional$epsilon $-NLMS algorithms. By exploiting the gradient descent direction we derive a computationally efficient and robust update scheme for the regularization parameter. Through experiments we demonstrate that the proposed algorithm outperforms conventional NLMS algorithms in terms of the convergence rate and the misadjustment error.     

A set of algorithms linking NLMS and block RLS algorithms

This paper describes a set of block processing algorithms which contains as extremal cases the normalized least mean squares (NLMS) and the block recursive least squares (BRLS) algorithms. All these algorithms use small block lengths, thus allowing easy implementation and small input-output delay. It is shown that these algorithms require a lower number of arithmetic operations than the classical least mean squares (LMS) algorithm, while converging much faster. A precise evaluation of the arithmetic complexity is provided, and the adaptive behavior of the algorithm is analyzed. Simulations illustrate that the tracking characteristics of the new algorithm are also improved compared to those of the NLMS algorithm. The conclusions of the theoretical analysis are checked by simulations, illustrating that, even in the case where noise is added to the reference signal, the proposed algorithm allows altogether a faster convergence and a lower residual error than the NLMS algorithm. Finally, a sample-by-sample version of this algorithm is outlined, which is the link between the NLMS and recursive least squares (RLS) algorithms     

Variable Step Size LMS Algorithm Based on Function Control

This paper proposes a function-controlled variable step size least mean square (VSLMS) algorithm for channel estimation in low-SNR or colored input signals. The proposed method aligns the step size update with the steady-state error and alleviates the impact of high-level noise. It improves the filter performance in terms of fast convergence rate and low misadjustment error. Simulation results demonstrate the effectiveness and verify the theoretic analysis of the proposed VSLMS algorithm.