A new variable step-size LMS method and its application in DOA estimation of OFDMA signals

To meet the requirements of quick positioning of mobile terminals from base stations(BSs)or third-party devices,as well as to improve the convergence speed and reduce the steady state maladjustment of the least mean square(LMS)method,a new logarithmic-sigmoid variable step-size LMS(LG-SVSLMS)was proposed and applied to estimate the direction of arrival(DOA)of orthogonal frequency division multiple access(OFDMA)signals.Based on the proposed LG-SVSLMS,a non-blind DOA estimation system for OFDMA signals was constructed.The proposed LG-SVSLMS adopts a new multi-parameter step-size update function which combines the sigmoid function and the logarithmic function.It controls the adjustment magnitude of step-size during the initial and steady state phases of the LMS method to achieve both a high convergence speed and low steady state maladjustment.Finally,simulation was conducted to verify the performance of the LG-SVSLMS.The simulation results show that the non-blind DOA estimation system based on the LG-SVSLMS can accurately estimate the DOA of the target signal in the scenario where interference signals from multi-source and multi-path fading signals arrive at the third-party devices asynchronously with the target signal,and the estimation deviation is within±3°.The non-blind DOA estimation for OFDMA signals with the proposed LG-SVSLMS is of great significance for the instant positioning technology of mobile terminals based on the adaptive antenna array.

CMA-MESO千米尺度变分同化系统中极小化控制变量的重构

重构GRAPES(Global/Regional Assimilation and Prediction System)全球、区域一体化变分同化系统中的极小化控制变量,提升中、小尺度同化分析能力,为中国气象局业务区域数值预报系统CMA-MESO提供千米尺度适用的同化方案。新方案用纬向风速(u)和经向风速(v)替代原有流函数和势函数作为新的风场控制变量,采用温度和地面气压(T,ps)替代原有非平衡无量纲气压作为新的质量场控制变量,同时不再考虑准地转平衡约束,而是采用连续方程弱约束保证分析平衡。背景误差参数统计和数值试验结果表明,采用重构后的极小化控制变量,观测信息传播更加局地,分析结构更加合理,避免了原方案在中、小尺度应用时存在的虚假相关问题。连续方程弱约束的引入,限制了同化分析中辐合、辐散的不合理增长,帮助新方案在分析更加局地的同时保证分析平衡。为期1个月的连续同化循环和预报试验结果表明,新方案可以减小风场和质量场分析误差,CMAMESO系统地面降水和10 m风场的预报评分显著提升。

New normalized LMS adaptive filter with a variable regularization factor

A new normalized least mean square(NLMS) adaptive filter is first derived from a cost function, which incorporates the conventional one of the NLMS with a minimum-disturbance(MD)constraint. A variable regularization factor(RF) is then employed to control the contribution made by the MD constraint in the cost function. Analysis results show that the RF can be taken as a combination of the step size and regularization parameter in the conventional NLMS. This implies that these parameters can be jointly controlled by simply tuning the RF as the proposed algorithm does. It also demonstrates that the RF can accelerate the convergence rate of the proposed algorithm and its optimal value can be obtained by minimizing the squared noise-free posteriori error. A method for automatically determining the value of the RF is also presented, which is free of any prior knowledge of the noise. While simulation results verify the analytical ones, it is also illustrated that the performance of the proposed algorithm is superior to the state-of-art ones in both the steady-state misalignment and the convergence rate. A novel algorithm is proposed to solve some problems. Simulation results show the effectiveness of the proposed algorithm.

VARIABLE STEP-SIZE BDF3 METHOD FOR ALLEN-CAHN EQUATION

In this work,we analyze the three-step backward differentiation formula(BDF3)method for solving the Allen-Cahn equation on variable grids.For BDF2 method,the discrete orthogonal convolution(DOC)kernels are positive,the stability and convergence analysis are well established in[Liao and Zhang,Math.Comp.,90(2021),1207–1226]and[Chen,Yu,and Zhang,arXiv:2108.02910,2021].However,the numerical analysis for BDF3 method with variable steps seems to be highly nontrivial due to the additional degrees of freedom and the non-positivity of DOC kernels.By developing a novel spectral norm inequality,the unconditional stability and convergence are rigorously proved under the updated step ratio restriction rk:=τk/τk−1≤1.405 for BDF3 method.Finally,numerical experiments are performed to illustrate the theoretical results.To the best of our knowledge,this is the first theoretical analysis of variable steps BDF3 method for the Allen-Cahn equation.

Optimal variable step-size LMS model and algorithm with independence assumption

To solve the contradiction between convergence rate and steady-state error in least mean square (LMS) algorithm, basing on independence assumption, this paper proposes and proves the optimal step-size theorem from the view of minimizing mean squared error (MSE). The theorem reveals the one-to-one mapping between the optimal step-size and MSE. Following the theorem, optimal variable step-size LMS (OVS-LMS) model, describing the theoretical bound of the convergence rate of LMS algorithm, is constructed. Then we discuss the selection of initial optimal step-size and updating of optimal step-size at the time of unknown system changing. At last an optimal step-size LMS algorithm is proposed and tested in various environments. Simulation results show the proposed algorithm is very close to the theoretical bound.

VARIABLE STEP-SIZE IMPLICIT-EXPLICIT LINEAR MULTISTEP METHODS FOR TIME-DEPENDENT PARTIAL DIFFERENTIAL EQUATIONS

Implicit-explicit （IMEX） linear multistep methods are popular techniques for solving partial differential equations （PDEs） with terms of different types. While fixed timestep versions of such schemes have been developed and studied, implicit-explicit schemes also naturally arise in general situations where the temporal smoothness of the solution changes. In this paper we consider easily implementable variable step-size implicit-explicit （VSIMEX） linear multistep methods for time-dependent PDEs. Families of order-p, pstep VSIMEX schemes are constructed and analyzed, where p ranges from 1 to 4. The corresponding schemes are simple to implement and have the property that they reduce to the classical IMEX schemes whenever constant time step-sizes are imposed. The methods are validated on the Burgers＇ equation. These results demonstrate that by varying the time step-size, VSIMEX methods can outperform their fixed time step counterparts while still maintaining good numerical behavior.

一种新型变步长CMA盲均衡算法

针对传统固定步长CMA盲均衡算法中收敛速度和剩余误差这对矛盾,提出了一种新型变步长恒模盲均衡算法,即由瑞利分布函数实施对其步长的调节,通过调整该步长公式中的两个参数以加快收敛速度和减小剩余误差,并且在此基础上对该算法进行了改进。用4QAM信号,通过典型电话信道对固定步长的CMA算法,基于瑞利步长的CMA和改进后的CMA算法进行计算机仿真。通过对仿真出的算法收敛曲线以及输出星座图进行分析,最终得出在瑞利步长算法的基础上改进后的CMA算法克服了前两种算法的缺点,即具有收敛速度更快,剩余误差更小的优点。

Variable step-size adaptive filtering algorithm based on an exponent sin function

This paper proposes a robust adaptive filter based on the exponent sin cost to improve the capability against Gaussian or multiple types of non-Gaussian noises of the adaptive filtering algorithm when dealing with time-varying/time-invariant linear systems function exponent sin(ExpSin).Then a variable step-size(VSS)-ExpSin algorithm is extended further.Besides,the stepsize,the convergence,and the steady-state performance of the proposed algorithm are validated experimentally.The Monte Carlo simulation results of linear system identification illustrate the principle and efficiency of this proposed adaptive filtering algorithm.Results suggest that the proposed adaptive filtering algorithm has superior performance when estimating the unknown linear systems under multiple-types measurement noises.

Superior step-size theorem and its application——Parallel variable step-size LMS filters algorithm

With independence assumption, this paper proposes and proves the superior step-size theorem on least mean square (LMS) algorithm, from the view of minimizing mean squared error (MSE). Following the theorem we construct a parallel variable step-size LMS filters algorithm. The theoretical model of the proposed algorithm is analyzed in detail. Simulations show the proposed theoretical model is quite close to the optimal variable step-size LMS (OVS-LMS) model. The experimental learning curves of the proposed algorithm also show the fastest convergence and fine tracking performance. The proposed algorithm is therefore a good realization of the OVS-LMS model.

一种变步长CMA算法的研究

采用固定步长的CMA算法使得收敛速度与精度存在制约关系,导致收敛效果不理想。为解决此问题,提出了一种变步长的CMA算法,即在算法收敛刚开始时增大步长值,从而加快收敛速度,在算法即将到达收敛点时,减小步长值,从而降低稳态误差。算法分析和仿真结果表明,改进的算法具有更快的收敛速度。

基于误差信号峰度的时变步长恒模盲均衡算法

论文针对固定步长恒模盲均衡算法的缺陷,提出了一种自适应时变步长恒模盲均衡算法,采用误差信号的峰度作为步长控制因子。经计算机仿真与理论分析表明,该算法与传统恒模算法相比,收敛速度加快,稳态剩余误差减小。

COMPENSATION CONTROL OF REAL-TIME UNBALANCE FORCE FOR ACTIVE MAGNETIC BEARING SYSTEM

Aiming at the stability and others properties of active magnetic bearing （AMB） system influenced by the periodic unbalance stimulation synchronous with rotor rotational speed, a new real-time adaptive feed-forward unbalance force compensation scheme is proposed based on variable step-size least mean square（LMS） algorithm as the feed-forward compensation controller. The controller can provide some suitable sinusoidal signals to com- pensate the feedback unbalance response signals synchronous with the rotary frequency, then reduce the fluctua- tion of the control currents and weaken the active control of AMB system. The variable step-size proportional to the rotational frequency is deduced by analyzing the principle of normal LMS algorithm and its deficiency in the application of real-time filtering of AMB system. Experimental results show that the new method can implement real-time unbalance force compensation in a wide frequency band, reduce the effect of unbalance stimulant force on the housing of AMB system, and provide convenience to improve rotational speed.

一种新的变步长常模盲均衡算法

常模盲均衡算法采用固定步长时存在收敛速度和稳态误差之间的矛盾,解决这一矛盾的有效方法是用变步长代替固定步长。在分析了常模算法误差特性的基础上,建立了步长因子和误差信号之间的一种非线性函数关系,分析了函数中参数对步长因子的控制,较好地满足了常模算法迭代过程对步长因子的要求,得到一种新的变步长常模算法。新算法能够在加快收敛速度的同时减小稳态误差,且具有较强的信道跟踪能力和抗干扰能力。理论分析和计算机仿真证实:新算法性能较好,具有很好的实用性。

湍流信道下无线光副载波盲均衡算法研究

建立了针对大气湍流时变信道的盲均衡系统模型.基于无线光副载波四相相移键控调制,在不同光强起伏方差下分析了两种自适应盲均衡算法的收敛性、稳定性和均方误差,对比了均衡前后星座图改善效果.结果表明:随着湍流强度的增加,变步长恒模算法较固定步长恒模算法收敛快、均方误差小,但其稳定性差,且比例因子逐渐减小算法才能收敛.探测器接收的信号经过两种盲均衡器后星座图聚敛性均得到有效改善.在相同信噪比下湍流信道与高斯信道相比,湍流信道算法迭代步长因子和比例因子取值较小才可收敛,均方误差大.两种盲均衡算法可有效改善湍流信道下星座图聚敛性,对提高无线光接收端星座图检测率具有一定的意义.

基于恒模准则的盲均衡算法仿真

阐述了用于信道盲均衡的恒模算法的数学模型和基本原理。针对恒模算法存在收敛速度慢和相位旋转等不足,对近年来出现的一些性能优良的基于恒模准则的盲均衡算法——变步长恒模算法、修正恒模算法和多模算法进行了分析与仿真,并对各种改进算法在不同调制方式下的优缺点进行了说明。最后得到不同算法均衡后的星座图和均方误差曲线,表明具有较好的均衡效果。

基于鲶鱼效应粒子群优化的变参误差盲均衡算法

为克服常模算法(CMA)收敛速度慢、稳态误差大的缺点,提出了基于鲶鱼效应粒子群算法优化的变参误差常模盲均衡算法(CEPSO-VSCMA)。该算法在变参误差常模盲均衡算法(VSCMA)的基础上,融入鲶鱼效应粒子群算法,利用粒子群的随机搜索,寻找全局最优解,同时结合鲶鱼效应,利用具有活力和竞争力的鲶鱼个体促使粒子群活跃起来,加快收敛。仿真结果表明:与CMA、VSCMA和基于粒子群算法优化的变参误差常数模盲均衡算法(PSO-VSCMA)相比,该算法提高了收敛速度、减小了均方误差。

基于二维恒模算法的直达波提纯技术

为了有效提取被多径杂波污染的直达波信号，采用了二维恒模盲均衡算法。该算法采用多天线多通道接收直达波信号，并综合利用接收信号的空域和时域信息。进一步采用变步长方法提高了算法的收敛速度，获得了较好的提纯效果。实验结果表明，改进的方法能较好地提纯被多径杂波污染的直达波信号，更具优越性。

基于变动量因子的常模盲均衡算法研究

常模算法是最常用的盲均衡算法之一,针对常模算法剩余误差较大、收敛速度慢以及误码率高等缺点,引入变动量因子对其进行修正,并采用无线数字通信系统输出信号对其进行仿真验。仿真结果表明:引入变动量因子后,常模盲均衡算法的剩余误差有所降低,误码率显著降低,收敛速度有一定程度的提高。

采用输出误差符号判决的变步长常数模盲均衡

针对固定步长常数模盲均衡算法在收敛速度和收敛精度上存在矛盾问题,提出了一种采用输出误差符号判决的变步长常数模盲均衡算法。在每次迭代后根据常数模准则和判决引导准则计算均衡器输出误差。如果在两种准则下输出误差符号一致,则对步长值进行修正,否则,根据自适应均衡原理利用均衡器输入信号计算最大步长值,均衡器权系数采用大步长值进行更新。与现有变步长盲均衡算法比较,无需人工设置参数,更利于工程实现。计算机仿真结果证明,采用输出误差符号判决的变步长常数模盲均衡具有良好的均衡性能。

基于误差信号自相关函数的变步长恒模盲均衡算法研究

提出了一种自适应变步长恒模盲均衡算法,利用剩余误差信号的自相关函数估计值作为控制步长的因子来自适应改变步长的大小,克服了恒模算法存在的固有缺陷。理论分析和仿真实验均表明该算法与恒模算法相比,在收敛过程中加快了收敛速度,收敛后又能减小对均衡器参数的误调,具有更小的稳态剩余误差。