基于零阶统计量的韧性归一化自适应时间延迟估计

依据零阶统计量理论,给出对数矩过程、对数宽平稳及对数各态遍历的定义,提出一种韧性的归一化自适应时间延迟估计方法(简称NZOSTDE).该算法用FIR滤波器对两个含有脉冲噪声的观测信号建模,利用不存在有限方差的脉冲信号经过对数变换后其各阶矩的存在性和几何功率的概念,在对数域基于最小均方误差(LMS)准则归一化自适应得到FIR滤波器的系数,该系数最大值对应的序号就是时间延迟的估计值.本文提出的新算法克服了基于分数低阶统计量(FLOS)算法的局限性.计算机仿真实验表明,NZOSTDE算法在强脉冲噪声环境下比归一化最小平均P范数时间延迟估计方法(简称NLMPTDE)算法更具有韧性.     

脉冲噪声环境下基于分数低阶循环相关的自适应时延估计方法

以α稳定分布作为噪声模型,研究了非高斯噪声对传统的二阶循环统计量的影响,提出了分数低阶循环相关的概念,研究并证明了其性质,对传统意义上的二阶循环统计量进行了广义化,并在此基础上结合自适应技术提出了一种基于分数低阶循环相关的自适应时延估计方法。计算机模拟表明,该方法可有效估计高斯噪声和脉冲噪声条件下的时变和非时变时延值,其性能不仅优于基于二阶循环相关的自适应时延估计算法,而且优于最小平均p范数(LMP)自适应时延估计方法。     

脉冲噪声环境下基于分数低阶循环相关的自适应时延估计方法

以α稳定分布作为噪声模型，研究了非高斯噪声对传统的二阶循环统计量的影响，提出了分数低阶循环相关的概念，研究并证明了其性质，对传统意义上的二阶循环统计量进行了广义化，并在此基础上结合自适应技术提出了一种基于分数低阶循环相关的自适应时延估计方法。计算机模拟表明，该方法可有效估计高斯噪声和脉冲噪声条件下的时变和非时变时延值，其性能不仅优于基于二阶循环相关的自适应时延估计算法，而且优于最小平均P范数（LMP）自适应时延估计方法。     

基于FLOC的ARMA SαS模型α谱估计方法

分析了基于分数低阶矩（FLOM）估计ARMA SαS模型参数的不足,根据分数低阶协方差（FLOC）的概念,提出了一种基于分数低阶协方差系数估计ARMA SαS模型参数的方法。在此基础上,给出了ARMA SαS模型的α谱估计。通过对给定ARMA SαS模型的α谱估计、α稳定分布噪声中正弦信号的估计与分辨进行仿真,详细比较了基于FLOM的ARMA SαS模型α谱估计和基于FLOC的ARMA SαS模型α谱估计的性能。结果表明,α值较小时,基于FLOC的ARMA SαS模型α谱估计的性能明显优于基于FLOM的ARMA SαS模型α谱估计。     

分数低阶α稳定分布噪声下HB加权自适应时间延迟估计新方法

针对LMS-HB自适应时间延迟估计方法在分数低阶α稳定分布噪声环境下的退化现象,依据分数低阶统计量理论,提出了基于分散系数最小化的LMP-HB自适应时延估计方法,并进一步提出了不依赖于参数估计的基于非线性变换的HB加权自适应时延估计方法。理论分析和计算机仿真结果表明,新方法在高斯和分数低阶α稳定分布噪声环境下具有良好的韧性。     

脉冲噪声环境下循环ESPRIT新方法

以a稳定分布作为噪声模型,研究了脉冲噪声环境下循环平稳信号的波达方向估计问题.针对在脉冲噪声环境中,基于传统二阶循环统计量的算法效果显著退化的问题,提出了分数低阶循环相关矩阵概念;并在此基础上,提出了分数低阶总体最小二乘(TLS)循环ESPRIT算法的2种形式.计算机仿真表明所提出的算法可有效地估计出脉冲噪声条件下的波达方向,其性能优于传统的基于二阶循环统计量的循环ESPRIT类算法,有潜在的应用前景.     

基于分数低阶协方差的AR SαS模型α谱估计

根据自回归(AR) SαS模型的α谱,分析了基于分数低阶矩(FLOM)法估计AR SαS模型参数的不足.提出了一种基于分数低阶协方差(FLOC)的AR SαS模型参数估计方法,并给出了基于FLOC的AR SαS模型α谱方法.分别对AR SαS模型参数的估计、α稳定分布噪声中单一正弦信号的估计和两个正弦信号的分辨进行了仿真.仿真结果表明,基于FLOC的AR SαS模型α谱估计方法对于不同的α值均具有较好的韧性.特别是在α值较小,即α稳定分布噪声概率密度函数(PDF)拖尾比较严重时,本文所提出的基于FLOC的AR SαS模型α谱估计方法,其性能明显优于基于FLOM的AR SαS模型α谱估计方法.     

α稳定分布噪声下数字频移键控信号的分数低阶循环谱分析

针对α稳定分布噪声环境下数字通信信号的二阶与高阶循环统计特征显著退化问题,结合分数低阶矩和共变理论对二进制频移键控（Frequency Shift Keying,FSK）信号的分数低阶循环谱公式进行了理论推导,并对2FSK信号在不同混合信噪比、分数阶因子和特征指数条件下的分数低阶循环谱进行了详细的仿真分析.理论和仿真结果表明:2FSK信号分数低阶与二阶的循环谱结构相同,其谱峰对应的循环频率相同,谱峰的幅度值不同,取决于循环谱的阶因子.相对于在低混合信噪比下失效的二阶循环谱,分数低阶循环谱对α稳定分布噪声具有更强的抗干扰性和适用性.     

脉冲噪声环境下一种韧性的时延与 多普勒频移联合估计法

由于α稳定分布噪声会降低基于二阶循环统计量的传统方法的性能,本文基于分数低阶统计量理论提出p阶循环相关的概念并给出相应性质及证明,在此基础上对已有的循环模糊函数进行了广义化.计算机仿真表明,这种广义的循环模糊函数能够在高斯和α稳定分布噪声条件下有效地联合估计时延和多普勒频移,其性能不仅优于基于二阶循环相关的CCA(循环模糊函数)法,也优于FLOAF(分数低阶模糊函数)法,是韧性的、具有更广泛应用意义的方法.     

Alpha稳定分布噪声中的韧性投影 近似子空间跟踪算法

 为了克服投影近似子空间跟踪算法(PAST)在脉冲噪声环境下性能的退化,本文以Alpha 稳定分布为脉冲噪声模型,依据韧性的M估计方法提出了一种新的代价函数,并推导出基于递归最小M估计的韧性投影近似自适应信号子空间跟踪算法(RLM_-PAST).由于采用了适合噪声模型的M估计函数,新算法与采用递归最小二乘估计的子空间跟踪算法相比,在稳定分布脉冲噪声环境下具有更好的性能.把新方法应用于波达方向(DOA)估计,数值仿真结果表明了该算法的有效性.     

Alpha稳定分布噪声环境下类M估计相关的DOA估计新算法

提出了一类适用于Alpha稳定分布随机变量的统计量—类M估计相关（MELC）,通过构造阵列输出的类M估计相关矩阵,提出了适用于Alpha稳定分布噪声环境下的波达方向（DOA）估计新算法,即MELC-MUSIC算法。仿真实验表明,在Alpha稳定分布噪声环境下,MELC-MUSIC算法在抗噪声特性、多源信号分辨性以及对不同形式信号（圆对称信号或非圆对称信号）的适应性方面获得比基于分数低阶统计量（FLOS）的MUSIC方法更好的估计性能。     

一种基于分数低阶协方差矩阵的波束形成新方法

利用稳定分布对具有脉冲特性的噪声进行建模，提出了一种新的分数低阶协方差概念，推导了一种基于分数低阶协方差矩阵的波束形成方法，并分析了其旁瓣特性。模拟表明新方法具有更高的信号干扰噪声比及更强的波束形成与旁瓣抑制能力。新算法在高斯和分数低阶稳定分布环境下比传统的算法具有更好的韧性。     

Constant Modulus Algorithm for Cochannel Signal Separation in Non-Gaussian Impulsive Noise Environments

The separation of cochannel signals is of interest in communication community. Some algorithms based on constant modulus (CM) have been previously developed to separate cochannel signals with the assumption of Gaussian channel noise. The mismatches of noise models between the assumed channel noise and the practical noise may occur. These mismatches will inevitably lead the performance of cochannel signals separation to degrade. In this paper the alpha-stable distribution is employed as noise model to simulate impulsive noise occurring in wireless channel. A constant modulus algorithm is proposed to separate the cochannel signals based on fractional lower-order statistics (FLOS). The convergence of the CM array is analyzed. Numerical simulations are presented to verify the accuracy of the analytical results.     

Parameter estimation based on fractional power spectrum under alpha-stable distribution noise environment in wideband bistatic MIMO radar system

This paper takes the alpha-stable distribution as the noise model and works on the parameter estimation problem of wideband bistatic Multiple-Input Multiple-Output (MIMO) radar system in the impulsive noise environment. In many applications, it is not appropriate to approximate the wideband signal by the narrowband model. Furthermore, the echo signal may be corrupted by the non-Gaussian noise. The conventional algorithms degenerate severely in the impulsive noise environment. Thus, this paper proposes a new wideband signal model and a novel method in wideband bistatic MIMO radar system. It combines the fractional lower order statistics and fractional power spectrum, for suppressing the impulse noise and estimating parameters of the target. Firstly, a new signal array model is proposed under the alpha-stable distribution noise model. Secondly, Doppler stretch and time delay are jointly estimated by peak searching of the FLOS-FPSD. Furthermore, two modified algorithms are proposed for the estimation of the direction-of-departure and direction-of-arrival, including the fractional power spectrum density based on MUSIC algorithm (FLOS-FPSD-MUSIC) and the fractional lower-order ambiguity function based on ESPRIT algorithm (FLOS-FPSD-ESPRIT). Simulation results are presented to verity the effectiveness of the proposed method.     

Joint estimation of time delay and frequency delay in impulsivenoise using fractional lower order statistics

New methods for time delay estimation and joint estimation of time delay and frequency delay in the presence of impulsive noise are introduced. First, degradation of the conventional approaches based on second-order statistics is shown both theoretically and experimentally. Then, a new class of robust algorithms are developed using the theory of alpha-stable distributions, including the fractional lower order covariance (FLOC) method, which is formulated for the time delay estimation problem and the fractional lower order ambiguity function (FLOAF), which is defined for the joint estimation of time delay and frequency delay. It is shown that these new methods are robust for both Gaussian and non-Gaussian impulsive noise environments. The improved performance is clearly demonstrated through detailed analysis and comprehensive simulations with computer-generated data as well as actual radar and sonar clutter data     

Parameter Estimation Based on Fractional Power Spectrum Density in Bistatic MIMO Radar System Under Impulsive Noise Environment

This paper takes an Alpha-stable distribution as the noise model to solve the parameter estimation problem of bistatic multiple-input multiple-output (MIMO) radar system in the impulsive noise environment. For a moving target, its echo often contains a time-varying Doppler frequency. Furthermore, the echo signal may be corrupted by a non-Gaussian noise. It causes the conventional algorithms and signal models degenerating severely in this case. Thus, this paper proposes a new signal model and a novel method for parameter estimation in bistatic MIMO radar system in the impulsive noise environment. It combines the fractional lower-order statistics (FLOS) and fractional power spectrum density (FPSD), for suppressing the impulse noise and estimating parameters of the target in fractional Fourier transform domain. Firstly, a new signal array model is constructed based on the \(\alpha \)-stable distribution model. Secondly, Doppler parameters are jointly estimated by peak searching of the FLOS–FPSD. Furthermore, two modified algorithms are proposed for the estimation of direction-of-departure and direction-of-arrival (DOA), including the fractional power spectrum density based on MUSIC algorithm (FLOS–FPSD–MUSIC) and the fractional lower-order ambiguity function based on ESPRIT algorithm (FLOS–FPSD–ESPRIT). Simulation results are presented to verity the effectiveness of the proposed method.     

Zero-Order Statistics: A Mathematical Framework for the Processing and Characterization of Very Impulsive Signals

Impulsive or heavy-tailed processes with infinite variance appear naturally in a variety of practical problems that include wireless communications, teletraffic, hydrology, geology, and economics. Most signal processing and statistical methods available in the literature have been designed under the assumption that the processes possess finite variance, and they usually break down in the presence of infinite variance. Although methods based on fractional lower-order statistics (FLOS) have proven successful in dealing with infinite variance processes, they fail in general when the noise distribution has very heavy algebraic tails. In this paper, we introduce a new approach to statistical moment characterization which is well defined over all processes with algebraic or lighter tails. Unlike FLOS, these zero-order statistics (ZOS), as we will call them, provide a common ground for the analysis of basically any distribution of practical use known today. Three new parameters, namely the geometric power, the zero-order location and the zero-order dispersion, constitute the foundation of ZOS. They play roles similar to those played by the power, the expected value and the standard deviation, in the theory of second-order processes. We analyze the properties of the new parameters, and derive a ZOS framework for location estimation that gives rise to a novel mode-type estimator with important optimality properties under very impulsive noise. Several simulations are presented to illustrate the potential of ZOS methods.     

Fast estimation of the parameters of alpha-stable impulsiveinterference

We address the problem of estimation of the parameters of the recently proposed symmetric, alpha-stable model for impulsive interference. We propose new estimators based on asymptotic extreme value theory, order statistics, and fractional lower order moments, which can be computed fast and are, therefore, suitable for the design of real-time signal processing algorithms. The performance of the new estimators is theoretically evaluated, verified via Monte Carlo simulation, and compared with the performance of maximum-likelihood estimators     

基于分数低阶统计量的双谱及其估计方法

稳定分布可更好地描述实际中所遇到的具有显著脉冲特性的随机噪声.为了更好地抑制信号背景中的非高斯噪声,本文提出了基于分数低阶的双谱定义,并给出在分数低阶有色噪声背景下双谱非参数和参数模型的估计方法.仿真结果表明,同传统的双谱估计相比较,非参数法分数低阶双谱估计能有效的识别信号,保留了信号的幅度和相位信息,但存在较大的估计方差.基于AR模型的分数低阶双谱估计具有最大的谱平坦度,能够有效地抑制噪声,具有良好的韧性.     

基于分数低阶ICA的混合噪声中脉冲噪声的消除方法

为了解决当信号中同时含有高斯噪声与α稳定分布脉冲噪声时,传统的基于二阶统计量的去噪方法会出现显著的性能退化的问题。通过基于负熵的分数低阶独立分量分析(ICA)算法先去除混合噪声中的脉冲噪声,然后利用SVD算法再去除混合信号中高斯噪声的方法,取得了较好的效果,且有效保护了混合信号中的纯净信号。