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.     

Modulation Recognition of MFSK Signals Based on Multifractal Spectrum

In order to solve the problem that modulation recognition of MFSK signals in alpha-stable distribution noise, a novel algorithm using multifractal spectrum is proposed. Multifractal spectrum characteristics of signals and noise are discussed firstly. Then algorithm extracts the difference between maximum and minimum values of spectrum as classification feature. Finally, algorithm employs threshold decision method to achieve modulation recognition of 2FSK, 4FSK and 8FSK signals. Numerical results show that algorithm has good performance in both alpha-stable distribution noise and Gaussian noise, and it is less affected by characteristic exponent of noise and data points.     

Robust M-estimate adaptive filtering

An M-estimate adaptive filter for robust adaptive filtering in impulse noise is proposed. Instead of using the conventional least-square cost function, a new cost function based on an M-estimator is used to suppress the effect of impulse noise on the filter weights. The resulting optimal weight vector is governed by an M-estimate normal equation. A recursive least M-estimate (RLM) adaptive algorithm and a robust threshold estimation method are derived for solving this equation. The mean convergence performance of the proposed algorithm is also analysed using the modified Huber (1981) function (a simple but good approximation to the Hampel's three-parts-redescending M-estimate function) and the contaminated Gaussian noise model. Simulation results show that the proposed RLM algorithm has better performance than other recursive least squares (RLS) like algorithms under either a contaminated Gaussian or alpha-stable noise environment. The initial convergence, steady-state error, robustness to system change and computational complexity are also found to be comparable to the conventional RLS algorithm under Gaussian noise alone     

SAR image filtering based on the heavy-tailed Rayleigh model.

Synthetic aperture radar (SAR) images are inherently affected by a signal dependent noise known as speckle, which is due to the radar wave coherence. In this paper, we propose a novel adaptive despeckling filter and derive a maximum a posteriori (MAP) estimator for the radar cross section (RCS). We first employ a logarithmic transformation to change the multiplicative speckle into additive noise. We model the RCS using the recently introduced heavy-tailed Rayleigh density function, which was derived based on the assumption that the real and imaginary parts of the received complex signal are best described using the alpha-stable family of distribution. We estimate model parameters from noisy observations by means of second-kind statistics theory, which relies on the Mellin transform. Finally, we compare the proposed algorithm with several classical speckle filters applied on actual SAR images. Experimental results show that the homomorphic MAP filter based on the heavy-tailed Rayleigh prior for the RCS is among the best for speckle removal.     

Data-adaptive algorithms for signal detection in sub-Gaussianimpulsive interference

We address the problem of coherent detection of a signal embedded in heavy-tailed noise modeled as a sub-Gaussian, alpha-stable process. We assume that the signal is a complex-valued vector of length L, known only within a multiplicative constant, while the dependence structure of the noise, i.e. the underlying matrix of the sub-Gaussian process, is not known. We implement a generalized likelihood ratio detector that employs robust estimates of the unknown noise underlying matrix and the unknown signal strength. The performance of the proposed adaptive detector is compared with that of an adaptive matched filter that uses Gaussian estimates of the noise-underlying matrix and the signal strength and is found to be clearly superior. The proposed new algorithms are theoretically analyzed and illustrated in a Monte-Carlo simulation     

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。     

Viterbi Decoding of Convolutional Codes in Symmetric α -Stable Noise

Algorithms developed with a Gaussian noise assumption perform poorly in impulsive noise, such as that described by the symmetric alpha-stable (SalphaS) distribution. We investigate the performance of antipodal signaling and Viterbi decoding of convolutional codes in SalphaS noise. We demonstrate that the p-norm branch metric is robust in SalphaS noise.     

SAR image denoising via Bayesian wavelet shrinkage based on heavy-tailed modeling

Synthetic aperture radar (SAR) images are inherently affected by multiplicative speckle noise, which is due to the coherent nature of the scattering phenomenon. This paper proposes a novel Bayesian-based algorithm within the framework of wavelet analysis, which reduces speckle in SAR images while preserving the structural features and textural information of the scene. First, we show that the subband decompositions of logarithmically transformed SAR images are accurately modeled by alpha-stable distributions, a family of heavy-tailed densities. Consequently, we exploit this a priori information by designing a maximum a posteriori (MAP) estimator. We use the alpha-stable model to develop a blind speckle-suppression processor that performs a nonlinear operation on the data and we relate this nonlinearity to the degree of non-Gaussianity of the data. Finally, we compare our proposed method to current state-of-the-art soft thresholding techniques applied on real SAR imagery and we quantify the achieved performance improvement.     

Alpha稳定分布噪声下级联恒模阵列及其稳定性分析

该文研究Alpha稳定分布噪声下级联韧性恒模阵列的稳定性。首先,提出一种新型的信号对消器,把本级阵列捕获的信号从接收数据中消除,并分析了该对消器达到的稳定状态。然后,以韧性的波束形成器和新型的信号对消器组成级联恒模阵列。分析了恒模信号和Alpha稳定分布噪声在级联恒模阵列间的传递情况。数值仿真验证了理论分析的结论,并对级联恒模阵列的多信号恢复进行了模拟。     

Robust Nonparametric Cyclic Correlation-Based Spectrum Sensing for Cognitive Radio

Cognitive radios sense the radio spectrum in order to find underutilized spectrum and then exploit it in an agile manner. Spectrum sensing has to be performed reliably in challenging propagation environments characterized by shadowing and fading effects as well as heavy-tailed noise distributions. In this paper, a robust computationally efficient nonparametric cyclic correlation estimator based on the multivariate (spatial) sign function is proposed. Nonparametric statistics provide additional robustness against heavy-tailed noise and when the noise statistics are not fully known. Asymptotic distribution of the spatial sign cyclic correlation estimator under the null hypothesis is established. Tests using constraint on false alarm rate are derived based on the estimated spatial sign cyclic correlation for single-user and collaborative spectrum sensing by multiple secondary users. Theoretical justification for detecting cyclostationary signals using the spatial sign cyclic correlation is provided. A sequential detection scheme for reducing the average detection time is proposed. Simulation experiments and theoretical results comparing the proposed method with cyclostationary spectrum sensing methods employing the conventional cyclic correlation estimator are presented. Simulations demonstrate the reliable and highly robust performance of the proposed nonparametric spectrum sensing method in both Gaussian and non-Gaussian noise environments.     

基于分数低阶统计量的盲多用户检测算法

多用户检测算法是抑制CDMA系统中多址干扰的重要手段,但广泛存在的非高斯信道噪声会降低以往的基于高斯噪声模型假设的算法性能.本文采用α稳定分布作为噪声模型,提出了基于分数低阶统计量的盲多用户检测算法,并对该算法进行了理论分析.仿真和分析表明,该算法具有很好的韧性,同时适用于高斯噪声和脉冲噪声环境.     

Time-variant forward-backward FIR denoising of piecewise-smooth signals

We address a novel time-variant forward-backward (FB) unbiased finite impulse response (UFIR) smoothing algorithm designed to denoise piecewise-smooth signals with known or well detectable edge positions. Owing to the variable averaging interval, the algorithm unites advantages of linear structures with robustness of nonlinear ones. The FB UFIR smoother has been examined in Gaussian and heavy-tailed noise environments and compared to the nonlinear myriad filter derived under the Cauchy statistics. We show that the solution proposed is able to preserve edges without jitter and provide efficient denoising with sufficient robustness against outliers and noise heavy tails.     

量测随机延迟下带厚尾噪声的鲁棒Student's t随机容积卡尔曼滤波器

针对量测随机延迟下带厚尾过程噪声和量测噪声的非线性状态估计问题，本文通过充分考虑量测一步随机延迟特性及过程噪声和量测噪声的"厚尾"特性，推导了一种新的鲁棒Student's t滤波器框架，并采用随机Student's t-球面相径容积规则近似计算Student's t权值积分，从而设计了一种新的鲁棒Student's t随机容积滤波器.首先，采用一组服从伯努利分布的随机序列来描述系统中可能存在的量测一步随机延迟现象，并采用Student's t分布刻画过程噪声和量测噪声中存在的"厚尾"特性；其次，从理论上证明了当自由度参数趋于无穷以及随机延迟概率为零时，该鲁棒Student's t滤波器就自动地降为标准的非线性高斯近似滤波器；最后，采用随机Student's t-球面相径容积规则给出了一种新的鲁棒Student's t随机容积滤波器，并通过协同转弯模型验证了该滤波器的有效性和优越性.     

一种冲击噪声环境中的二维DOA估计新方法

该文提出了一种新的在冲击噪声环境中基于阵列输出信号分数低阶矩的二维测向方法稳健的协变异波达方向矩阵法。该方法利用冲击噪声和SS过程的特点,扩展了原波达方向矩阵法的信号模型和应用环境,对冲击噪声有较好的抑制作用,增强了算法的通用性和稳健性,弥补了传统的基于二阶或高阶统计量的子空间测向算法不能应用于冲击噪声环境的不足,计算机仿真验证了该算法的可行性和有效性。     

Hybrid Polynomial Filters for Gaussian and Non-Gaussian Noise Environments

Traditional polynomial filtering theory, based on linear combinations of polynomial terms, is able to approximate important classes of nonlinear systems. The linear combination of polynomial terms, however, yields poor performance in environments characterized by Gaussian and heavy tailed distributions. Weighted median and weighted myriad filters, in contrast, are well known for their outlier suppression and detail preservation properties. It is shown here that the weighted median and weighted myriad methodologies are naturally extended to the polynomial sample case, yielding hybrid filter structures that exploits the higher-order statistics of the observed samples while simultaneously being robust to outliers for both Gaussian and heavy-tailed distributions environments. Moreover, the introduced hybrid polynomial filter classes are well motivated by analysis of cross and square term statistics of Gaussian and heavy-tailed distributions. A presented asymptotic tail mass analysis shows that polynomial terms, both under Gaussian and heavy-tailed noise statistics, have heavier tails than the observed samples, indicating that robust combination methods should be utilized to avoid undue influence of outliers. Further analysis shows weighted median processing of polynomial terms for the Gaussian noise case, and weighted median and weighted myriad processing of cross and square terms, respectively, for the heavy-tailed noise case, are justified from a maximum likelihood perspective. Filters parameter optimization procedures are also presented. Finally, the effectiveness of hybrid filters is demonstrated through simulations that include temporal, spectrum, and bispectrum analysis     

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。     

Robust Wigner distribution with application to the instantaneousfrequency estimation

The Wigner distribution (WD) produces highly concentrated time-frequency (TF) representation of nonstationary signals. It may be used as an efficient signal analysis tool, including the cases of frequency modulated signals corrupted with the Gaussian noise. In some applications, a significant amount of impulse noise is present. Then, the WD fails to produce satisfactory results. The robust periodogram has been introduced for spectral estimation of this kind of noisy signals. It can produce good concentration for pure harmonic signals. However, it is not so efficient in the cases of signals with rapidly varying frequency. This is the motivation for introducing the robust WD. It is a reliable TF representation tool for wide class of nonstationary signals corrupted with impulse noise. This distribution produces good accuracy of the instantaneous frequency (IF) estimation. Using the Huber (1981) loss function, a generalization of the WD is presented. It includes both the standard and the robust WD as special cases. This distribution can be used for TF analysis of signals corrupted with a mixture of impulse and Gaussian noise. The presented theory is illustrated on examples, including applications on the IF estimation and time-varying filtering of signals corrupted with a mixture of the Gaussian and impulse noise. The case study analysis of the IF estimators' accuracy, based on the standard and the robust WD forms, is performed. In order to improve the IF estimation, a median filter is applied on the obtained IF estimate     

Gaussian sum particle filtering

We use the Gaussian particle filter to build several types of Gaussian sum particle filters. These filters approximate the filtering and predictive distributions by weighted Gaussian mixtures and are basically banks of Gaussian particle filters. Then, we extend the use of Gaussian particle filters and Gaussian sum particle filters to dynamic state space (DSS) models with non-Gaussian noise. With non-Gaussian noise approximated by Gaussian mixtures, the non-Gaussian noise models are approximated by banks of Gaussian noise models, and Gaussian mixture filters are developed using algorithms developed for Gaussian noise DSS models. As a result, problems involving heavy-tailed densities can be conveniently addressed. Simulations are presented to exhibit the application of the framework developed herein, and the performance of the algorithms is examined.     

脉冲噪声环境下改进的顽健循环时延估计算法

研究了脉冲噪声环境下循环平稳信号的时延估计问题,针对脉冲噪声环境中基于传统二阶谱相关函数的时延估计方法性能退化问题,提出了基于分数低阶循环谱的改进顽健算法。相对于传统算法,新算法对脉冲噪声、高斯噪声、干扰信号都具有较好的抑制作用。仿真结果证明了算法的有效性和顽健性。     

Subspace-based direction-of-arrival estimation using nonparametricstatistics

The problem of subspace estimation using multivariate nonparametric statistics is addressed. We introduce new high-resolution direction-of-arrival (DOA) estimation methods that have almost optimal performance in nominal conditions and are robust in the face of heavy-tailed noise. The extensions of the techniques for the case of coherent sources are considered as well. The proposed techniques are based on spatial sign and rank concepts. We show that spatial sign and rank covariance matrices can be used to obtain convergent estimates of the signal and noise subspaces. In the proofs, the noise is assumed to be spherically symmetric. Moreover, we illustrate how the number of signals may be determined using the proposed covariance matrix estimates and a robust estimator of variance. The performance of the algorithms is studied using simulations in a variety of noise conditions including noise that is not spherically symmetric. The results show that the algorithms perform near optimally in the case of Gaussian noise and highly reliably if the noise is non-Gaussian