基于四阶累积量对角切片的短波自适应通信信号检测

短波自适应通信信号的检测是现代电子战信号处理的一个重要研究课题,本文提出了基于四阶累积量对角切片的短波自适应通信信号检测方法.文章推导了有限长度信号四阶累积量对角切片的分段估计方法,分析了其渐进性能,分析表明该估计方法降低了估计方差;论文介绍了信号检测原理,借助于计算机仿真研究了高斯白噪声和色噪声及不同信噪比下不同检测方法的性能.仿真对比结果验证了该方法的有效性.     

色噪声环境下单基地MIMO雷达分布式目标角度估计

针对传统的二阶统计量角度估计算法在高斯色噪声环境下估计性能急剧下降甚至失效的问题,该文提出一种基于四阶累积量的单基地MIMO雷达相干分布式目标角度估计算法。首先建立单基地MIMO雷达的相干分布式目标信号模型,求取信号的四阶累积量矩阵;利用特征值分解分离出相互正交的信号子空间与噪声子空间,根据多重信号分类(MUSIC)算法原理,获得阵列的空间谱函数,通过谱峰搜索得到分布式目标的中心波达方向。该算法充分利用了四阶累积量对高斯过程的不敏感性,能够很好地抑制高斯色噪声对角度估计的影响。仿真结果证明了该算法的正确性和有效性。     

Applications of cumulants to array processing. II. Non-Gaussiannoise suppression

The main motivation of using higher order statistics in signal processing applications has been their insensitivity to additive colored Gaussian noise. The main objection to those methods is their possible vulnerability to non-Gaussian noise. The authors investigate the effects of non-Gaussian ambient noise on cumulant-based direction-finding systems using the interpretation for the information provided by cumulants for array processing applications described in Dogan and Mendek. they first demonstrate the suppression of uncorrelated non-Gaussian noise that has spatially varying statistics. Then, they indicate methods to suppress spatially colored non-Gaussian noise using cumulants and an additional sensor whose measurement noise component is independent of the noise components of the original array measurements. They also indicate the noise suppression properties of the virtual-ESPRIT algorithm proposed in Dogan and Mendel. In addition, they propose a method that combines second- and fourth-order statistics together in order to suppress spatially colored non-Gaussian noise. Finally, they also illustrate how to suppress spatially colored non-Gaussian noise when the additional sensor measurement is not available. Simulations are presented to verify the results     

Harmonic retrieval in colored non-Gaussian noise using cumulants

This paper addresses the harmonic retrieval problem in colored linear non-Gaussian noise of unknown covariance and unknown distribution. The assumptions made in the reported studies that the non-Gaussian noise is asymmetrically distributed and no quadratic phase coupling occurs are released. Using the elaborately defined fourth-order cumulants of the complex noisy observations, which are obtained by Hilbert transform, we can estimate either the correlation or the AR polynomial of the non-Gaussian noise via cumulant projections or ARMA modeling; then, the prewhitening or prefiltering techniques can be employed to retrieve harmonics, respectively. Simulation results are presented to demonstrate the effectiveness of the proposed algorithms     

Harmonic retrieval using higher order statistics: a deterministicformulation

Given a single record, the authors consider the problem of estimating the parameters of a harmonic signal buried in noise. The observed data are modeled as a sinusoidal signal plus additive Gaussian noise of unknown covariance. The authors define novel higher order statistics-referred to as “mixed” cumulants-that can be consistently estimated using a single record and are insensitive to colored Gaussian noise. Employing fourth-order mixed cumulants, they estimate the sinusoid parameters using a consistent, nonlinear matching approach. The algorithm requires an initial estimate that is obtained from a consistent, linear estimator. Finally, the authors examine the performance of the proposed method via simulations     

THE FOURTH-ORDER CUMULANTS BASED SPECTRALESTIMATION METHOD AND ITS APPLICATIONTO DIRECTION-FINDING

Traditional approaches of spatial spectral estimation are usually based on the second-order statistics. The higher-order cumulants and the poly-spectrum contain more information and are capable of reducing the Gaussian noise. In this paper, we present a new spectrum estimation method for direction-finding, the FOMUSIC algorithm, which is based on the eigen-structure analysis of the fourth-order cumulants. The derivation of the algorithm is given in detail and its performance is illustrated by both the computer simulations and the experiments of a direction-finding system. The obtained results demonstrate that the fourth-order cumulants based method outperforms the traditional methods, especially when the noise is an unknown colored one.     

四阶累积量稀疏表示的DOA估计方法

针对现有稀疏重构DOA估计算法不能抑制噪声项以及在高斯色噪声背景下不再适用的问题,本文提出了基于四阶累积量稀疏重构的DOA估计方法。首先,利用接收数据的四阶累积量构建了稀疏表示模型,该模型抑制了噪声项;其次对四阶累计量矩阵进行奇异值分解,化简了稀疏表示模型,通过奇异值分解,不仅减小了数据规模,而且进一步抑制了噪声。对于稀疏表示模型的求解,先利用信号子空间与噪声子空间的正交特性选取权值矢量,然后利用加权l1范数法对模型求解实现DOA估计。理论分析和仿真实验表明本文算法在高斯白噪声和色噪声背景下均适用;能够处理非相干和相干信号,且在低信噪比条件下,对相干信号有更高的估计精度;较之同类的稀疏重构算法,本文算法具有较低的算法复杂度和更高的角度分辨力。      

Estimation of frequency-delay of arrival (FDOA) using fourth-orderstatistics in unknown correlated Gaussian noise sources

A new family of nonparametric and parametric methods based on fourth-order statistics for the estimation of the frequency-delay of arrival (FDOA) between two sensor signal measurements, corrupted by correlated Gaussian noise sources in an unknown way, is presented. The new family of FDOA estimation methods utilizes the fourth-order cumulants or 1-D Fourier transforms of sliced fourth-order cumulants of the two signal measurements. It is demonstrated that the new family of FDOA estimation methods suppresses the effect due to correlated Gaussian measurement noises and outperforms existing second-order statistics-based FDOA estimation methods using either cross-ambiguity function or MUSIC algorithm. Various simulation results are presented for different types of signals, different lengths of data, and different signal-to-noise ratios     

房间环境下基于四阶累积量的语音时延估计

主要研究了利用四阶累积量在房间环境下的语音信号时延估计。根据模拟实验环境和实际实验环境下的仿真结果,分别比较了在高斯白噪声情况下与有色高斯噪声情况下基于二阶统计量的广义互相关法和基于四阶累积量的时延估计法性能,验证了四阶累积量法的有效性。仿真结果表明四阶累积量法具有很好的鲁棒性。     

A Least-Squares-Based Algorithm for Identification of Non-Gaussian ARMA Models

A new recursive method for estimating the parameters of autoregressive moving average (ARMA) models is presented in this paper. The recursive linear identification method is developed using higher-order statistics of the observed output data and is based on a least-squares solution. Namely, a matrix consisting of third-order statistics (or cumulants) of the observed output data is constructed so that it almost possesses a full rank structure. The signal is embedded in a Gaussian noise that may be colored. The system is driven by a zero-mean independent and identically distributed non-Gaussian process. The excitation signal is unobserved. Simulation results are given to illustrate the performance of the proposed algorithm with respect to existing well-known methods.     

Performance analysis of cyclic statistics for the estimation ofharmonics in multiplicative and additive noise

The problem of estimating the frequencies of harmonics in multiplicative and additive noise is addressed. The cyclic mean (CM) can be used if the multiplicative noise has nonzero mean; the cyclic variance (CV) can be used whether or not the multiplicative noise has zero mean. This paper answers the following question: under what conditions should we use the CV instead of the CM? The criteria used are the ease of detection and the accuracy of estimation. The CV is preferable to the CM if the coherent to noncoherent harmonic power ratio is less than a threshold that depends on the first four cumulants; when the noises are colored, this threshold becomes frequency dependent. Third- and fourth-order cyclic statistics are also studied, and it is shown that they will always be outperformed either by the CM or CV when the multiplicative noise is symmetric     

基于子空间旋转不变性的加性有色噪声中谐波频率的估计

噪声中的谐波恢复问题是信号处理领域的一个典型问题,在众多领域中有着广泛的应用。本文主要研究加性有色噪声中谐波频率的估计问题,提出了一种基于子空间旋转不变性的谐波频率的高分辨率估计方法。利用观测信号的自协方差函数构造了一个协方差矩阵,通过对协方差矩阵的特征值进行理论分析,结合子空间旋转不变性,得到了加性有色噪声中谐波的频率和协方差矩阵之间的一种内在联系。利用这个性质可以估计加性有色噪声中谐波的频率。本文方法对于有色噪声的模型无任何假设,而且对于噪声的分布也没有限制,对于高斯和非高斯有色噪声都适用。仿真实验验证了本文所提算法的有效性。      

Extending HOC-based methods for identifying the diagonal parameters of quadratic systems

In this paper, methods developed for the linear case of identifying the diagonal parameters of quadratic systems are extended to nonlinear case. Firstly, nonlinear relationships between model kernels and output cumulants are presented. Secondly, the relationship linking output cumulants and the coefficients of systems presented in the linear case, is extended to the general case of nonlinear quadratic systems identification. According to this concept, two nonlinear approaches are developed, the first use the fourth-order cumulants, and the second combined the third- and fourth-order cumulants. The numerical simulation results, for various signal to noise ratio (SNR) and 200 Monte Carlo runs, show that the proposed approaches achieve better accuracy, as compared with the related algorithm in the literature. Furthermore, the second algorithm is more precise in high noise environment (smallest \(\mathrm{SNR}=0\) dB), but the first algorithm more efficient in the weak noise environment case (highest SNR \(\ge \) 8 dB) comparing to using others methods.     

高斯噪声下差分跳频信号的高分辨率频率检测

差分跳频(DFH)是一种新的高速短波通信体制,它利用相邻跳变频率的变化而不是载频本身来携带信息。跳变频率检测是实现DFH的关键技术之一。本文利用四阶累积量研究了(色)高斯噪声下基于ARMA建模法的DFH信号频率检测,并针对由于模型阶数估计过高而产生的虚检频率,提出一种充分利用信号先验信息的改进算法。仿真结果证明了该方法的有效性,尤其是在低信噪比时仍然能够实现精确检测。     

Texture decomposition by harmonics extraction from higher order statistics

In this paper, a method of harmonics extraction from Higher Order Statistics (HOS) is developed for texture decomposition. We show that the diagonal slice of the fourth-order cumulants is proportional to the autocorrelation of a related noiseless sinusoidal signal with identical frequencies. We propose to use this fourth-order cumulants slice to estimate a power spectrum from which the harmonic frequencies can be easily extracted. Hence, a texture can be decomposed into deterministic components and indeterministic components as in a unified texture model through a Wold-like decomposition procedure. The simulation and experimental results demonstrated that this method is effective for texture decomposition and it performs better than traditional lower order statistics based decomposition methods.     

Applications of cumulants to array processing .I. Apertureextension and array calibration

An interpretation for the use of cumulants in narrowband array processing problems is proposed. It is shown how fourth-order cumulants of multichannel observations increase the directional information compared with second-order statistics. Based on the interpretation, it is shown how cumulants can be used to increase the effective aperture of an arbitrary antenna array. The amount of partial information necessary to jointly calibrate an arbitrary array and estimate the directions of far-field sources is also investigated. It is proven that the presence of a doublet and use of fourth-order cumulants is sufficient to accomplish this task. The proposed approach is computationally efficient and more general than covariance-based algorithms that have addressed the calibration problem under constraints. A class of beamforming techniques is proposed to recover the source waveforms. Proposed estimation procedures are based on cumulants, which bring insensitivity to the spatial correlation structure of additive Gaussian measurement noise. Simulations are provided to illustrate the use of the proposed algorithms     

基于高阶累积量的空时分组码盲识别算法研究

针对MISO通信系统的空时分组码盲识别问题,提出了一种基于高阶累积量的空时分组码盲识别算法。首先,给出了MISO接收信号模型,利用高阶累积量的性质分析得到接收信号的四阶累积量的表达式;然后,利用编码矩阵的特性,证明接收信号在不同时延向量下的四阶累积量呈现非零值,其非零值取决于STBC的类型;最后,采用四阶累积量的实验值与理论值的最小欧式距离盲识别空时分组码的类型。仿真结果表明,即使在低信噪比条件下,所提方法能够较好地识别空时分组码。     

Estimation of multipath channel response in frequency selectivechannels

A novel discrete-time method is proposed for estimating the impulse response of a frequency-selective digitally modulated communication channel. The received signal is first demodulated and sampled and then the fourth-order cumulants of the resulting discrete-time sequence are estimated. The method estimates the channel impulse response from the complex cepstrum of the aforementioned fourth-order cumulants (i.e. tricepstrum). The method depends only on the second- and fourth-order statistics of the transmitted sequence and is capable of reconstructing nonminimum-phase impulse responses. Monte Carlo simulation results demonstrate the effectiveness of the method, its low sensitivity to observation noise, and its improved performance in terms of probability of error or the reconstructed transmitted sequence     

Cumulant-based method for bearing estimation in the presence ofnonGaussian noise

Bearing estimation algorithms based on the cumulants of array data have been developed to suppress additive spatially correlated Gaussian noises. In practice, however, the noises encountered in signal processing environments are often non-Gaussian, and the applications of those cumulant-based algorithms designed for Gaussian noise to non-Gaussian environments may severely degrade the estimation performance. The authors propose a new cumulant-based method to solve this problem. This approach is based on the fourth-order cumulants of the array data transformed by DFT, and relies on the statistical central limit theorem to show that the fourth-order cumulants of the additive non-Gaussian noises approach zero in each DFT cell. Simulation results are presented to demonstrate that the proposed method can effectively estimate the bearings in both Gaussian and non-Gaussian noise environments     

A hybrid approach to harmonic retrieval in non-Gaussian ARMA noise

Addresses the harmonic retrieval problem in colored noise. As contrasted to the reported studies in which Gaussian noise was assumed, this paper focuses on additive non-Gaussian ARMA noise. Our approach is hybrid in the sense that third-order cumulants are first used to identify the AR part of the non-Gaussian noise process, and then correlation-based high-resolution methods are used for the filtered process to estimate the number of harmonics and their frequencies. Simulation examples are presented to demonstrate the high resolution of this approach