Time delay estimation between two phase shifted signals via generalized cross-correlation methods

This paper examines the generalized cross correlation (GCC) method for estimating time delay between two phase shifted replicas of a common signal which are embedded in additive noise. The analysis applies for widesense jointly stationary narrow-band signal and noise and is independent of signal, noise, and phase distributions. The paper derives expressions for the estimation error, specifically bias and mean square error (MSE), by starting with the cross correlation method and then extending the results to the GCC method. Assuming symmetric spectra signals, we derive two optimal weigth functions (OWF) that minimize the above MSE. With the first OWF the maximum of the absolute value of the GCC function has to be found; this is identical to the Wax maximum likelihood (ML) method where Gaussian signals possessing uniformly distributed phase were assumed. With the second OWF the zero of the absolute value of the GCC function has to be found. For signals possessing non-symmetric spectra (e.g. single side band modulated signals) the OWF can be obtained numerically, by minimizing the MSE, e.g. by using variational techniques. Using the cross correlation method we derive a simplified expression for the MSE, which is to be used instead of a previously published result.     

Blind separation of impulsive noise from corrupted audio signal

The authors present a new method for separating the impulsive noise from a corrupted audio signal. It is shown that if the audio signal is assumed to be Gaussian distributed, the third-order cumulants of the impulsive noise can be separated, based upon the corrupted audio signal. The impulsive noise can then be reconstructed via the relationship between the bispectrum and the Fourier spectrum. Finally, the audio signal is restored by simply subtracting the reconstructed impulsive noise from the signal     

Statistical performance of the first order phase difference digitalinstantaneous frequency estimator

The authors derive exact analytical expressions for the PDF of instantaneous frequency estimate and the mean squared error (MSE) of a first order phase difference estimator in Gaussian white noise. The MSE is also derived in terms of linearised circular mean squared error, and is then compared to the Cramer-Rao bounds     

Improved bispectrum estimation based on modified group delay

This article proposes an improved estimation method for the bispectrum of a system or signal, by applying the modified group delay (MMGD) in the bispectrum domain. To achieve a higher frequency resolution, the bispectrum is computed in frequency domain and further to reduce the variance preserving the frequency resolution, MMGD is applied in the bispectrum domain. The proposed method due to its better frequency resolution not only properly detects the phase coupled frequencies but also reduces the bispectrum magnitude estimate’s variance significantly compared to that of biperiodogram. Compared to the proposed method, though the windowed bispectrum (WB) provides a better reduction in variance, it is unable to detect the coupled frequencies due to its poor frequency resolution. For an AR process in the presence of noise (SNR = 4 dB), the system magnitude estimate by the proposed method has a 27.63% lower normalized sum sample mean square error (NSSMSE) than that by the WB. Also for a non-minimum phase system in presence of noise (SNR = 7 dB), the phase estimation by the new approach has 8.6% lower NSSMSE than that by WB and also it is marginally better than that obtained by applying MMGD in system group delay domain.     

AR model order selection based on bispectral cross correlation

A novel method is presented for optimal model order selection for autoregressive (AR) bispectrum estimation. The method depends solely on the data and requires no a priori information about the process. The method selects the model order that maximizes the cross correlation between the direct (fast Fourier transform-based) bispectrum estimate and the autoregressive bispectrum estimate. Simulation results are reviewed which demonstrate the method's performance for the case of quadratically coupled sinusoids embedded in white Gaussian noise     

Waveform estimation from noisy signals with variable signal delayusing bispectrum averaging

A technique based on bispectrum averaging is described for generally recovering the signal waveform from a set of noisy signals with variable signal delay. The technique does not require explicit time alignment of signals and any initial estimate of signal. The technique, however, does not yield estimates of the signal position. A comparison is made of two algorithms for recovering the Fourier amplitude and the Fourier phase from an averaged bispectrum. These algorithms are the recursive method and the least squares method. The methods are numerically investigated using computer-generated data and a physiological signal and noise. The advantages and disadvantages of these different algorithms are discussed. Some experimental results for the evoked potential studies that demonstrate the technique are given. The results show the effectiveness of the technique: various potential applications of the technique might be expected     

非高斯相关噪声中高斯信号的时延估计

高阶统计量在信号处理中成功的应用例子之一是估计高斯相关噪声中非高斯信号的时延参数.本文则研究非高斯相关噪声中高斯信号的时延估计问题,提出了一种解决该问题的混合方法.该方法先计算观测值的三阶累积量,然后利用累积投影公式计算观测噪声的二阶统计量,最后利用互相关方法确定信号时延参数.仿真结果验证了该方法的有效性.     

高阶累积量在红外热像损伤检测信号分析中的应用

针对常规红外检测信号的脉冲相位法没有考虑测量噪音,简单的Fourier变换对数据信息的挖掘不足、利用率不高的问题,提出在处理中引入非高斯特性分析,应用三阶累积量和双谱估计对信号进行分析,提取发生损伤时信号的特性信息,得到分辨完好区域与损伤区域的特征判据。给出信号分析中三阶累积量和双谱的定义,分析其幅值和相位的对角切片谱在提取损伤特征方面的优势,最后对比分析两者在实际检测中的效果。结果表明:利用该方法具有良好的抗高斯和非高斯对称分布型噪音的优点,且运算量小、计算速度快。同时,弥补了传统脉冲相位法中幅值谱不宜使用的缺点。     

On time delay estimation with unknown spatially correlated Gaussiannoise using fourth-order cumulants and cross cumulants

The problem of estimating the difference in arrival times of a linear non-Gaussian signal at two spatially separated sensors is considered. The signal is assumed to be corrupted by spatially correlated Gaussian noises of unknown cross correlation. A parameter estimation approach is adopted, and the fourth-order cumulant statistics of the noisy measurements are exploited to obtain the time delay estimate. Specific and mild sufficient conditions are given for time delay identifiability via a persistence of excitation condition. Illustrative Monte Carlo simulation examples are also presented     

基于高阶统计量的多模噪声中的信号检测

按照概率密度函数形状,给出了一种比较通用的非高斯噪声模型——多模噪声。多模噪声总体上属于非高斯噪声,但兼容了高斯噪声。改进了高阶统计量的双谱算法,给出一种基于双谱的多模噪声中信号的检测方法,并在此基础上结合无惯性非线性变换器和双谱技术,改进了传统的自适应幅频干扰抑制器,可以精确估计或检测信号。仿真表明该方法可以抑制高斯噪声,同时在强噪声和复杂背景下可以以较高的检测概率检测出信号,优于传统的似然比检测。     

The evaluation of error probabilities for intersymbol and cochannelinterference

An efficient series that can be used to calculate the probability of error in a binary symmetric channel with intersymbol interference and additive noise is derived. The series is derived by representing the noise complementary probability distribution function by an exact or approximate Fourier series. Bounds on the accuracy of the estimate are derived for Gaussian noise. Examples show that only a small numerical effort may be required to compute error probabilities of interest using the series. Applications to both finite and infinite intersymbol interference systems are discussed. A similar technique is used to derive series representations for the probability of error of additive noise channels with cochannel interference or with combined intersymbol and cochannel interferences. The accuracy of the results is bounded for Gaussian noise     

Asymptotic Bias and Variance of Conventional Bispectrum Estimates for 2-D Signals

In this paper, we derive the asymptotic bias and variance of conventional bispectrum estimates of 2-D signals. Two methods have been selected for the estimation: the first one – the indirect method – is the Fourier Transform of the weighted third order moment, while the second one – the direct method – is the expectation of the Fourier component product. Most of the developments are known for 1-D signals and the first contribution of this paper is the rigorous extension of the results to 2-D signals. The calculation of the bias of the direct method is a totally original contribution. Nevertheless, we did all calculations (bias and variance) for both method in order to be able to compare the results. The second contribution of this paper consists of the comparison of the theoretical bispectrum estimate bias and variance with the measured bias and variance for two 2-D signals. The first studied signal is the output of a non-minimal phase linear system driven by a non-symmetric noise. The second signal is the output of a non-linear system with Gaussian input data. In order to assess the results, we performed the comparison for both methods with different sets of parameters. We show that the maximum bias coefficient is the one of the 1-D case multiplied by the dimensionality of the signal for both methods. We also show that the estimate variance coefficient is the 1-D case coefficient with a power equal to the signal dimensionality.Received October 21, 2002; Revised December 2003; Accepted March 25, 2004; First Online Version published in December 2004     

基于双谱理论的雷达辐射源指纹特征提取

针对雷达辐射源指纹特征提取困难的问题,提出了基于双谱切片法和双谱围线积分法,提取辐射源指纹特征的方法。介绍了二相编码信号的无意调制,仿真了理想情况和含有相位噪声的二相编码信号的时域波形。阐述了含相位噪声雷达信号的双谱估计,仿真了含相位噪声的二相编码信号的双谱图及等高图。最后利用双谱切片法和双谱围线积分法,提取了辐射源的指纹特征,通过计算机仿真实验验证了该方法的可实施性。     

Bearing estimation in the bispectrum domain

A new array processing method is presented for bearing estimation based on the cross bispectrum of the array output data. The method is based on the asymptotic distribution of cross-bispectrum estimates and uses maximum likelihood theory. It is demonstrated that, when the noise additive sources are spatially correlated Gaussian with unknown cross-spectral matrix (CSM), the cross-bispectrum method provides better bearing estimates than the stochastic maximum likelihood method with known CSM. Analytical studies and simulations are given to document the performance of the new method     

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     

复杂噪声环境下基于LVD的LFM信号参数估计

针对传统的线性调频(LFM)信号参数估计方法平滑交叉项时,会出现参数估计精度降低和计算复杂度增加等问题,该文引入LVD(LVs Distribution)方法,该方法可以在参数空间直接显示中心频率和调频斜率(CFCR)。LVD首先对对称参数瞬时自相关函数(PSIAF)进行尺度变换,消除信号在时间轴上的线性频率偏移,然后对尺度变换后的时间变量作2维傅里叶变换,将1维LFM信号转化为2维单频信号。信号各分量在LVD平面表现为多个独立尖峰,使交叉项的能量聚集影响可忽略不计,且信号各峰值所在位置对应于各信号分量的中心频率和调频斜率。LVD可有效抑制高斯噪声,但在脉冲性较强的稳定分布噪声中,该方法在CFCR域的性能退化甚至失效。对此,该文结合分数低阶统计量理论,提出一种稳定分布噪声环境下的分数低阶LVD新方法。仿真实验表明该方法在高斯噪声和脉冲噪声环境下均可稳定工作,具有较好的鲁棒性。     

Realization of the Gauss-in-Gauss detector using minimum-mean-squared-error filters (Corresp.)

Alternative structures for the optimum detection of Gaussian signals in Gaussian noise are derived that can be interpreted in terms of minimum-mean-squared-error (MMSE) estimators of signal and noise. The realization is useful when the statistics of the signal or noise or both are unknown since the detector can be implemented in an adaptive mode by using tapped delay lines whose weights are adjusted recursively to yield the minimum-mean-squared-error estimate of certain components of the incoming waveforms.     

Parameter estimation and spectral analysis of the discrete nonlinear secondorder Wiener filter (NSWF)

In many problems of digital signal processing, it is required to determine a model matching the statistics of a given observation of a generally non-Gaussian random process. Because of the wide range of systems that can be represented by Volterra series and Wiener expansions, the discrete nonlinear second-order Wiener filter (NSWF) driven by white Gaussian noise has been used in this study to match the statistics of a discrete zero-mean stationary non-Gaussian random process. First, we derive the autocorrelation function and show that it does not provide sufficient information necessary for estimating the parameters of the proposed model. Next, we derive the third-order moment sequence and show that it provides additional information that can be used in conjunction with the autocorrelation function to solve the problem. The power spectrum and bispectrum of the discrete NSWF have been also derived.     

Signal space detection for recording channels with jitter noise

A delay-constrained sequence detector is considered for recording channels whose major impediments include intersymbol interference (ISI) and magnetic transition jitter noise. The jitter noise is data-dependent, and a given noise sample is correlated with neighboring noise samples. A sequence detector with a finite decision delay can be formulated in a finite dimensional vector space. For a correlated noise channel, the decision boundary is generally quadratic. We present a technique for obtaining a minimal set of hyperplanes approximating a quadratic decision boundary with a negligible performance loss. In this process, a distance measure, which is consistent with the notion of the effective SNR, is defined and used as a design parameter to trade the complexity and performance. As an achievable performance bound, we derive the effective SNR for the maximum-likelihood sequence detector (MLSD) for these channels. The performance of the partial response maximum likelihood (PRML) detector commonly adopted for current data storage channels as well as the Viterbi algorithm (VA) based on the traditional Euclidean metric, which serves as the MLSD for additive white Gaussian noise, are also analyzed and compared with that of the proposed signal space detector     

Compact range radar cross-section measurements using a noise radar

This paper discusses the measurement of radar cross section (RCS) with a very low-cost system that transmits band-limited random noise over the band from 1.0 to 4.0 GHz. The received signal is correlated with a delayed version of the transmitted signal. A variable delay line is used to obtain the response at various delay times. This yields the radar target impulse response as a function of delay. This can be transformed to yield both the amplitude and phase of the scattering matrix in the frequency domain