Detection of non-Gaussian signals by bispectrum-U detector

A method for detecting non-Gaussian stationary signals in additive Gaussian noise using a bispectrum-U test is presented. The performance of the proposed detection statistic is compared to the conventional bispectrum χ² detector     

Detection of weak signals in non-Gaussian noise

A locally optimum detector structure is derived for the detection of weak signals in non-Gaussian environments. Optimum performance is obtained by employing a zero-memory nonlinearity prior to the matched filter that would be optimum for detecting the signal were the noise Gaussian. The asymptotic detection performance of the locally optimum detector under non-Gaussian conditions is derived and compared with that for the corresponding detector optimized for operations in Gaussian noise. Numerical results for the asymptotic detection performance are shown for signal detection in noise environments of practical interest.     

Detection of weak random signals in IID non-Gaussian noise

This paper considers the detection of weak random signals in circularly symmetric, independent, identically distributed noise. Locally optimum detectors and ad hoc nonlinearities are considered, with asymptotic expressions provided for evaluation of detection performance. The analytical expressions are used to evaluate the robustness of detectors to mismatch in the noise models. Finite-sample Monte Carlo simulation results indicate the reliability of these asymptotic measures in cases of practical interest. The results show that, as has been found for detection of weak known signals in non-Gaussian noise, reasonably configured ad hoc nonlinearities are nearly optimum and robust to modest errors in the noise statistics     

Detecting a transient signal by integrated polyspectrum

A method for detecting a transient signal in additive Gaussian noise via an integrated polyspectrum is presented. The performance of the proposed detection statistic, relative to a conventional energy detector and a bispectral detector is demonstrated     

Detection and estimation of signals in noise when one or both are non-Gaussian

An examination is made of the basic principles and results of the theory of detection and estimation of signals in noise, which is not limited to the condition that the useful signal and noise be Gaussian and that the noise be additive. Formulas are obtained [(23) and (25)] for likelihood ratios which are useful in the Markovian as well as in the non-Markovian case. The results are specialized for the case of diffusion noise and fixed but unknown signal parameters, when it is possible to effectively utilize the theory of conditional Markov processes. Estimation by the quasi-linear theory is also discussed, the applicability of which is limited not by the Markovian condition, but by the condition of high a posteriori accuracy. In conclusion, a generalization is given of the theory for the case of adaptive detection and estimation, when the a priori information is replaced by learning. In this case, application of the theory of conditional Markov processes makes it possible to obtain, besides the previous equations of Gaussian approximation, similar equations for the unknown parameters.     

Detection of non-Gaussian signals: a paradigm for modernstatistical signal processing [and prolog]

Non-Gaussian signals arise in a wide variety of applications, including sonar, digital communications, seismology, and radio astronomy. In this tutorial overview, a hierarchical approach to signal modeling and detector design for non-Gaussian signals is described. In addition to being of interest in applications, this problem serves as a paradigm within which most of the areas of active research in statistical signal processing arise. In particular, the methodologies of nonlinear signal processing, higher order statistical analysis, signal representations, and learning algorithms, all can be juxtaposed quite naturally in this framework     

Detection of baseband signals using a delta modulator

The performance of a digital delta modulator when used as a repeater for binary non-return-to-zero signals between a noisy channel and an error-free link is analyzed. A Markov chain is used to model the accumulator output (observation process) of the device, and a Bayes test with a probability of error criterion is formulated to evaluate its performance in additive band-limited Gaussian channel noise. The key design parameters of sampling rate and accumulator range are varied for computation of performance degradation relative to the optional matched filter. Numerical results are presented that demonstrate the feasibility of this technique     

Adaptive frequency estimation of sinusoidal signals in colored non-Gaussian noises

This paper studies the problem of sinusoidal frequency estimation in colored non-Gaussian ARMA noises. A new adaptive approach is proposed by using the second-and third-order statistics of the measurements. Because of the simultaneous establishment of the signal and noise models, the new approach is applicable for tracking the frequencies at each time instant for stationary and nonstationary signal and/or noise cases. The effectiveness of the new approach is demonstrated by extensive computer simulations. As expected, the approach proposed in this paper outperforms the correlation-based approaches in suppressing the effects of the colored non-Gaussian ARMA noises.     

Detection of tone signals using a nonlinear energy tracker

A simple scheme is proposed for detecting tone signals narrowly spaced in frequency. By employing Teager's energy tracker as a preprocessor, the tone detector can be implemented without the use of sharp notch filters. The proposed detector is applied to distinguishing ITU-T V.8 and V.25 tone signals. The detector performance is analysed and verified by computer simulation     

On blind beamforming for multiple non-Gaussian signals and theconstant-modulus algorithm

A new method for blindly separating multiple cochannel non-Gaussian signals received by a sensor array is presented. The method is based on a cumulant-based least-squares criterion that, for identically distributed negative-kurtosis signals, is proven to be identical to the “2-2” constant-modulus (CM) cost function commonly used by CM algorithms. A computationally simple algorithm is proposed to minimize the criterion. The algorithm performs well even when the number of samples is small, thus allowing its application in dynamic environments (e.g., moving emitters). For the special case of two signals only, the minimization is obtained analytically. Simulation results are included     

A comparison of optimized higher order spectral detectiontechniques for non-Gaussian signals

Using the Gaussian noise rejection property of higher order spectra (HOS), HOS-based detectors have been proposed that outperform conventional second-order techniques in certain scenarios. Based on statistical tests proposed by Suhha Rao and Gabr (1980), as well as Hinich (1982), Kletter and Messer (1990), and Hinich and Wilson (1990), have developed similar bifrequency-domain detectors that are dependent on bispectral estimates of the observation process. Formalizing the estimate consistency requirements and the asymptotics for these detectors, we derive a new F-test statistic. We consider the detrimental effects of using spectral estimates in the denominator of Hinich's test. We determine refined conditional distributions for third- and fourth-order versions of his detector. We also modify his test for colored scenarios. Extending the bispectral detectors to their kth-order counterparts, we calculate the optimal smoothing bandwidth to use in constructing the HOS estimates, producing the best detection performances for both our F-test and Hinich's test with our refined distributions. These new bandwidths yield significant improvements in detector performance over previous results. For the finite sample case, our calculations characterize the tradeoff between the two detectors and demonstrate that a larger smoothing bandwidth than the one suggested by previous researchers should be used. Our calculations are verified using simulations for both white and colored cases     

Suboptimum detection of weak signals in non-Gaussian noise (Corresp.)

A suboptimum detector structure is developed for the detection of weak signals in non-Gaussian noise. In contrast to locally optimum detectors, the suboptimum detector structure is relatively easy to implement and is shown to perform well for a wide range of underlying noise distributions. The robustness of simple limiter detectors is discussed. The extension of the concept of a suboptimum detector to an adaptive detector for operating in an unknown noise environment is also discussed.     

应用非高斯重尾分布模型的子带滤波

图像经小波处理后,其细节分量具有明显高尖峰重拖尾分布的非高斯特性.据此,提出一种广义高斯α稳定分布的双参数柯西混合描述模型,并给出了相应的基于贝叶斯收缩和最大后验概率收缩的非线性滤波器的设计技术.通过与小波软门限滤波器方法比较,并对含加性噪声的标准图像进行抑制实验,结果表明,设计的滤波器具有较好的子带滤波效果,达到了有...     

利用非线性自适应技术检测微弱的瞬时信号

本文根据局部流形理论,提出了一类非线性自适应预测滤波模型。仿真结果显示,本文提出的自适应预测滤波模型具有很强的非线性近似能力,可以检测淹没在超混沌或杂波环境中的瞬时信号。     

Recursive estimation of images using non-Gaussian autoregressivemodels

We consider recursive estimation of images modeled by non-Gaussian autoregressive (AR) models and corrupted by spatially white Gaussian noise. The goal is to find a recursive algorithm to compute a near minimum mean square error (MMSE) estimate of each pixel of the scene using a fixed lookahead of D rows and D columns of the observations. Our method is based on a simple approximation that makes possible the development of a useful suboptimal nonlinear estimator. The algorithm is first developed for a non-Gaussian AR time-series and then generalized to two dimensions. In the process, we draw on the well-known reduced update Kalman filter (KF) technique of Woods and Radewan (1977) to circumvent computational load problems. Several examples demonstrate the non-Gaussian nature of residuals for AR image models and that our algorithm compares favorably with the Kalman filtering techniques in such cases.     

Optimum classification of non-Gaussian processes using neuralnetworks

A prerequisite for target detection in synthetic aperture radar and moving target imaging radars is an ability to classify background clutter in an optimal manner. Such radar clutter can frequently be modelled as a correlated nonGaussian process with, for example, Weibull or K statistics. Maximum likelihood (ML) provides an optimum classification scheme but cannot always be formulated when correlations are present. In such circumstances, nonlinear, adaptive filters are required which can learn to classify the clutter types: a role to which neural networks are particularly suited. The authors investigate how closely neural networks can approach optimum classification. To this end, a factorisation technique is presented which aids convergence to the best possible solution obtainable from the training data. The performances of factorised networks are compared with the ML performance and the performances of various intuitive and approximate classification schemes when applied to uncorrelated K distributed images. Furthermore, preliminary results are presented for the classification of correlated processes. It is seen that factorised neural networks can produce an accurate numerical approximation to the ML solution and will thus be of great benefit in radar clutter classification     

Detection of radar signals in conditions of full prior information when using stochastic signals for probing

Probabilistic characteristics of coherent detection of reflected signals with the fully known parameters when using stochastic soundings radio signals are determined. Analytical expression for probability density of decision statistics for the cases of presence at detector??s input of reflected signal only, interference only, and both signal and interference is obtained. Dependency of false alarm probability on threshold ratio and dependency of hit probability on signal-to-interference ratio for different values of bandwidth-duration product of stochastic signal are computed. A family of radar detection performances characteristics for fixed bandwidth-duration product and different values of false alarm probability is calculated.     

Detection in incompletely characterized colored non-Gaussian noisevia parametric modeling

The problem of detecting a weak signal known except for amplitude in incompletely characterized colored non-Gaussian noise is addressed. The problem is formulated as a test of composite hypotheses, using parameteric models for the statistical behavior of the noise. A generalized likelihood ratio test (GLRT) is employed. It is shown that for a symmetric noise probability density function the detection performance is asymptotically equivalent to that obtained for a similar detector designed with a priori knowledge of the noise parameters. Non-Gaussian distributions are found to be more favorable for the purpose of detection than the Gaussian distribution. The computational burden of the GLRT may be partially reduced by employing a Rao efficient score test which shares all the nice asymptotic properties of the GLRT for small signal amplitudes. Computer simulations of the performance of the Rao detector support the theoretical results     

Adaptive energy detection of quasi-deterministic signals in the presence of the non-Gaussian noise

Analytical expressions for the parameters of the adaptive energy detection of the quasi-deterministic radio signals in the presence of the Lichter noise are derived. The effect of the random amplitude distribution of radio signals on the decision statistics of detection is analyzed.