Signals In Impulsive Noise Research Articles

Time–frequency-based detection in impulsive noise environments using α-stable noise models

We develop near-optimal test statistics for the detection of arbitrary non-stationary second-order random signals in impulsive noise, modelled using a bivariate, isotropic α-stable distribution. The test statistics are derived by approximating the noise model using a mixture of Gaussians, trained using an expectation-maximisation algorithm. We consider the extension to the case when the signal to be detected is subjected to an unknown time–frequency or time-scale shift, and show that approximations to locally optimal test statistics can be implemented using bilinear time–frequency or time-scale representations. We demonstrate that the performance of the locally optimal linear receiver is poor in even mildly impulsive noise; the alternative detection statistics proposed in this paper offer considerably enhanced performance.

Robust parameter estimation of a deterministic signal in impulsive noise

This paper presents a robust class of estimators for the parameters of a deterministic signal in impulsive noise. The proposed technique has the structure of the maximum likelihood estimator (MLE) but has an extra degree of freedom: the choice of a nonlinear function (which is different from the score function suggested by the MLE) that can be adjusted to improve robustness. The effect of this nonlinear function is studied analytically via an asymptotic performance analysis. We investigate the covariance of the estimates and the loss of efficiency induced by nonoptimal choices of the nonlinear function, giving special attention to the case of /spl alpha/-stable noise. Finally, we apply the theoretical results to the problem of estimating the parameters of a sinusoidal signal in impulsive noise.

Automatic classification of wideband acoustic signals

Until now, very few contributions were published in the field of wideband acoustic signal recognition, especially for handling impulsive noise signals such as glass breaking, detonations, or door slams, as encountered in security applications, where the signals are highly nonstationary and composed of higher frequency components. This paper shows how the audio alarm recognition problem can efficiently be tackled using either pattern recognition methods relying on Bayes classifiers, or on artificial neural networks (ANN). After extraction of filterbank coefficients in the acoustic analysis module, typical feature vectors are achieved from the concatenation of k consecutive signal frames, in order to exploit dynamic temporal information. The redundancy induced by this dynamic modeling requires a reduction of the feature space dimension, performed with a conventional principal component analysis. The performance of both systems is evaluated experimentally (7000 tests) for the classification of three types of noise events (glass breaking, door slams, and stationary noises). The score of correct classification reaches 99% for the statistical approach, and 98% for the ANN-based system. It is further noticed that errors do not occur on the same signal files for both methods. Thus robustness enhancement can be reasonably expected, when using hybrid methods or fusion strategies.

Near optimal detection of signals in impulsive noise modeled with a symmetric /spl alpha/-stable distribution

There has been great interest in symmetric /spl alpha/-stable distributions which have proved to be very good models for impulsive noise. However, most of the classical non-Gaussian receiver design techniques cannot be extended to the symmetric /spl alpha/-stable noise case since these techniques require an explicit compact analytical form for the probability density function (PDF) of the noise distribution which /spl alpha/-stable distributions do not possess. A new analytical representation has been suggested for the symmetric /spl alpha/-stable PDF which is based on scale mixtures of Gaussians. Based on this new analytical representation, this paper introduces a novel near-optimal receiver for the detection of signals in symmetric /spl alpha/-stable noise. The performance of the new receiver is very close to the locally optimum receiver and is significantly better than the performance of previously suggested sub-optimum receivers. The new technique has important potential in radar, sonar, and other applications.

Statistical reconstruction and analysis of autoregressive signals in impulsive noise using the Gibbs sampler

Modeling and reconstruction methods are presented for noise reduction of autocorrelated signals in non-Gaussian, impulsive noise environments. A Bayesian probabilistic framework is adopted and Markov chain Monte Carlo methods are developed for detection and correction of impulses. Individual noise sources are modeled as Gaussian with unknown scale (variance), allowing for robustness to heavy-tailed impulse distributions, while the underlying signal is modeled as autoregressive (AR). Results are presented for both artificial and real data from voice and music recordings, and comparisons are made with existing techniques. The new techniques are found to give improved detection and elimination of impulses in adverse noise conditions at the expense of some extra computational complexity.

Adaptive weighted myriad filter algorithms for robust signal processing in α-stable noise environments

Stochastic gradient-based adaptive algorithms are developed for the optimization of weighted myriad filters (WMyFs). WMyFs form a class of nonlinear filters, motivated by the properties of /spl alpha/-stable distributions, that have been proposed for robust non-Gaussian signal processing in impulsive noise environments. The weighted myriad for an N-long data window is described by a set of nonnegative weights {w/sub i/}/sub i=l//sup N/ and the so-called linearity parameter K>0. In the limit, as K/spl rarr//spl infin/, the filter reduces to the familiar weighted mean filter (which is a constrained linear FIR filter). Necessary conditions are obtained for optimality of the filter weights under the mean absolute error criterion. An implicit formulation of the filter output is used to find an expression for the gradient of the cost function. Using instantaneous gradient estimates, an adaptive steepest-descent algorithm is then derived to optimize the weights. This algorithm involves a very simple update term that is computationally comparable to the update in the classical LMS algorithm. The robust performance of this adaptive algorithm is demonstrated through a computer simulation example involving lowpass filtering of a one-dimensional chirp-type signal in impulsive noise.

Optimum detection over Rayleigh-fading, dispersive channels, with non-Gaussian noise

The paper discusses the problem of detecting one out of M Gaussian correlated signals in impulsive noise, modeled as a compound-Gaussian, possibly correlated process. We first show that, for uncorrelated noise, the detection problem admits one and the same optimum-in the sense of attaining minimum error probability-solution, independent of the noise statistics: the optimum detector, in fact, amounts to an estimation block, aimed at measuring the short-time noise power spectral density (PSD), whose output is fed to a bank of estimators-correlators, each keyed to one of the M admissible waveforms and to the estimated noise PSD. We also give suggestions for realizing a suboptimum receiver, with reduced complexity, which again is canonical in its structure. As for the performance analysis, we focus on binary frequency-shift keying (BFSK) signaling: we provide numerical results for two particular channel correlations and for Cauchy-distributed noise. These results indicate that, like for the general Gauss-Gauss case, the performance depends on the energy contrast, as well as on the "time-bandwidth" product of the useful signal. Moreover, noise spikiness seems to negatively affect the performance, in the sense that heavier and heavier high-amplitude tails of the noise marginal distribution give rise to higher and higher error probabilities for fixed energy contrast and time-bandwidth signal product.

Fuzzy prediction and filtering in impulsive noise

Additive fuzzy systems can filter impulsive noise from signals. Alpha-stable statistics model the impulsiveness as a parametrized family of probability density functions or unit-area bell curves. The bell-curve parameter α ranges through the interval (0, 2] and gives the Gaussian bell curve when α = 2 and gives the Cauchy bell curve when α = 1. The impulsiveness grows as α falls and the bell curves have thicker tails. Only the Gaussian statistics have finite variances or finite higher moments. An additive fuzzy system can learn ellipsoidal fuzzy rule patches from a new pseudo-covariation matrix or measure of alpha-stable covariation. Mahalanobis distance gives a joint set function for the learned if-part fuzzy sets of the if-then rules. The joint set function preserves input correlations that factored set functions ignore. Competitive learning tunes the local means and pseudo-covariations of the alpha-stable statistics and thus tunes the fuzzy rules. Then the covariation rules can both predict nonlinear signals in impulsive noise and filter the impulsive noise in time-series data. The fuzzy system filtered such noise better than did a benchmark radial basis neural network.

Optimum detection of fading signals in impulsive noise

This paper deals with the synthesis and the analysis of optimum receivers to detect one out of M equally likely, equi-energy, fading signals in impulsive noise, modelled as a compound Gaussian, possibly correlated process. We show that the conventional coherent and incoherent detectors are still optimum, independent of the noise as well as the fading probability density functions. The performance analysis has been carried on with reference to the general case of arbitrarily distributed disturbance: in order to simplify the analysis, asymptotical expressions have been developed for high signal-to-noise ratios as well as high signal space dimensionality. Interestingly enough, this allows separating the effect of the noise spikyness from that of the fading law. Results indicate that, for deep fading, the noise marginal distribution does not dramatically affect the error probability, nor is it influential on the limit operating characteristics corresponding to infinite signal space dimensions. For non-fluctuating signals, instead, the noise distribution plays a primary role: spiky noise usually produces performance impairment; moreover, the limit performance in impulsive disturbance may exhibit marked deviations from the well-known stepwise shape which is typical of Gaussian channels. >

Nonparametric density estimation and detection in impulsive interference channels. II. Detectors

For pt. I see ibid., vol.42, no.2-4, p.1684-1697 (1994). Nonlinear processing significantly enhances detector performance in nongaussian noise relative to that of linear detectors. Several nonparametric detection schemes for impulsive noise channels are formulated using the nonparametric probability density estimators developed in Part I. The likelihood ratio test and the small-signal (locally optimum) nonlinearity provide the basis for the formulation of these nonparametric detection schemes. Several modifications to these basic strategies are used to compensate for inaccuracies in the density estimates. In particular, for the problem of detecting a known signal in impulsive noise, two modifications to the standard likelihood ratio test are considered: the first is adapted from robust statistics, whereas the second, the "L/sub 1/-error-based" detector is specifically formulated for use with density estimates. Both schemes are found to perform close to the optimum likelihood ratio detector for a wide variety of impulsive noise densities. From the merits of these two tests, a new detection scheme that approximates the locally optimum nonlinearity is then developed. This detector, which uses the nonparametric density estimators developed in Part I, is shown to perform very well for the wide variety of impulsive and heavy tailed densities considered in the study. This nonparametric-density-estimate-based detector is also shown to outperform more conventional nonparametric detectors in impulsive noise.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Nonparametric density estimation and detection in impulsive interference channels. I. Estimators

For pt. I see ibid., vol.42, no.2-4, p.1684-1697 (1994). Nonlinear processing significantly enhances detector performance in nongaussian noise relative to that of linear detectors. Several nonparametric detection schemes for impulsive noise channels are formulated using the nonparametric probability density estimators developed in Part I. The likelihood ratio test and the small-signal (locally optimum) nonlinearity provide the basis for the formulation of these nonparametric detection schemes. Several modifications to these basic strategies are used to compensate for inaccuracies in the density estimates. In particular, for the problem of detecting a known signal in impulsive noise, two modifications to the standard likelihood ratio test are considered: the first is adapted from robust statistics, whereas the second, the L/sub 1/-error-based detector is specifically formulated for use with density estimates. Both schemes are found to perform close to the optimum likelihood ratio detector for a wide variety of impulsive noise densities. From the merits of these two tests, a new detection scheme that approximates the locally optimum nonlinearity is then developed. This detector, which uses the nonparametric density estimators developed in Part I, is shown to perform very well for the wide variety of impulsive and heavy tailed densities considered in the study. This nonparametric-density-estimate-based detector is also shown to outperform more conventional nonparametric detectors in impulsive noise. >