Signals In non-Gaussian Noise Research Articles

Optimum data receivers for low SNR data signals in non-gaussian noise and intersymbol interference: receiver structures and their performance analysis

The paper concerns the design of locally optimum data receivers for dispersive non- Gaussian channels. A number of approaches are considered for the optimisation of the receiver when the detection is carried out either on a bit-by-bit or a block basis. A number of interesting receiver structures are shown to result when the design is carried out (a) by assuming the knowledge of adjacent bits (decision-feedback approach), (b) by composite hypothesis testing, or (c) by the maximum likelihood sequence estimation approach. Although the design here has been carried out using baseband signal representations, it should be possible to obtain similar results for bandpass modulations. Performance characteristics of these receiver structures based on bounds on the error probability have also been presented. Numerical evaluation of the error probability is carried out for a lowpass symmetric impulse response channel in the presence of a generalised Gaussian noise. Comparison of the numerical results for different receivers yields some interesting insights into the relative performance of the various receivers.

A robust running-window detector and estimator for step-signals in contaminated Gaussian noise

An N-point window is applied to noisy data to recover stepped signals in non-Gaussian noise. Robust measures of signal step level and noise distribution spread are used to detect sequential clusters of data points which are statistically significantly different, thereby detecting the step. Using conventional analysis-of-variance methods, but with robust parameter estimates, false alarm probabilities are set reasonably accurately, and miss probabilities and signal level estimates are shown by simulation to yield good results. Applications to Kalman filtering, seismic and well-log data, and image processing are indicated.

Optimum and Suboptimum Space-Diversity Detection of Weak Signals in Non-Gaussian Noise

The structure of the locally optimum space-diversity detector for coherent detection of a bandpass signal subject to amplitude fluctuations in the presence of narrow-band non-Gaussian noise is derived and its large-sample performance is evaluated. For easy implementation a suboptimum structure is proposed. It consists of local detectors performing independent local decisions and of a central processor that, working according to simple logical schemes (OR or AND), performs the global decision based on the local ones. Numerical results and a comparison between the performances of both proposed structures are presented and discussed.

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.

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.

The asymptotic performance of two-sample nonparametric detectors when detecting nonfluctuating signals in non-Gaussian noise (Corresp.)

The asymptotic relative efficiencies (ARE) of generalized sign (GS), Mann-Whitney (MW), modified Savage (MS), and modified rank squared (MRS) two-sample nonparametric detectors are compared with those of the mean and median parametric detectors. The signal is assumed to be nonfluctuating, and the background noise is assumed to be lognormal or to be characterized by a contaminated normal distribution. It is shown that using the asymptotic relative efficiency measure the performance of nonparametric detectors increases appreciably as the noise distribution deviates from normality.

Acoustic signal processing extensions on ’’optimum detection of signals in non-Gaussian noise’’

In a recent paper, Sheehy derived optimum processing structures for use in detection of signals in additive non-Gaussian noise. An analytical form was postulated for the distribution of the noise intensity level and found to be in good agreement with experimental data. Since this data was not presented in the article, it is the intent of this letter to clarify the nature of the experimental data previously reported.

Optimum detection of signals in non-Gaussian noise

The purpose of this paper is to derive optimum processing structures for use in the detection of signals in additive non-Gaussian noise. The cases chosen for analysis are of particular interest in sonar detection problems since it has been reported that ambient ocean noise may, under sone conditions, deviate from the Gaussian model. The processing structures are considered to be models of the likelihood ratio which is an optimum test no matter what the signal and noise statistics, and optimum single channel and array processors are derived for the small signal-to-noise ratio cases where (1) the signal is completely known, and (2) the signal is a noiselike, not necessarily Gaussian, zero-mean process. Expressions are derived which compare the performance of processors optimized for non-Gaussian noise with those optimized for Gaussian noise for each of the two cases, with transfer functions for the required optimum nonlinear filters and the expected improvements in performance determined using some ’’typical’’ non-Gaussian probability density functions. Justification of these particular density functions is beyond the scope of this paper except to note that very good agreement is obtained with some published experimental data. New results include the derivation of optimum array processors for the detection of plane wave signals when the array is steered at the signal arrival angle, in a non-Gaussian noise field and the development of expressions to predict their performance for the case where the signal is a zero-mean, noiselike process.

Locally optimum detection of discrete-time stochastic signals in non-Gaussian noise

Two basic models are considered for the problem of detecting small, zero-mean stochastic signals in non-Gaussian noise processes. Appying the theory of local tests, a general detector structure is derived for each of these models. A third (suboptimal) scheme based on null-zone detection is also proposed and a technique for optimizing its parameters is discussed. Using the criterion of asymptotic relative efficiency, the performance of these three detectors and of a power detector are compared under each of the proposed models.

Robust Detectors for Signals in Non-Gaussian Noise

The robustness of suboptimal nonlinear detectors for known discrete-time signals in non-Gaussian noise is investigated. The measure of robustness used is the degradation of asymptotic relative efficiency (compared to a linear detector) from that achieved by an optimal nonlinear detector. The first order density of non-Gaussian noise is modeled as a mixture of a small variance Gaussian background noise pdf and a large variance impulsive pdf.

Robust detection to stochastic signals (Corresp.)

In this correspondence we evaluate both the large and small sample performance of a limiter-quadratic detector (LQD) for the detection of a Gaussian signal in non-Gaussian noise. The LQD is shown to be robust for small as well as large sample sizes.

Detectors for discrete-time signals in non-Gaussian noise

The structure and performance of a class of nonlinear detectors for discrete-time signals in additive white noise are investigated. The detectors considered consist of a zero-memory nonlinearity (ZNL) followed by a linear filter whose output is compared with a threshold. That this class of detectors is a reasonable one to study is apparent from the fact that both the Neyman-Pearson optimum and the locally optimum (i.e., weak-signal optimum) detectors for statistically independent noise samples can be put into this form. The measure of detector performance used is the asymptotic relative efficiency (ARE) of the nonlinear detector under study with respect to a linear detector appropriate for the same detection problem. A general expression for this ARE is given along with the result that the non-linearity maximizing this expression is any linear function of the nonlinearity in the appropriate constant-signal locally optimum detector. To illustrate the structure and performance of these nonlinear detectors for a wide range of non-Gaussian noise distributions, three general classes of symmetric, unimodal, univariate probability density functions are introduced that are generalizations of the Gaussian, Cauchy, and beta distributions.