Signals In Additive White Noise Research Articles

Likelihood ratios for signals in additive white noise

We present a formula for likelihood functionals for signals in which the corrupting noise is modelled as white noise rather than the usual Wiener process. The main difference is the appearance of an additional term corresponding to the conditional mean square error. By way of one application we consider the ‘order-disorder’ problem of Shiryayev.

Likelihood ratios for signals in additive white noise

We present a formula for likelihood functionals for signals in which the corrupting noise is modelled as white noise rather than the usual Wiener process. The main difference is the appearance of an additional term corresponding to the conditional mean square error. By way of one application we consider the ‘order-disorder’ problem of Shiryayev.

A sample path property of matched-filter outputs with applications to detection and estimation

The stochastic process at the output of a matched filter, when the latter is excited by its proper signal in additive white noise, has a mean function proportional to its covariance function. Sample path properties of a Gaussian process with the mean proportional to the covariance, conditioned such that it assumes a given value at the instant of the peak in the mean, are independent of signal amplitude. Formal and rigorous proofs and a detection-theoretical interpretation of this result are presented. It is then applied to the calculation of the detection probability of a rectangular signal of unknown time of arrival and to bounding the threshold effect in the estimation of the time of arrival. A novel passage time result is derived in the Appendix.

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.