Random Signal In Additive Noise Research Articles

On the score functions of the two-sample locally optimum rank test statistic for random signals in additive noise

The test statistic of the two-sample locally optimum rank detector is derived for weak random signals in additive noise. It is shown that the two-sample locally optimum rank detector for random signals has interesting similarities to the one-sample locally optimum rank detector for random signals. The detector may also be viewed as a generalization of the two-sample locally optimum rank detector for known signals. Some examples and properties of the score functions constituting the locally optimum rank test statistic are investigated.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Locally optimum rank detection of correlated random signals in additive noise

Nonparametric detection of a zero-mean random signal in additive noise is considered. The locally optimum detector based on signs and ranks of observations is derived, for good weak-signal detection performance under any specified noise probability density function. This detector is shown to have interesting similarities to the locally optimum detector for random signals. It may also be viewed as a generalization of the locally optimum rank detector for known signals. Examples of the test statistic of the detector are given for some specific noise probability density functions. Asymptotic and finite sample-size performance of the locally optimum rank detector is also considered. >

Nonparametric Hard Limiting and Sign Detection of Narrow-Band Deterministic and Random Signals

Hard limiting or sign detection schemes for low-pass known and random signals in additive noise are popular as very simple signal detectors maintaining constant values for their false-alarm probabilities under the rather weak assumption that the sampled noise observations have zero median values. For nonparametric detection of narrow-band signals the natural extension of the zero medians assumption is the zero marginal medians assumption on the in-phase and quadrature noise components. Nonparametric detectors operating under this assumption are developed here for narrow-baud signals; these can be taken to be the logical counterparts of the low-pass sign correlator and polarity coincidence correlator detectors of low-pass theory. The concept of conditional testing, which has been applied previously to obtain efficient multilevel versions of low-pass sign detection schemes, is shown to enter quite naturally in the definition of narrow-band counterparts of the sign correlator and the polarity coincidence correlator detectors. It is also shown that under the diagonal symmetry extension of the low-pass univariate symmetry condition on the noise probability density function, multilevel extensions of these conditional test narrow-hand detectors may also be defined as counterparts of the multilevel conditional test schemes for low-pass signals.

Resolution of overlapping random signals (Corresp.)

This correspondence is concerned with the estimation and resolution of overlapping random signals in additive noise. Two resolution schemes are presented; one is optimal and the other has computational advantages. It is shown that the overlapping signals are not resolvable if the eigenfunctions constitute a complete basis.

Optimum weighting functions for the detection of sampled signals in noise

The problem of designing a linear predetection filter for the detection of a sampled random signal in additive noise is considered. The design of the filter is based on an optimality criterion which maximizes the signal-to-noise ratio enhancement. The optimum weighting function obtained in this manner has the advantage that it is independent of signal characteristics and depends only on the covariance function of the noise. The optimum filter, for general covariance functions, is obtained for <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N = 2, 3</tex> and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</tex> samples. The asymptotic solution for large <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</tex> is also presented by employing results from the theory of Teeplitz forms. In addition, the complete solution for all <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</tex> is given for several particular covariance matrices. An application of the results is made to the problem of designing a linear predetection filter in a moving target indication (MTI) radar system. The optimum weighting function for <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N = 2</tex> is a single-cancellation unit, while that for <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N = 3</tex> is similar but not quite the same as a double-cancellation unit. It is shown that the signal-to-noise ratio enhancement provided by the double-cancellation scheme is <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1.76</tex> db worse than that of the optimum filter when the noise has a Gaussian covariance function.