(A) nonparametric detector based on the median-shift sign

Abstract

In this thesis, we propose a new detector based on the median-shift sign. We call it the median-shift sign (MSS) detector, which is an extension of the classical sign detector. We also show some properties of the optimum median -shift values. We first analyze the problem of detecting a dc signal in noise of known probability density function (pdf). The MSS detector with the optimum median-shift value, the optimum MSS detector, performs slightly better than the sign detector in Gaussian noise: it has the best performance among the detectors compared in Laplacian and Cauchy noise. It is shown that the MSS detectors with constant median-shift values are nearly equal to the optimum MSS detector. We also analyze the problem of detecting a dc signal when only partial information is available on the noise. In this case, the MSS detectors with constant median-shift values are used. The MSS detectors are almost equal to the sign detector in Gaussian noise:they perform better than the sign and Wilcoxon detectors for most signal ranges in Laplacian and Cauchy noise. Because the false alarm rate of the MSS detector is constant, the MSS detector is a nonparametric detector. The MSS detectors with small constant median-shift values have simple structure and perform better than the sign and Wilcoxon detectors for most signal ranges in non-Gaussian noise.