An analysis of the median-shift sign detector under various noise distributions

We propose a new detector of which the basis is on the median-shift (MS) sign: the median-shift sign (MSS) detector is a generalization of the classical (standard) sign detector. We obtain the finite sample size and asymptotic optimum MS values for various noise probability density functions (pdfs). We analyze the problem of detecting known signals in noise of known distributions. The optimum MSS detector is shown to perform better than the sign detector in Gaussian noise: it has the best performance among the detectors compared in the non-Gaussian noise cases. It is noteworthy that the performance of the MSS detectors with constant MS values are nearly equal to that of the optimum MSS detector. We also investigate signal detection when only partial information is available on the noise. The MSS detectors with constant MS values perform almost equal to the sign detector in Gaussian noise: they perform better than the sign and Wilcoxon detectors for most signal strength ranges in the non-Gaussian noise cases. ( 1998 Elsevier Science B.V. All rights reserved.