Nonparametric detection of narrow-band signals in additive white Gaussian noise by means of level-crossing rate

Abstract

This dissertation is concerned with nonparametric detection of a narrow-band Gaussian signal and a fixed sine wave signal in white Gaussian noise by means of the level-crossing rate of a received signa. The major contribution of this study is the development of engineering design criteria for selecting a level threshold and a decision threshold in a simple but practical level-crossing receiver. The optimum level setting is derived to yield a maximum mean separation between the level-crossing rates when the signal is present and when the signal is absent. A closed form solution is obtained for the Gaussian signal case. For the fixed sine wave case we obtain a simple equation which can be easily solved by numerical methods to yield the optimum level setting. Complete statistics of the level-crossing rate of a signal are not available. Consequently a nonparametric procedure, hypothesis testing, is used to find the decision threshold to determine when the signal is present. In nonparametric detection systems no assumption is made as to the form of input distributions. Two non-parametric tests, the Kolmogorov-Smirnov test and the Mann-Whitney test, are used to develop the decision threshold. The test statistic is the level-crossing rate. The Mann-Whitney test is shown to perform better than the Kolmogorov-Smirnov test when the level is set to maximize the mean separation.