Known Signal Detection with Signs and Ranks

The problem of signal detection can be considered as a parameter testing problem of a null hypothesis against an alternative hypothesis, as we have seen in Chapters 2–4, for example. As a consequence, the knowledge of a priori information on the parameter is essential for establishing the hypothesis testing problem. Unfortunately, it is very difficult, if not impossible, to exactly estimate the value of a parameter in practice. It is well-known that the design of a suitable discrete-time detector for signals in corrupting noise is sometimes complicated because of inexact knowledge of the statistics of the noise process: if we are not able to get a priori information on the distribution of the parameter, we cannot design an optimum parametric detector. Although we may estimate the parameters in some cases, small deviations of the parameters from the theoretic model in the real environment may lead sometimes to a significant performance degradation of the optimum parametric detector. Specifically, the performance of a detector is quite sensitive to the statistics of the noise process, and an optimum detector based on Neyman-Pearson lemma often performs poorly in the case where a priori knowledge of the noise statistics is not exact. In such a case, we shall need nonparametric detectors, which ensure a constant falsealarm probability. The best known nonparametric detectors are those based on signs and ranks of the received data samples.