Optimization of the two-sample rank Neyman-Pearson detector

The development of optimal algorithms concerned with rank considerations in the case of finite sample sizes involves considerable mathematical difficulties. The present investigation provides results related to the design and the analysis of an optimal rank detector based on a utilization of the Neyman-Pearson criteria. The detection of a signal in the presence of background noise is considered, taking into account n observations (readings) x1, x2, ... xn in the experimental communications channel. The computation of the value of the rank of an observation is calculated on the basis of relations between x and the variable y, representing interference. Attention is given to conditions in the absence of a signal, the probability of the detection of an arriving signal, details regarding the utilization of the Neyman-Pearson criteria, the scheme of an optimal rank, multichannel, incoherent detector, and an analysis of the detector.