The application of order statistic filters in detection systems

In this paper the performance of a digital processor, referred to as the order statistic (OS) filter, is analyzed as a noncoherent processor in a detection system. The statistical description of the output of the OS filter is presented in terms of the filter parameters and the statistics of the input. The mathematical form of this description, for the case of independent and identically distributed inputs, is used to develop general input output relations of the filter. These relationships are used to indicate the critical factors that affect the performance of the OS filter, and a quantitative expression is presented to determine the rank of the OS filter necessary for optimal detection performance. It is shown that the OS filter with extreme ranks (minimum and maximum detectors) performs well in situations where a significant skewness difference exists between the different classes of input signals. As the skewness difference between the classes decreases, the performance of the OS filter with extreme ranks degrades, while the performance of the OS filter for intermediate ranks is robust over this change.