An asymptotic relative performance measure for signal detectors based on the correlation information of statistics

Abstract

Signal detectors generally utilize nonlinear statistics of an original observation rather than the original observation as it is. The sign statistic, a typical example of the nonlinear statistics, is the sign information of an observation and the sign detector relies only on the sign statistic. Since either detector might be of a better performance depending on the situation, it is quite important to determine which is the best performer among the detectors, based on the given situational information about noise and signal strength. In this letter, a qualitative analysis is presented that the correlation coefficients between the statistics and original observation can be used to predict the asymptotic performance of a detector utilizing one of the statistics, relative to the other detectors.