Approximated parameters of signal detection and disstinction quality basd on first moments of logarithm of likelyhood ratio

摘要

The formulas are suggested for the approximated of the quality parameters (probabilicy) of signal detection and distinction based on the difference of the mathematical waiting of the logarithm of the likelyhood ratio of the observed values in the presence and absence of the detected signals. In particular cases of the statistical models of the observed values (signal and jamming signal) this approximation coincides with the accurat formulas for the signal detection probability at the spetisied probability of the false alarm. For ather investigation by the numeric methods of the statistical models of signal and jamming signal of approximation accuracy is no worse then 10-15 %. It is also shown what in general case the suggested approximation, provided the accuracy is not worse, then 30% of the estimation value of the detection (distinction) probability. The presented approximation is recommended for obtaining the analysis of detection (discrimination) parameters in the case when it is impossible to obtain the exact analitical expressions for the probability of signal detection or discrimination because of complexity or impossibility of finding the laws of sufficienty statistics distribution.