Analysis of the effect of multiplicative noise on the conditions of signal resolution according to a statistical criterion

We analyzed the effect of multiplicative noise on signal resolution characteristics when a statistical criterion for processing is used in the receiving device. The receiver is optimal for resolving two signals in the sense of detecting against the background of additive white noise. It is shown that the complex envelope of the signal at the output of the analyzed receiver can be considered as a flat vector with correlated components having different variances. However, with fast multiplicative noise, the named components become uncorrelated, and their variances become equal. It is shown that the delay time resolution intervals and frequency shift resolution intervals with known statistical characteristics of signals, additive and multiplicative noise are uniquely determined by the probabilities of correct and false resolution. It is pointed out that the use of a statistical criterion allows us to determine quantitative values of resolution intervals in a fairly wide range of changes in the parameters of additive and multiplicative noise, significantly exceeding the Woodward criterion for example. Thus, the use of statistical criteria leads to an increase in the efficiency of radio systems.