Accuracy of Measuring the Frequency and Time of Arrival of the Useful Signal in the Presence of Additive and Multiplicative Low Level Noise

Abstract

The influence of fluctuating stationary multiplicative low level noise acting simultaneously with additive noise on the accuracy of measurement of non-energy information parameters of the signal is estimated. It is shown, that the degree of influence of multiplicative noise on the accuracy of frequency measurement is completely determined by the spectrum of the square of the signal envelope and the spectral characteristics of the noise modulation function. The influence of slow and fast multiplicative noise on the information parameters of the signal is analyzed. It is pointed out that the errors in measuring the time of arrival of the signal due to the presence of multiplicative noise depend on both the signal envelope and its phase structure. It is shown that the low-level multiplicative noise has a stronger effect on the accuracy of measurement of the arrival time than on the accuracy of measurement of the frequency of the useful signal. The influence of multiplicative and additive noise on the accuracy of measuring the non-energy parameters of the useful signal is quantified for practically important cases: for small purely phase distortions of the signal, a radio pulse with a bell-shaped envelope and a constant pulse-modulated frequency.