Methodical Approach to Determining the Statistical Characteristics of Code Phase Manipulated Signal in Information Systems

Abstract

A methodological approach to determining the statistical characteristics of the phase-shifted signal observed against a white noise background is considered. Parametric and non-parametric consistency criteria have been widely used to test the hypothesis of the form of the law of probability distribution of random variables. The parametric criteria include Pearson's c2 and its modification of Nikulin's c2. Nonparametric criteria – Kolmogorov – Smirnov, w2 Mises, Anderson – Darling, Rainy and others. In the foreign scientific literature, the term W2 Mises is used for the Anderson – Darling criterion. When testing simple hypotheses, the following order of criteria (by their power) is given preference: c2 Pearson; Anderson – Darling; Kolmogorov – Smirnov; w2 Mises. When testing complex hypotheses, the order changes: w2 Mises; Kolmogorov – Smirnov; Anderson – Darling; c2 Nikulin; c2 Pearson. With the known sample volume, according to the selected rule, the number of intervals of the histogram is calculated and it is constructed according to the set of realizations of the received signal. After that, a comparison is made with the reference law of distribution. The steps of comparison are well known and do not need a separate explanation. Mathematical modeling and processing of its results with the help of Mathcad software package 14 is carried out. We will test the hypothesis about the normal law of distribution of the input mixture of signal and noise by the criterion c2 Pearson. The results of simulation modeling and computational experiment with the above approach show that the statistical characteristics of the additive mixture of phase-manipulated signal and white noise in the energy-hidden mode of operation of electronic means are subject to laws that are qualitatively close and generally approximated by normal laws.