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.

The law of distribution of the output effect differs from the normal one at the output of the receiving path realized on the basis of autocorrelation algorithm with quadrature processing. When there is no signal at the input of the receiver, the distribution of the output effect corresponds to Rayleigh’s or Rayleigh – Rice’s law in condition of its presence. The probability density distribution at the output of an incoherent auto correlation receiver with quadrature processing is considered in relation to the input level of the energy-concealed phase-manipulated signal. In order to detect a useful signal it is necessary that, at the output of the receiver, the signal / noise ratio exceeds the detection threshold determined by the Neumann – Pearson criterion according to the given probability of false alarm. The level of the signal-to-noise ratio at the output of an incoherent autocorrelation receiver with quadrature processing has been calculated. A characteristic feature of the presented graphs is the linear dependence of the output signal / noise ratio relative to the input signal. This feature is observed in the input signal / noise ratio which is less than one. The curves for the distribution of the probability density of the input signal mix and noise corresponding to the generalized Rayleigh’s law (Rayleigh-Rice) are constructed in the book. There is a shift of curves for the abscissa axis according to the given probabilities of false alarms and accumulation time (observation). It is evident from the given graphs that the offset of the abscissa of the input signal value / noise ratio significantly depends on the accumulation of the input mixture time. The curves for detecting an energy-concealed phase-manipulated signal by a non-coherent autocorrelation receiver with quadrature processing on the basis of the probability density distribution are obtained. The results of the calculations indicate that detection of a phase-manipulated signal on the background of "white" noise is possible in case of an input-to-noise ratio of less than one, that is, up to -32 dB in real time (up to 0.1 s).