Detection of a correlation signal against the background of noise (occurence) is an important task of primary information processing in modern radio engineering systems of information transmission, control, navigation, radio monitoring and radiolocation. The reception of radio signals is accompanied by many accidental factors, which lead to the fact that the additive mixture very often has a non-causal distribution. For this reason, the methods of the theory of probability and mathematical statistics are used for the acceptance and processing of the accepted signal, and the acceptance and detection is regarded as a mathematical problem. Receiving capabilities of radio engineering systems are largely determined by the detection characteristics, which, in turn, depend on the tightness with the received signal. In order to ensure the compliance, it is necessary to know the law of distribution of the intensity and probability of the output effect of the receiver. The knowledge of the distribution of the probability of frequency determines the characteristics of the detection of the receiver of radio engineering systems and provides a wide range of functional possibilities in the execution of statistical tasks in the primary processing of information. Analytical expressions that determine the probability of correct detection through the probability of the hibnothreshold signal/noise ratio at the receiver output for coherent signals with a uniform initial phase and a nakagami-like amplitude are presented. On the basis of the obtained analytical expressions a family of curves was created for signal models, where fluctuations are very small or absent in general and which are adequately described by Nakagami’s law of dispersion.

No abstract

No abstract

The article considers the possibility of increasing the capability of detecting a useful radio signal against the background of noise and simultaneously reducing the possibility of mistaking noise fluctuations for a signal. Moreover, if it is absent then the Neumann-Pearson statistical test should be used. This criterion is a partial case from the class of criteria consisting in the calculation of the likelihood ratio and does not require knowledge of a priori probabilities of the presence or absence a useful signal while constructing an optimal receiver and Bayesian methods are used. The effectiveness of the detection procedure according to the Neumann-Pearson test is characterized by the probability of correct detection at a fixed false alarm probability. These probabilities depend on the signal-to-noise ratio at the output of the detection device. So, an important preparatory stage of the reception immunity analysis is the study of this parameter which is very important in the section of statistical radio engineering. It is known that the optimal detection of a signal against a background of white noise is reduced to the correlation integral calculation. This calculation can be done directly by using a multiplier and integrator (correlation method), by using a filter that is optimal for this signal (filter method) or by using a correlation-filter method. The presence of a priori uncertainty during signal reception makes it impossible to create an optimal (consistent) receiving path and therefore makes it impossible to obtain the required value of the signal-to-noise ratio at the output of the detection device. In this case, an autocorrelation algorithm is used which is resistant to a priori uncertainty of signal parameters and is “optimal” while detecting signals of unknown shape. The most general character for determining the signal/noise ratio has an expression for the case of an incoherent single-channel autocorrelation algorithm for detecting a noisy signal against a background of stationary white noise (interference). For example, quite a large number of scientific works are devoted to the interference immunity issue of the correlation reception method. They mainly consider the interference immunity of correlation receivers when a mixture of harmonic signal and noise passes through them. The circuits with the same average frequencies of multiplying processes and etc. are analyzed. There are also known works in which formulas relating the value of the signal-to-noise ratio at the output of the receiving path for a complex signal to the input signal-to-noise ratio are given. In the above works, idealized cases are considered, namely, when the observation is conducted on a fairly long observation interval but the real observation interval is quite limited. In this case, the averaging is carried out over a limited time interval and it is necessary to take into account the intercorrelation relations between the signal and noise, therefore, along with the signal-signal, noise-noise, signal-noise and noise-signal components, we will have the following mutual correlation moments between the combinations of signal and noise component. The issue of an autocorrelation receiver when passing an additive mixture of signal and white noise at a limited observation interval is investigated in which the immunity index is considered and a general solution of the signal/noise ratio based on the deviation criterion is obtained. Therefore, obtaining an analytical expression that establishes the relationship between the signal-to-noise ratio at the input and output of the receiver is very important and relevant. The purpose of the article is to obtain an analytical expression of the signal-to-noise ratio value at the threshold device input of an incoherent autocorrelation receiver at a limited observation interval.

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.