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## Statistical demodulators for frequency shift keying with fast frequency hopping

This work is devoted to the problems of information transmission with frequency shift keying and fast frequency hopping in special channels where the signal/noise ratio is low, and a high energy interfering signal is present. We propose a demodulation algorithm that is significantly more stable to the influence of a powerful interfering signal as compared to other known algorithms. Under these conditions, we show a statistical criterion that lets one significantly reduce error probability on the demodulator’s output. For the chosen criterion we prove several lemmas that let us speed up the demodulation algorithm. Computer modeling results show that the proposed demodulation algorithm has better correcting ability under a powerful interfering signal than previously known ones.

We consider the transformation of the weighted statistics using its components. These statistics allow you to change in the test the sensivity of amplitudes and frequences of derivations from the hypothetical distributions. The collection of Karhunen-Loeve expansions is considered.We discuss also the statistics based on the components. Two new forms of the statistics are considered.

For more than 60 years, the Anderson–Darling test is most frequently used among all Cramér–von Mises (omega-square) tests. This statistic modifies a classical empirical process defined within the [0, 1] interval by multiplying it by weighting function ψ(*t*) = (*t*(1–*t*))–1/2. The weighting function redistributes the test sensitivity to deviations of the distribution function of the observed stochastic quantity from a hypothetical distribution function in different its segments. However, the tests with other weighting functions may also be of interest in practice. New formulas for the eigenvalues of the Anderson–Darling statistic are proposed. The statistic “inverse” to the Anderson–Darling statistic with weighting function ψ(*t*) = (*t*(1–*t*))1/2 is considered. Tests with other weighting functions may also be of interest when weighted Cramér–von Mises statistics are used. The table of quantiles of statistics with weighting functions ψ(*t*) = *t*α(1–*t*)β, α >–1, β >–1 is presented. The quantiles are given for 36 different combinations of parameters α >–1 and β >–1. The table was calculated using accurate numerical methods and without application of modeling techniques.

We construct and study new goodness-of-fit tests for the power distribution based on the Puri-Rubin characterization and using U-empirical distribution functions. We describe their limiting distributions and large deviations. Next we find their local Bahadur efficiency for common alternatives and study the conditions of local optimality.

The collection represents proceedings of the XVIII international conference “Problems of Theoretical Cybernetics” (Penza, 19–23 June, 2017), that is sponsored by Russian Foundation for Basic Research (project N 17-01-20217-г). The conference subject area includes: control systems synthesis, complexity, reliability, and diagnostics; automata; computer languages and programming; graph theory; combinatorics; coding theory; theory of pattern recognition; mathematical programming and operations research, mathematical theory of intelligence systems; applied mathematical logic; functional systems theory; optimal control theory; applications of cybernetics in natural science and technology.

In the previous works we have considered decoding coded FSK modulation (similar to Kautz-Singleton codes) transmitted in a channel with strong interference by using a two-sample goodness-of-fit statistics. In this work we consider the applicability of different one-sample goodness-of-fit statistics for the decoding. Using a computer simulation we show that using these statistics may yield lower error rates relative to the known decoders. The most notable of them are Anderson Darling statistic that has the lowest error rates for narrow-band interference and Pearson's x2 and Kuiper statistics that are more resilient to wide-band interference. We can conclude that one-sample goodness-of-fit statistics can be used for Kautz-Singleton codes decoding with relatively low error rates in case of strong interference in the channel.

Consideration was given to the omega square Cramer–von Mises tests intended to verify the goodness hypothesis about the distribution of the observed multivariable random vector with the distribution in the unit cube. The limit distribution of the statistics of these tests was defined by the distribution of an infinite quadratic form in the normal random variables. For convenience of computing its distribution, the residue of the quadratic form was approximated by a finite linear combination of the χ2-distributed random variables. Formulas for determination of the residue parameters were established.

The collection represents proceedings of the nineth international conference "Discrete Models in Control Systems Theory" that is held by Lomonosov Moscow State Uneversity and is dedicated in 90th anniversary of Sergey Vsevolodovich Yablonsky's birth. The conference subject are includes: discrete functional systems; discrete functions properties; control systems synthesis, complexity, reliability, and diagnostics; automata; graph theory; combinatorics; coding theory; mathematical methods of information security; theory of pattern recognition; mathematical theory of intellegence systems; applied mathematical logic. The conference is sponsored by Russian Foundation for Basic Research (project N 15-01-20193-г).

Generalized error-locating codes are discussed. An algorithm for calculation of the upper bound of the probability of erroneous decoding for known code parameters and the input error probability is given. Based on this algorithm, an algorithm for selection of the code parameters for a specified design and input and output error probabilities is constructed. The lower bound of the probability of erroneous decoding is given. Examples of the dependence of the probability of erroneous decoding on the input error probability are given and the behavior of the obtained curves is explained.

The dynamics of a two-component Davydov-Scott (DS) soliton with a small mismatch of the initial location or velocity of the high-frequency (HF) component was investigated within the framework of the Zakharov-type system of two coupled equations for the HF and low-frequency (LF) fields. In this system, the HF field is described by the linear Schrödinger equation with the potential generated by the LF component varying in time and space. The LF component in this system is described by the Korteweg-de Vries equation with a term of quadratic influence of the HF field on the LF field. The frequency of the DS soliton`s component oscillation was found analytically using the balance equation. The perturbed DS soliton was shown to be stable. The analytical results were confirmed by numerical simulations.

Radiation conditions are described for various space regions, radiation-induced effects in spacecraft materials and equipment components are considered and information on theoretical, computational, and experimental methods for studying radiation effects are presented. The peculiarities of radiation effects on nanostructures and some problems related to modeling and radiation testing of such structures are considered.