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# Article-1_12-2018

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AN EXAMPLE OF THE SYNTHESIS OF OPTIMAL INVARIANT SIGNAL TRANSMISSION SYSTEM OF THE MESSAGE

Ivan I. Pavlov, the Siberian state University of telecommunications and Informatics, Novosibirsk, Russia, IIPavlov@ngs.ru

Abstract
The word «invariant», «invariant» means «unchanging». These terms were originally used in mathematics, and the invariant is a quantity (or mathematical expression, formula) that characterizes some mathematical or physical object and does not change with certain transformations of it. One of the methods of synthesis of systems with constant parameters invariant to additive noise is the method of finding the optimal signal. The operator of demodulation Fpot N is chosen as the optimal with respect to the noise N, and the relative invariance to the noise X is achieved by choosing the signal S,
minimizing the effect of interference X at the output of the demodulator by a particular criterion. In this article, the problems of optimal signal synthesis are discussed in more detail. Recall that here we consider the system of transmission of discrete information with constant parameters and, therefore, they can be invariant only with respect to quasi-deterministic noise. A mathematical model of a quasi-deterministic noise is a quasi-deterministic random process, the implementation of which is described by functions of a given type containing one or more random parameters. Practical examples of quasi-deterministic noise can be narrow-band (spectrum-focused) noise, which can be represented as a harmonic oscillation with random amplitude, frequency and phase, pulse noise, etc. Quasideterminant disturbance can be written as deterministic functions of time with random parameters
a, b, g, etc. In the simplest case, which we will consider random parameter one. According to the relative invariance condition, to find the optimal signal, it is necessary to minimize the value of Fopt N(S, x). Consider the standard optimization criterion and optimization on the basis of uniform criteria.

Keywords: noise, signal, synthesis, function, additive noise, invariance, optimization.

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