Method of synthesis of signal-code constructions for secretive noise-proof data transmission radio systems

摘要

The paper presents the results of the development of a method and an algorithm for the synthesis of optimal basic signalcode structures in the form of code binary sequences, with a minimum criterion for the side lobes of the periodic autocorrelation function of the indicated sequences. To develop this method, approaches based on set theory and number theory were used. The method is based on a discrete representation of the periodic autocorrelation function of sequences in the form of a system of equations defined on a set of integers, set-theoretic interpretation of the constituent parts of sequences, their integer transformations, mutual properties and relations. A number of transformations of the constituent parts of the sequences are developed, analytical expressions for the dependence of the sum modulus of the sequence elements on the sum of the side lobe levels of their periodic autocorrelation function are derived, and the necessary conditions for the existence of sequences are defined and formulated. The relationship between the parameters of the code binary sequence and the canonical representation of the Euler function on the dimension of the sequence is determined. Analytical relationships between the levels of the side lobes of the periodic autocorrelation function and the parameters of the transformed sequence structures are obtained. The criterion of the effectiveness of the developed method and the corresponding algorithm is the ratio of the number of all possible variants of code binary sequences of a given dimension to a quantity that is determined by the developed algorithm; an expression was obtained to estimate the indicated amount. This efficiency is confirmed by the results of simulation and experimental research. The developed method can be used for the creation of secretive noise-proof data transmission radio systems, remote control systems, radar, and communications.