Search for complex m-sequences for phase modulation of signal-code structures in on-board control systems

Currently, M-sequence phase-modulated signals are widely used in radar, radio navigation and data exchange systems due to their unique correlation properties. However, despite their advantages, high levels of side lobes of the autocorrelation function (ACF) can significantly reduce the reliability of the corresponding detection systems. The search for new complex M-sequences with lower levels of side lobes of the normalized ACF is an urgent and important task for increasing noise immunity and reliability in modern detection systems. Objective. The purpose of the study is to develop and justify a method for reducing the level of side lobes (SL) of the ACF by searching for new complex values of M-sequences. This is achieved by replacing the traditional alphabet [1; −1] with an asymmetric [1; −exp(φi)], after which the expressions describing the SL of the normalized autocorrelation function (NACF) are calculated, according to which such values of φ are determined at which the SL have the lowest level. Methods. The paper uses analytical methods for deriving expressions describing the levels of the ACF sidelobes, algorithms for numerical search for complex values of M-sequences, as well as methods of computer modeling and experiments to estimate the levels of the ACF sidelobes based on the expressions found. Results. In this paper, a search for new complex values of M-sequences was carried out and a study of the characteristics of their ACF was conducted. The obtained results include graphs and dependencies showing a decrease in the levels of the ACF sidelobes due to the found new complex values of M-sequences in order to form a phase-modulated signal-code structure. Practical significance. The practical application of code structures, which are new complex M-sequences, demonstrated and thereby confirmed the improvement of their correlation characteristics. This approach can be used to improve the efficiency of onboard small-sized radar systems for monitoring the earth's surface, including multi-position ones, as well as in digital communication and radio navigation devices that require high reliability and noise immunity.