The Object of the research is the processes of formation and processing of signals in channels with fading. The subject of the research is a method for increasing the efficiency of signal-code constructions with internal signals of the CPFM and external convolutional codes in the conditions of phase shifts. Research methods. The theoretical and methodological foundations of the work are mathematical methods of signal theory, applied coding theory, methods of probability theory, algebraic group theory, finite difference theory, mathematical statistics, simulation modeling. Using the mathematical apparatus of the algebraic theory of groups and the theory of finite differences, a differential algorithm for modulating/demodulating signals of the CPFM is synthesized; Using methods of simulation modeling and mathematical statistics, a reduction in the search time of convolutional codes was achieved. Theoretical and practical results: the model for transmitting information over radio channels with phase shifts was further developed - the use of mathematical methods for calculating finite differences for the synthesis of differential modulation algorithms for modulating / demodulating CPFM signals was proposed, which makes it possible to increase the energy efficiency of the SCC by searching for optimal error-resistant codes; For the first time, a new method was developed for optimal noncoherent demodulation of differential CPFM signals, and a structure of a demodulator suitable for use in quasistationary channels was developed on this basis. Unlike existing circuits, the developed demodulator is insensitive to constant phase shifts of signals in the channel, which results in an increase in noise immunity of the information transmission system. A patent for a utility model was obtained for the method; the method of search for convolutional codes has been improved, in which, unlike existing methods, on the basis of the well-known property of the mathematical expectation of random variables, it is proposed to use mathematical expectation as the upper limit of the required free distance, which results in a reduction in search time; an improved method for search of non-binary convolutional codes for channels with a CPFM using the criterion of maximum free distance was implemented. The developed programs allow one to search for the generating polynomials of optimal non-binary codes with distances close to the upper boundary by given parameters (the number of signal levels M, encoder parameters); an algorithm for extracting signals of clock synchronization of the CPFM signal is implemented, which is based on the use of incoherent signal processing procedures, do not require the use of preliminary information about the frequency and phase of the signal, which allows us to recommend the developed method as part of the algorithms of incoherent demodulation of CPFM signals; A new alternative method for increasing the specific speed using composite Walsh-Barker sequences was implemented, the orthogonality of which allows the simultaneous transmission of several composite signals modulated by information symbols on the same carrier, followed by their separation by appropriate matched filters.
