Generalized mathematical model of a radio signal in various bases

The purpose of this article is to develop a generalized mathematical model of a radio signal in various bases. The proposed model allows us to generalize the known models of radio signals in basis functions of sine/cosine, basis functions of spline characters, bases of spline-Vilenkin-Chrestenson functions, bases of spline-Pontryagin-Vilenkin-Chrestenson functions, etc., constructed on the basis of spline-algebraic harmonic methods analysis. For the generalized model, special cases are formulated for the considered spaces of basis functions. Block diagrams and timing diagrams are presented that explain the main stages of the formation and processing of radio signals in various bases. Using the simulation method in the Matlab environment, the noise immunity of the proposed radio signals was assessed. Analysis of the obtained results showed that radio signals generated on the basis of a generalized mathematical model in various noise immunity bases under AWGN conditions are comparable (and even have a slight advantage) with similar signals generated in the bases of classical exponential functions. An assessment of structural secrecy is presented. It is shown that the structural secrecy of radio signals generated in various bases is ensured by the formation of signals in a priori unknown bases, the parameters of which: group, ring, spline order and number of the basis function change in accordance with a given code word, also unknown to potential unauthorized processing systems. Structural secrecy manifests itself in the incorrect choice of basis when processing signal data for reception, which entails an expansion of the signal spectrum. As a result, incorrect estimation of signal parameters and incorrect setting of the demodulator occurs.