Methods of searching for systems of complex nonlinear discrete signals optimal by the minimax criterion

Abstract

Among the main directions of improving information security indicators, noise immunity and secrecy of information and communication systems (ICS), we can single out areas related to the use of channels with high frequency redundancy, significant spatial, structural, energy and temporal secrecy. To ensure frequency redundancy at the physical level, discrete signals are widely used, in which the manipulated parameters (amplitude, phase, frequency) change at strictly fixed time intervals. The law of variation of these parameters is set by discrete sequences that completely determine the properties of discrete signals and are often identified with them. In the synthesis of signal systems (for use in protected ICS), they strive to provide certain properties of signals, first of all: a given structural secrecy in determining the laws of signal formation; improved ensemble properties (existence for almost any period value, a significant amount of the signal system); necessary (to ensure the desired value of the noise immunity of the reception) correlation properties. Based on the criteria of maximum likelihood, minimax criterion, the fundamental boundary of the Cramer-Rao assessment, the requirements to the choice of signal systems for a wide range of multi-user ICS applications are formulated. In particular, large ensembles of nonlinear complex signals are proposed as signals — physical data carriers in ICS. It is shown that such signals have improved (in comparison with the widely used classes of linear signals) ensemble, correlation, structural and other properties. The aforementioned allows to improve such performance indicators of the ICS as noise immunity, electromagnetic compatibility, secrecy and information security, which is very important for some general and critical ICS applications. The possibility of using the proposed signal systems in solving classical problems of optimal reception is shown: detection and discrimination of signals, estimation of signal parameters. In this case (due to the good correlation properties of the proposed signal systems), the necessary (for the corresponding tasks) indicators of noise immunity of signal reception and the accuracy of the estimation of signal parameters are provided.