Statistical properties of derived signal systems

Abstract

The search for effective methods of synthesis of discrete signals (sequences) that correspond to the potentially possible limiting characteristics of correlation functions and possess the necessary correlation, structural, ensemble properties remains an urgent problem. The authors have proposed a method for the synthesis of derivatives of signal systems, for which orthogonal signals are used as the initial ones, and nonlinear discrete complex cryptographic signals (CS) are used as generating signals. The synthesis of the latter ones is based on the use of random (pseudo-random) processes, including algorithms for cryptographic information transformation. Derivative signals synthesized in this way have improved (in comparison with linear signal classes) ensemble and correlation properties, while the statistical properties of such signal systems remain unexplored. The paper presents the results of testing derived signal systems using the tests defined in FIPS PUB 140 and NIST 800-22. Analysis of the results obtained allows us to assert that the statistical properties of this class of derived signals satisfy the requirements for pseudo-random sequences: unpredictability, irreversibility, randomness, independence of symbols, etc. In essence, such signals do not differ from random sequences. The use of the proposed class of derived signals will improve the performance of signal reception noise immunity, information security and secrecy of the ICS functioning.