Application of Fractal Theory, Fractional Operators, Textures, Scaling Effects, and Nonlinear Dynamics Methods in the Synthesis of New Information Technologies in Radio Electronics (Specifically, Radiolocation)

Abstract

In this review, we present the main results on the creation of new information technologies based on textures, fractals, fractional operators, scaling effects, and nonlinear dynamics methods that were obtained from 1979 to the present at the Kotelnikov Institute of Radioengineering and Electronics, Russian Academy of Sciences (IRE, RAS). It is shown that new dimensional and topological (not energy!) signs or invariants that are combined under the generalized concept of “sampling topology” ~ “fractal signature” were proposed for the first time and then applied. Texture and fractal-scaling (topological) methods for detecting super-weak signals and fields in intense noise and interferences are proposed. A new type and a new method of modern radiolocation, namely, fractal-scaling or scale-invariant radiolocation was proposed, discovered, and developed. This entails fundamental changes in the structure of theoretical radiolocation, as well as in its mathematical apparatus.