Fractals in radar and radio physics: 40 years of research experience

A review of the main scientific results on creation of new information technologies on the basis of textures, fractals, fractional operators and non-linear dynamic methods which were obtained by the author has been presented in this work. The researchers are conducted in the framework of scientific direction «Fractal radio physics and fractal radio electronics: designing of fractal radio systems» which is being developed by the author starting from 1979 and up to the present. 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 superweak 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. The fractal radiolocation postulates were developed: (1) intelligent signal/image processing based on the theory of fractional measures and scaling effects for calculating the field of fractal dimensions D, (2) the sample of the received signal in noise belongs to the class of stable non-Gaussian probability distributions of the D signal, and (3) the topology maximum with the minimal energy of the input random signal (i.e., the maximal «escape» from the energy of the received signal). These postulates open new possibilities for ensuring stable operation at a small signal/(noise + interference) ratio or an increase in the radar range. These studies are priorities in the world and serve as a basis for the further development and substantiation of the practical application of fractal-scaling and texture methods in modern radiophysics, radio-electronic systems, and nanotechnology, as well as in the creation of fundamentally new and more accurate fractal-texture (topological) methods for detecting and measuring the parameters of radio signals in the space–time radar channel for electromagnetic wave propagation with scattering.