A.A. Potapov - Dr. Sc. (Phys.-Math.), Professor, Member of Russian A.M. Prokhorov Academy of Engineering Sciences and Russian Academy of Natural Sciences; President of cooperative Chinese-Russian laboratory of informa-tional technologies and signals fractal processing (China, Guanzhou); Main Research Scientist, Kotel\'nikov IRE of RAS (Moscow). E-mail: potapov@cplire.ru

Currently the inadequacy of conventional physical models is clearly felt. Effectiveness of radio physical researches can be significantly enhanced by taking into account fractality of wave phenomena which develop at every stage of radiation, scattering and propagation of waves in different media. Revolutionary steps which consist in transfer of integer measure signals obtained by a system to the fractional measure space and following calling of scaling ratios allow to bring absolutely new ideas and methods into conventional areas of classical radio physics and radio electronics and to get results rather unexpected for practice which are however physically valid. The main purpose of this work is to interpret the main directions of radio physics, radio engineering and radio location in «fractal» language that makes new ways and generalizations on future promising radio systems. The new kind and approach of up-to-date radiolocation: fractal-scaling or scale-invariant radiolocation has been proposed. It leads to basic changes in the theoretical radiolocation structure itself and also in its mathematical apparatus. The fractal radio systems conception, sampling topology, global fractal-scaling approach and the fractal paradigm underlies the scientific direction established by the author in Russia and over the world for the first time. The author has been investigating these issues for exactly 35 years. The results of big practical and scientific importance obtained by the author were published in four summary reports of the Presidium of Russian academy of science (2008, 2010, 2012, 2013) and in the report for the Government of Russian Federation (2012). In the author\'s works the determinant conception of processing of low-contrast images was from the beginning involved unlike foreign works. The model of the images which are being analyzed has been developed with taking into account additive and multiplicative background interferences during the processing of complex (objects and targets are presented) two-dimensional textural scenes. For the first time in the world a calculation of the complete ensemble of 28 textural signs and its synchronous analysis for real (optical and radar in the millimeter range (MMW) at wavelength 8,6 mm) and also synthesized textures on the basis of autoregressive models was performed by the author in IREE RAS as long ago as early eighties of XX century. Application of fractional processing usually requires a large number of area images in different scales. We proposed algorithms which use convolution operations and allow to do with only single images. It is proven that the fractal processing of optical and radar (in the millimeter radio waves range) images leads to practically same results. Thus for now we have sufficiently harmonious conceptions which explain a phenomenon of stable detection of super weak signals in intensive interferences on the basis of fractal-scaling methods and even can control these phenomena. The basis of the fractal detecting theory is results of fractal researches of essentiality of processes occurring during using the fractional measure theory and physical scaling theory in the radiolocation. In our opinion the obtained researches of the new experimental data in aggregate with the previous data give us enough information for proving of the fundamentals of theory and methods which were put forward by the author as long ago as the end of XX century. Application of fractals, scaling effects and fractional operators may mean the future of radio electronics because all the previous and current radio electronics is based solely (and only!) on the theory of integer-valued functions and does not take into account the frac-tional measure in information theory. Introduction of the fractal conception into radio physics, radio location, radio engineering and functional radio electronics is not only proved but is required.

 

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4. Potapov A.A. Fraktaly v radiofizike i radiolokacii: Topologija vyborki. M.: Universitetskaja kniga. 2005. 848 s.
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16. Potapov A.A., Galkina T.V., Orlova T.I., KHljavich JA.L. Metod vydelenija konturov protjazhennykh determinirovannykh obektov v stokhasticheskikh poljakh // Radiotekhnika i ehlektronika. 1991. T. 36. № 11. S. 2240−2242.
17. Potapov A.A. Fraktaly i khaos kak osnova novykh proryvnykh tekhnologijj v sovremennykh radiosistemakh / Dopolnenie k kn.: Kronover R. Fraktaly i khaos v dinamicheskikh sistemakh / Per. s angl. pod red. T.EH. Krenkelja. M.: Tekhnosfera. 2006. S. 374−479.
18. Potapov A.A. Radiofizicheskie ehffekty pri vzaimodejjstvii ehlektromagnitnogo izluchenija millimetrovogo diapazona voln s okruzhajushhejj sredojj // Zarubezhnaja radioehlektronika. 1992. № 8. S. 36−76; № 9. S. 4−28; № 11. S. 23−48; 1993. № 3. S. 36−48; № 7−9. S. 32−49; 1994. № 7/8. S. 11−30; 1995. № 1. S. 27−36 (zhurnalnyjj variant monografii).
19. Potapov A.A. Issledovanie vlijanija rastitelnogo pokrova na obratno rassejannoe pole millimetrovykh voln // Radiotekhnika i ehlektronika. 1991. T. 36. № 2. S. 239−246.
20. Pavelev V.A., Potapov A.A. Vlijanie zemnojj poverkhnosti na strukturu impulsnogo signala v diapazone millimetrovykh voln // Radiotekhnika i ehlektronika. 1994. T. 39. № 4. S. 573−582.
21. Potapov A.A. K teorii funkcionalov stokhasticheskikh polejj obratnogo rassejanija // Radiotekhnika i ehlektronika. 2007. T. 52. № 3. S. 261−310.
22. Potapov A.A., German V.A. Detection of Artificial Objects with Fractal Signatures // Pattern Recognition and Image Analysis. 1998. V. 8. № 2. P. 226−229.
23. Potapov A.A., German V.A. Primenenie fraktalnykh metodov dlja obrabotki opticheskikh i radiolokacionnykh izobrazhenijj zemnojj poverkhnosti // Radiotekhnika i ehlektronika. 2000. T. 45. № 8. S. 946−953.
24. Potapov A.A. Fraktaly v distancionnom zondirovanii // Zarubezhnaja radioehlektronika. Uspekhi sovremennojj radioehlektroniki. 2000. № 6. S. 3−65.
25. Potapov A.A. Fraktaly v radiofizike i radiolokacii. EHlementy teorii fraktalov // Radiotekhnika i ehlektronika. 2000. T. 45. № 11. S. 1285−1292.
26. Potapov A.A. Fraktaly v radiofizike i radiolokacii. Fraktalnyjj analiz signalov // Radiotekhnika i ehlektronika. 2001. T. 46. № 3. S. 261−270.
27. Potapov A.A. Fraktaly v radiofizike i radiolokacii. Osnovy teorii rassejanija voln fraktalnojj poverkhnostju // Radiotekhnika i ehlektronika. 2002. T. 47. № 5. S. 517−544.
28. Potapov A.A. Fraktalnyjj analiz v sovremennykh zadachakh radiolokacii i radiofiziki // Radiotekhnika. 2003. № 8. S. 55−66.
29. Potapov A.A., German V.A. O metodakh izmerenija fraktalnojj razmernosti i fraktalnykh signatur mnogomernykh stokhasticheskikh signalov // Radiotekhnika i ehlektronika. 2004. T. 49. № 12. S. 1468−1491.
30. Guljaev JU.V., Nikitov S.A., Potapov A.A., German V.A. Idei skejjlinga i drobnojj razmernosti v skheme fraktalnogo obnaruzhitelja radiosignalov // Radiotekhnika i ehlektronika. 2006. T. 51. № 8. S. 968−975.
31. Potapov A.A., German V.A. Metody fraktalnojj obrabotki slabykh signalov i malokontrastnykh izobrazhenijj // Avtometrija. 2006. T. 42. № 5. S. 3−25.
32. Potapov A.A., Guljaev JU.V., Nikitov S.A., Pakhomov A.A., German V.A. Novejjshie metody obrabotki izobrazhenijj / Pod red. A.A. Potapova. M.: FIZMATLIT. 2008. 496 s. (monografija - po grantu RFFI № 07-07-07005).
33. Potapov A.A. Fraktalnyjj metod i fraktalnaja paradigma v sovremennom estestvoznanii. Voronezh: IPC «Nauchnaja kniga». 2012. 108 s.
34. Leonov K.N., Potapov A.A., Ushakov P.A. Ispolzovanie invariantnykh svojjstv khaoticheskikh signalov v sinteze novykh pomekhoustojjchivykh shirokopolosnykh sistem peredachi informacii // Radiotekhnika i ehlektronika. 2014. T. 59. № 12. S. 1209−1229.
35. Potapov A.A., Laktjunkin A.V. CHastotnaja funkcija kogerentnosti prostranstvenno-vremennogo radiolokacionnogo kanala formirovanija izobrazhenijj anizotropnojj fraktalnojj poverkhnosti i fraktalnykh obektov // Radiotekhnika i ehlektronika. 2015. T. 60. № 9.
36. Potapov A.A.Fractals and Scaling in the Radar: A Look from 2015 // Book of Abstracts 8th Int. Conf. (CHAOS - 2015) onChaoticModeling, SimulationandApplications (26−29 May 2015. Paris. France. Greece). Paris: HenriPoincareInstitute. 2015.
37. Potapov A.A.New Conception of Fractal Radio Device with Fractal Antennas and Fractal Detectors in the MIMO - Systems // Book of Abstracts 3rd Int. ScientificSymp. «The Modeling of Nonlinear Processes and Systems (MNPS-2015)» (22−26 June, 2015. Russia. Moscow). M.: JAnus-K. 2015.
38. Foukzon J., Men-kova E., Potapov A.A. The Solution Classical Feedback Optimal Control Problem for m-Persons Differential Game with Imperfect Information // Open Journal of Optimization. 2013. V. 2. № 1. P. 16−25 (http://www.scirp.org/journal/ojop).
39. Podosenov S.A., Potapov A.A., Foukzon Dzh., Menkova E.R. Negolonomnye, fraktalnye i svjazannye struktury v reljativistskikh sploshnykh sredakh, ehlektrodinamike, kvantovojj mekhanike i kosmologii: V 3-kh t. / Pod red. A.A. Potapova. M.: LENAND. 2015. 1200 s.