Property of Self-Similarity Between Baseband and Modulated Signals

  • Shuai Liu
  • Weiling Bai
  • Gautam Srivastava
  • J. A. Tenreiro MachadoEmail author


The increment of communication technologies and the development of signal processing require efficient identification techniques for communication radiation. However, the complex characteristics of electromagnetic environment are not adequately handled by linear methods. Since the fractal theory is well suited for nonlinear problems, the relation of self-similarity (SS) between baseband and modulated signals is studied in this paper. Indeed, the existence of SS’s relation between the baseband and modulated signals is proved and verified under certain conditions. Finally, the analysis and extraction of individual signal fingerprint features in communication radiation source is constructed. Experimental results show that the proposed property SS is effective in the identification and classification of communication radiation sources.


Modulated signal Signal classification Self-similarity Fractal Hurst index 



The research is supported by the Open Project Program of the State Key Laboratory of Complex Electromagnetic Environment Effects on Electronics and Information System under Grant 2019K0104B.


  1. 1.
    Antoniou A (2016) Digital signal processing. McGraw-Hill, New YorkGoogle Scholar
  2. 2.
    Ishimaru A (2017) Electromagnetic wave propagation, radiation, and scattering: from fundamentals to applications. John Wiley & Sons, HobokenCrossRefGoogle Scholar
  3. 3.
    Tarasov VE (2015) Electromagnetic waves in non-integer dimensional spaces and fractals. Chaos, Solitons Fractals 81:38–42MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Mandelbrot BB (1982) The fractal geometry of nature. WH freeman, New YorkzbMATHGoogle Scholar
  5. 5.
    Higuchi T (1988) Approach to an irregular time series on the basis of the fractal theory. Physica D 31(2):277–283MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Zhenling L (2013) Fractal theory and application in city size distribution. Inf Technol J 12(17):4158–4162CrossRefGoogle Scholar
  7. 7.
    Cossio M, Moridis G, Blasingame TA (2013) A semianalytic solution for flow in finite-conductivity vertical fractures by use of fractal theory. SPE J 18(01):83–96CrossRefGoogle Scholar
  8. 8.
    Topper B, Lagadec P (2013) Fractal crises–a new path for crisis theory and management. J Conting Crisis Manag 21(1):4–16CrossRefGoogle Scholar
  9. 9.
    Escultura EE (2013) Chaos, turbulence and fractal: theory and applications. Int J Modern Nonlinear Theor Appl 2(03):176CrossRefGoogle Scholar
  10. 10.
    Juan-ping W, Ying-zheng H, Jin-mei Z, et al (2010) Automatic modulation recognition of digital communication signals//Pervasive Computing Signal Processing and Applications (PCSPA), 2010 First International Conference on. IEEE, p 590–593Google Scholar
  11. 11.
    Yi-bing L, Jing-chao L, Yun L (2011) The identification of communication signals based on fractal box dimension and index entropy. J Converg Inf Technol 6(11):201–208Google Scholar
  12. 12.
    Li Y, Nie W, Ye F, et al (2014) A pulse signal characteristic recognition algorithm based on multifractal dimension. Math Probl Eng 2014Google Scholar
  13. 13.
    Li J, Ying Y (2014) Individual radiation source identification based on fractal box dimension//Systems and Informatics (ICSAI), 2014 2nd International Conference on. IEEE, p 676–681Google Scholar
  14. 14.
    Li B, Chen S, Dong J, et al. (2015) Multi-scale fractal analysis of modulation signals//Sixth International Conference on Electronics and Information Engineering. International Society for Optics and Photonics 9794:979412Google Scholar
  15. 15.
    Tang Z, Li S (2016) Steady signal-based fractal method of specific communications emitter sources identification//Wireless Communications, Networking and Applications. Springer, New Delhi, p 809–819Google Scholar
  16. 16.
    Wu L, Zhao Y, Wang Z, et al. (2017) Specific emitter identification using fractal features based on box-counting dimension and variance dimension//2017 IEEE International Symposium on Signal Processing and Information Technology (ISSPIT). IEEE, p 226–231Google Scholar
  17. 17.
    Guo S, White R E, Low M (2018) A comparison study of radar emitter identification based on signal transients//Radar Conference (RadarConf18), 2018 IEEE. IEEE, p 0286–0291Google Scholar
  18. 18.
    Yu Y, Baoliang L, Jingshan S, et al (2010) The application of vibration signal multi-fractal in fault diagnosis//Future Networks, 2010. ICFN'10. Second International Conference on. IEEE, p 164–167Google Scholar
  19. 19.
    Ziaja A, Barszcz T, Staszewski W (2012) Fractal based signal processing for fault detection in ball-bearings//Condition Monitoring of Machinery in Non-Stationary Operations. Springer, Berlin, Heidelberg, p 385–392Google Scholar
  20. 20.
    Jiao W, Jiang Y, Shi J (2017) Early-stage monitoring on faults of rolling bearings based on fractal feature extraction//Technology, Networking, Electronic and Automation Control Conference (ITNEC), 2017 IEEE 2nd Information. IEEE, p 173–178Google Scholar
  21. 21.
    Eke A, Herman P, Kocsis L et al (2002) Fractal characterization of complexity in temporal physiological signals. Physiol Meas 23(1):R1CrossRefGoogle Scholar
  22. 22.
    Raghavendra BS, Dutt DN (2010) Signal characterization using fractal dimension. Fractals 18(03):287–292MathSciNetCrossRefzbMATHGoogle Scholar
  23. 23.
    Azami H, Bozorgtabar B, Shiroie M (2011) Automatic signal segmentation using the fractal dimension and weighted moving average filter. J Electro Comput Sci 11(6):8–15Google Scholar
  24. 24.
    Rangayyan RM, Oloumi F, Wu Y et al (2013) Fractal analysis of knee-joint vibroarthrographic signals via power spectral analysis. Biomed Signal Proces 8(1):23–29CrossRefGoogle Scholar
  25. 25.
    Paulraj MP, Yaccob SB, Yogesh CK (2014) Fractal feature based detection of muscular and ocular artifacts in EEG signals//Biomedical Engineering and Sciences (IECBES), 2014 IEEE Conference on. IEEE, p 916–921Google Scholar
  26. 26.
    Zlatintsi A, Maragos P (2013) Multiscale fractal analysis of musical instrument signals with application to recognition. IEEE Trans Audio Speech Lang Process 21(4):737–748CrossRefGoogle Scholar
  27. 27.
    Park JS, Kim SH (2014) Emotion recognition from speech signals using fractal features. Int J Softw Eng Appl 8(5):15–22Google Scholar
  28. 28.
    Berizzi F, Dalle-Mese E (1999) Fractal analysis of the signal scattered from the sea surface. IEEE Trans Antennas Propag 47(2):324–338CrossRefzbMATHGoogle Scholar
  29. 29.
    Berizzi F, Dalle-Mese E (2002) Scattering from a 2D sea fractal surface: fractal analysis of the scattered signal. IEEE Trans Antennas Propag 50(7):912–925CrossRefzbMATHGoogle Scholar
  30. 30.
    Wang C, Xu J, Zhao X et al (2012) Fractal characteristics and its application in electromagnetic radiation signals during fracturing of coal or rock. Int J Min Sci Technol 22(2):255–258CrossRefGoogle Scholar
  31. 31.
    Maragos P, Sun FK (1993) Measuring the fractal dimension of signals: morphological covers and iterative optimization. IEEE Trans Signal Process 41(1):108CrossRefzbMATHGoogle Scholar
  32. 32.
    Raghavendra BS, Dutt DN (2010) Computing fractal dimension of signals using multiresolution box-counting method. International Journal of Information and Mathematical Sciences 6(1):50–65Google Scholar
  33. 33.
    Xie Z, Zhai M, Liu X (2017) Research on fractal characteristics of broadband power line communication signal//Wireless Communications, Signal Processing and Networking (WiSPNET), 2017 International Conference on. IEEE, p 373–378Google Scholar
  34. 34.
    Ma YJ, Zhai MY (2018) Fractal and multi-fractal features of the broadband power line communication signals. Comput Electr EngGoogle Scholar
  35. 35.
    Karagiannis T, Faloutsos M (2002) SELFIS: A tool for self-similarity and long-range dependence analysis//1st workshop on Fractals and Self-Similarity in Data Mining: Issues and Approaches (in KDD)Google Scholar
  36. 36.
    Hurst HE (1951) Long-term storage capacity of reservoirs. Trans Am Soc Civ Eng 116:770–799Google Scholar
  37. 37.
    Peters EE, Peters D (1994) Fractal market analysis: applying chaos theory to investment and economics. John Wiley & Sons, HobokenGoogle Scholar

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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.College of Information Science and EngineeringHunan Normal UniversityChangshaChina
  2. 2.College of Computer ScienceInner Mongolia UniversityHohhotChina
  3. 3.Key Laboratory of Symbolic Computation and Knowledge Engineering of Ministry of EducationJilin UniversityChangchunChina
  4. 4.Research Center for Interneural Computing, 40402China Medical UniversityTaichung (Taiwan)China
  5. 5.Department of Mathematics and Computer ScienceBrandon UniversityBrandonCanada
  6. 6.Department of Electrical Engineering, Institute of EngineeringPolytechnic of PortoPortoPortugal

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