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Analyzing Chaos Systems and Fine Spectrum Sensing Using Detrended Fluctuation Analysis Algorithm

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  • Javier S. González-Salas
  • Modar S. Shbat
  • Francisco C. Ordaz-Salazar
  • Jorge Simón

Abstract

A numerical study that uses detrended fluctuation analysis (DFA) algorithm of time series obtained from linear and nonlinear dynamical systems is presented. The DFA algorithm behavior toward periodic and chaotic signals is investigated and the effect of the time scale under analysis is discussed. The displayed results prove that the DFA algorithm response is invariant (stable performance) to initial condition and chaotic system parameters. An initial idea of DFA algorithm implementation for fine spectrum sensing (SS) is proposed under two-stage spectrum sensor approach with test statistics based on the scaling exponent value. The outcomes demonstrate a promising new SS technique that can alleviate several imperfections such as noise power uncertainty and spatial correlation between the adjacent antenna array elements.

Suggested Citation

  • Javier S. González-Salas & Modar S. Shbat & Francisco C. Ordaz-Salazar & Jorge Simón, 2016. "Analyzing Chaos Systems and Fine Spectrum Sensing Using Detrended Fluctuation Analysis Algorithm," Mathematical Problems in Engineering, Hindawi, vol. 2016, pages 1-18, May.
    • Handle: RePEc:hin:jnlmpe:2865195
    DOI: 10.1155/2016/2865195
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