Feodor Vybornov, Alexander Pershin, Alexander Rakhlin, Olga Sheiner Features of modern diagnostic methods of ionospheric turbulence Radiophysical Research Institute 25/12a, Bolshaya Pecherskaya str., Nizhny Novgorod, , Russia ABSTRACT: In the present paper we considered the question about practical application of various research methods self-similar structure of the ionospheric turbulence: the spectral correlation method, the multidimensional structure functions method, the wavelet transform method (WT), the method of multifractal-detrended fluctuation analysis (MF-DFA). Also we study the applicability of the method of maxima of wavelet transform modulus (WTMM) for remote sensing of small-scale ionospheric turbulence. The first time presented the results of processing of transionospheric signals at a frequency 150 MHz obtained by the method of analysis the non- stationary signals - MF-DFA. The values of scaling exponent obtained by this method were close to the values obtained by the structural functions (SF) method. Also shows the results of processing of the transionospheric signals using different wavelets. Here is presented a comparative analysis of the complex continious wavelet transform (CCWT) methods and WTMM for diagnostic of ionospheric turbulence.

Task of the study: research of multifractal properties of the ionospheric turbulence based on: a)the study of the scaling properties of the signal parameters; b)construction of the multifractal spectrum (spectrum of singularities). The applied methods of treatment: SF, MF-DFA, WTMM and CCWT methods. Features techniques multifractal analysis of the received signal: currently, the most known methods of multifractal analysis are: the method of multidimensional structure functions (SF), a multifractal-detrended fluctuation analysis method (MF-DFA), methods based on wavelet transform (CCWT and WTMM). The generality of these methods of signal processing with fractal structure consists is that: The scale analysis is based on a calculation of the partial function F of order q. Scaling exponent for a partial function F of order q is computed as a linear interpolation of F in a double logarithmic scale Multifractal analysis uses the Legendre transform.

The result of applying SF and MF-DFA methods to the analyzed signal Scaling properties: scaling curve in logarithmic scale is more linear signal processing by the MF-DFA method, than using the method of SF. Both methods produced similar values of the scaling exponent. Multifractal spectrum: multifractal spectra obtained by both methods has a typical bell shape. Spectrum according to the method of MF-DFA was somewhat more "narrow" than the singularity spectrum according to the SF method. * To demonstrate the methods of data processing with fractal structure was used recording the amplitude of the signal from the satellite system Sail on a frequency of 150 MHz, 29 March 2006.

The result of applying the methods of the WT (CCWT and MMWT) to the analyzed signal Scaling curves obtained by the methods of CCWT (left) and MMWT(rigth)

Conclusion 1.These results suggest that physical studies of the fractal structure of the ionospheric plasma, along with the use of SF should be guided by the modern method of processing non-stationary signals MF-DFA. 2.Application of the currently popular methods of wavelet transform to analyze the ionosphere by radio sounding revealed a number of difficulties: the choice of wavelet significantly affect the linearity of the scaling curve constructed multifractal spectrum according to wavelet processing was not always possible primarily due to a significant error in assessment index scaling. 3.Application of simple complex wavelet transform may have some advantages over the WTMM method becose: characterizes the entire set of data on the analyzed interval; the result of processing is not dependent on any search criteria to extract the skeleton of "effective" coefficients of the wavelet transform; the empirical scaling curve is more "smooth" than the processing method WTMM. It should be noted that the quasi-homogeneous structure of the correlation function of weak amplitude fluctuations of the transionosphere satellite signals reproduces the same structure as the weak phase fluctuations of the signals at the output of the inhomogeneous ionospheric layer. As fast satellite signal phase fluctuations in the ionosphere caused by the small-scale heterogeneous structure of the ionospheric plasma, then exploring multifractal structure of the amplitude fluctuations of signals received on Earth, we can actually get the understanding of the structure of small-scale ionospheric turbulence.