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Ternopil’ State Technical University named after Ivan Pul’ui

U K R A I N E. Ternopil’ State Technical University named after Ivan Pul’ui. International Conference on Inductive Modelling 2008, Kyiv. National University “Lvivs’ka Politechnica”. Reconstruction of Algorithms for Spread Spectrum Signals Detection into a Frame of Inductive Modeling Methods.

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Ternopil’ State Technical University named after Ivan Pul’ui

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  1. U K R A I N E Ternopil’ State Technical University named after Ivan Pul’ui International Conference onInductive Modelling 2008, Kyiv National University “Lvivs’ka Politechnica”

  2. Reconstruction of Algorithms for Spread Spectrum Signals Detection into a Frame of Inductive Modeling Methods Bohdan Yavorskyy, Yaroslav Dragan, Lubomyr Sicora Kaf_BT@tu.edu.te.ua

  3. Can we to explainby an Inductive Modeling Methoda succesful detectionof a Spread Spectrum Signalwith unknown spectrum spreads?

  4. Spread Spectrum Signal after wide-band ADC Signal to Noise Ratio (SNR)

  5. Introduction backgrounds • Optimum detectors has been expressed in a coordinate free way in terms of RKHS inner products[Kailath T, Poor H.V. Detection of Stochastic Processes// IEEE, Trans. Information Theory, vol. IT-44, pp. 2230-2299, 1998]. • Orthonormal expansions for second-order stochastic processes, a general expression for the reproducing kernel inner product in terms of the eigenvalues and eigenfunctions of a certain operator has been analyzed in[Parzen E. Extraction and Detection Problems and Reproducing Kernel Hilbert Spaces// J. SIAM Control, vol. 1, pp. 35-62, 1962]. • A some problems in signal detection applications were designed [Oya A., Ruiz-Molina J.C., Navarro-Moreno J. An approach to RKHS inner products evaluations. Application to signal detection problem// ISIT-2002, Lausanne, Switzerland, June 30-July 5, p. 214, 2002] • Detection methods for either stationary Gaussian noise of known autocorrelation or of noise plus a FHS of known hop epoch, unknown phase or energy above a minimum levels are based on [1-3] had been developed[Taboada F., Lima A., Gau J., Jarpa P., Pace P.C. Intercept receiver signal processing techniques to detect low probability of intercept radar signals, ICASSP.-2002] • A factor of fatal increasing of a complexity and decreasing of a quality of detection of completely unknown FHS in the ADC of radioradiation by the RKHS method was declined in RHS in a Hilbert space over Hilbert space (HSoHS) [Yavorskyy B. Vyyavlennya skladnyh syhnaliv z nevidomymy parametramy v radiovyprominyuvannyah// Radioelektronica ta telecomunicatsii.- № 508, 2004.-с. 58-64]

  6. Threshold for detection at a given -fault probability Ф (·) - standard function, , - dispersion and expectation for signal Probabilityof detection Signal Detection  [Котельніков, Cameron, Martin, Middelton, Peterson, Siegert, Jacobs, Wald, Woodward, Wozencraft] , (1) (2) (3) (4)

  7. Signal Representation in [J.Fourier-Н.А. Колмогоров-N.Wiener-Karhunen-Loév-E.Parzen] (5) (6) (7) (8)

  8. SHIFT operator CORRELATION operator

  9. The Narrow Band SignalRepresentation (1.5) s s

  10. The Signal with Known Spectrum Spreads, Representation (1.5) Schema of detection

  11. Characteristics of Detection (1.4 ) of the Known Spread Spectrum Signal

  12. Representation (1.5) of the Signalwith Unknown Spread Spectrum a wide-band ADC of SSS

  13. Characteristics (1.4) of Detection of the Spread Spectrum Signal (a wide-band ADC of SSS)

  14. SHIFT operator ? CORRELATION operator ? ?

  15. The Function Representation in the HSoHS — stochastic measure — spectral measure — probability measure (D-ergodisity) (K-isomorphism) (9) (10) (11) (12) (13) (14)

  16. Rigged Hilbert Space with Reproduced Correlation Kernel Ordering of representations: S >O – [S.Vatanabe],S >C – [Ya.Dragan]

  17. Conditions of Existence [Vitali]: [Розанов]: [Драґан]: , (15)

  18. The Likelihood Ratio and Detection Test Statistic (16) — RHS with RKHS as an one of rigging spaces is over Hilbert space K-frequencies components (17)

  19. - spectral density; , - numberof spectral componentsEnergyis concentrate on ,-spectral band of SSS

  20. Methods & Equations (18) - an optimal estimation of spectra , ; by method with parameter (19)

  21. Generationof the Indexes ADC R — cycle shift register of indexing (m-sequence), М – period of correlation (SSS epoch),N – quantity of correlation components (is determined by relation between periods of spectra harmonics and hops)

  22. Computation of The Expectation (а) — component’s (b) — process

  23. Algorithm of Befitting Detection

  24. Results of Befitting Computation of spectral components

  25. Caracteristics (1.4) of Befitting Detection

  26. Conclusion Detection of s(t) in ADC of x(t) Eigen function of operator for spectra Spreading Spectra of x(t) Bases function Eigen function of common Shift operator Conditions of existence Inner product functional ? ?

  27. Thank You

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