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Ternopil’ State Technical University named after Ivan Pul’ui PowerPoint PPT Presentation

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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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Ternopil’ State Technical University named after Ivan Pul’ui

International Conference onInductive Modelling 2008, Kyiv

National University “Lvivs’ka Politechnica”

Reconstruction of Algorithms for Spread Spectrum Signals Detection into a Frame of Inductive Modeling Methods

Bohdan Yavorskyy, Yaroslav Dragan, Lubomyr Sicora

[email protected]

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

Spread Spectrum Signal after wide-band ADC

Signal to Noise Ratio (SNR)

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]

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]






Signal Representation in [J.Fourier-Н.А. Колмогоров-N.Wiener-Karhunen-Loév-E.Parzen]





SHIFT operator


The Narrow Band SignalRepresentation (1.5)



The Signal with Known Spectrum Spreads, Representation (1.5)

Schema of detection

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

Representation (1.5) of the Signalwith Unknown Spread Spectrum

a wide-band ADC of SSS

Characteristics (1.4) of Detection of the Spread Spectrum Signal

(a wide-band ADC of SSS)

SHIFT operator





The Function Representation in the HSoHS

— stochastic measure

— spectral measure

— probability measure









Rigged Hilbert Space with Reproduced Correlation Kernel

Ordering of representations: S >O – [S.Vatanabe],S >C – [Ya.Dragan]

Conditions of Existence






The Likelihood Ratio and Detection Test Statistic


— RHS with RKHS as an one of rigging spaces is over Hilbert space

K-frequencies components


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

Methods & Equations


- an optimal estimation of spectra , ;

by method with parameter


Generationof the Indexes


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)

Computation of The Expectation

(а) — component’s (b) — process

Algorithm of Befitting Detection

Results of Befitting Computation

of spectral components

Caracteristics (1.4) of Befitting Detection



of s(t) in

ADC of x(t)

Eigen function of operator

for spectra Spreading


of x(t)



Eigen function

of common

Shift operator


of existence






Thank You

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