u k r a i n e
Skip this Video
Download Presentation
Ternopil’ State Technical University named after Ivan Pul’ui

Loading in 2 Seconds...

play fullscreen
1 / 27

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

  • Uploaded on

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.

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
Download Presentation

PowerPoint Slideshow about ' Ternopil’ State Technical University named after Ivan Pul’ui' - jerom

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
u k r a i n e
U K R A I N ETernopil’ 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
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]
signal detection cameron martin middelton peterson siegert jacobs wald woodward wozencraft
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 n wiener karhunen lo v e parzen
Signal Representation in [J.Fourier-Н.А. Колмогоров-N.Wiener-Karhunen-Loév-E.Parzen]






SHIFT operator



SHIFT operator





the function representation in the hsohs
The Function Representation in the HSoHS

— stochastic measure

— spectral measure

— probability measure









rigged hilbert space with reproduced correlation kernel
Rigged Hilbert Space with Reproduced Correlation Kernel

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

conditions of existence
Conditions of Existence






the likelihood ratio and detection test statistic
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 number of spectral components energy is concentrate on spectr al band of sss
- spectral density; , - numberof spectral componentsEnergyis concentrate on ,-spectral band of SSS
methods equations
Methods & Equations


- an optimal estimation of spectra , ;

by method with parameter


generation of the indexes
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
Computation of The Expectation

(а) — component’s (b) — process


Results of Befitting Computation

of spectral components



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