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The stationary variance of a posteriori error signal processing in noise with band pass spectrum of quadrature processing

DOI 10.18127/j00338486-201908(11)-06


V.M. Artyushenko – Dr.Sc.(Eng.), Professor, Head of Department of Information Technology and Management Systems, Technological University (Korolyov, Moscow region)
V.I. Volovach – Dr.Sc.(Eng.), Associate Professor, Head of Department of Information and Electronic Service, Volga Region State University of Service (Togliatti)

The issues related to the determination of the stationary dispersion of a posteriori error of signal processing under the influence of noise with the band pass spectrum during quadrature processing are considered and analyzed. The analysis is based on the use of methods of nonlinear Markov filtering and quasi-optimal algorithms of demodulation (filtering) of signals.
The equations defining the algorithm of forming the optimal estimates of the information process and the evolution of posterior variance. It is assumed that the signal is affected by both correlated and uncorrelated additive noise. To determine the steady-state variance averaging is performed both on the set and on the time of the components included in the expression of a posteriori variance. The found expressions for determining the stationary a posteriori error completely coincide with the expressions obtained for fluctuation noise.
The coefficients of amplitude suppression are introduced, taking into account the increase in the accuracy of demodulation of the information sequence due to the difference between the PDF of the transition of the formation process and the quadratures of additive noise from Gaussian ones. A quantitative assessment of increasing the accuracy of demodulation from the value of these coefficients, as well as from the value of the generalized signal-to-noise ratio (GSNR) is made. An increase in the amplitude suppression coefficient of the quadrature components of the strip additive noise or, equivalently, an increase in the difference between the PDF of the quadrature components and the Gaussian one leads to a decrease in the value of the stationary dispersion of the demodulation of the formation process. The same result is the growth of GSNR and the increase in the correlation coefficient of the demodulated process.
The case of phase-modulated signal demodulation is considered as an example. The GSNR depends on the phase modulation index of the carrier signal and its amplitude. An increase in the latter parameters leads to an increase in GSNR and a decrease in stationary dispersion. Shows the graphical dependence, illustrating the quality of the demodulated FM signal for different values of correlation coefficient and GSNR the quadrature processing. When the demodulated signal is exposed to a strip additive noise, the work on the quadrature components of the noise in comparison with the processing of its instantaneous values for the FM signal provides a win in the accuracy of demodulation twice.

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