The Stationary Variance of a Posteriori Error of Amplitude-Phase Signal Processing in non-Gaussian Noise with Band-Pass Spectrum

Abstract

Analysis of basic questions of determination of stationary dispersion of posteriori error of amplitude-phase processing of signals under influence of non-Gaussian noise with limited spectrum is carried out. Such noise occurs when reflected from the underlying surface and concentrated reflectors. In the stationary mode of operation of demodulators, it is convenient to consider the stationary (steady-state) variance value of the posterior error of demodulation of useful signals. The criterion of optimality is often the maximum posterior density of the probability distribution. Expressions are obtained that determine the algorithm for the formation of an optimal estimate of the information process and the evolution of a posteriori dispersion, as well as stationary dispersion for cases of additive noise. Coefficients of envelope suppression (amplitude) and phase of additive non-Gaussian interference with band spectrum are introduced, in which components of Fischer information matrix are used. These coefficients allow us to take into account the difference between the density of the distribution of the probability of the envelope transition (amplitude) and the phase of band-pass noise from Gaussian. Quantitative estimation of influence of value of suppression coefficients on accuracy of signal demodulation is obtained. It has been shown that the stationary posteriori dispersion depends substantially on both the values of the generalized signal-to-interference ratio and the correlation coefficient of the demodulated process. Increase of non-Gaussian interference suppression coefficients leads to decrease of stationary posterior error.