ESTIMATION OF THE NON-ENERGY PARAMETER OF THE RADIO SIGNAL IN COMBINATION WITH THE TRUNCATED ESTIMATION OF THE DISPERSION OF ADDITIVE ASYMMETRIC-KURTOSIS NOISE

Abstract

The traditional approach to estimating signal parameters is to use an noise model with a Gaussian probability density distribution. However, this assumption does not always realistically reflect the processes in communication channels, and the efficiency of such algorithms is significantly reduced if the noise distribution differs from Gaussian. The complexity of the mathematical noise model leads to computational difficulties, so it is necessary to look for convenient approaches to describe non-Gaussian noise. The paper proposes to use an noise model that is described by a finite sequence of initial moments and cumulants. In this case, it is possible to use the polynomial maximization method, which is essentially similar to the maximum likelihood method. According to this method, an arbitrary probability density distribution is approximated by a stochastic polynomial. The higher the degree of the polynomial, the more accurately it describes the real probability density distribution. In the case where the distribution of non-Gaussian noise does not differ significantly from the Gaussian one, good results can be achieved even with low degrees of the stochastic polynomial. In this work, the degree of closeness of the distributions is determined by the coefficients of asymmetry and kurtosis. We will call such a noise model asymmetric-kurtosis. It is assumed that the statistical nature of the cumulative coefficients of the 3rd and 4th orders is constant and their values are known a priori. The noise power (2nd order cumulant) can change, so its value must be estimated together with the informative parameter of the signal. The accuracy of the estimation of the 2nd order cumulant is not of fundamental importance, therefore, to simplify the computational procedure, it is proposed to use the method of maximizing a truncated polynomial. At the same time, the full method of maximizing a polynomial is used to estimate the non-energy parameter of the signal. The accuracy of the estimation increases with the increase in the degree of the polynomial, but this leads to the complication of the algorithm for finding the joint estimate. Therefore, the combined use of the methods of maximizing the full and truncated polynomials allows you to maintain a reasonable compromise between the high accuracy of the algorithms and the technical simplicity of their implementation.