Probability functions for modulus and angle of the non-Gaussian complex variate

Abstract

Algorithms and methods of radio-signals processing are developed in the assumption of Gaussian distribution of the quadrature components in the modern communication and radio-systems. Their independence, non-correlation and variances equality leads to the Rayleigh and Rice distributions of the modulus depending on the availability of the regular component in the radio channel. Moreover, phase distribution is considered to be uniform one. However, features of signal propagation lead to the changing of distributions parameters of the quadrature components in the modern radio channels or make distributions non-Gaussian. In this report, we present uniform and universal method of representing of the quadrature components as mixtures of Gaussian distributions with using the stochastic spectra of probability distribution. Probability distributions of the amplitude and phase are the mixture of distributions known in the correlation theory. Results of modeling are presented.