ДВУХЛУЧЕВАЯ МОДЕЛЬ С ДИФФУЗНЫМ ЗАМИРАНИЕМ МОЩНОСТИ СИГНАЛА

Abstract

One of the main objectives of the mathematical theory of communication is definition of the most essential characteristics of system of information transfer. One of important quantitative indices of system is the probability of erroneous reception in various communication channels. The special class of communication channels is represented by channels in which a dying down of signals is considered. For the mathematical description of a dying down the density of distribution of probabilities is used, in particular. The variety of the various distributions meeting in scientific literature, is connected as with the assumptions used for justification of distribution, and to their compliance to physical properties of channels. In article the dual-beam model with a diffuzny dying down of capacity of a signal (TWDP model) is considered and mathematical statement of a problem of calculation of a noise stability for a communication channel with additive white Gaussian noise and a dying down described within this model is formulated. It is shown that the TWDP model used for the description of a dying down, includes not only a classical releevsky and raysovsky dying down, but also covers a class of two-modal distributions, characteristic for some modern wireless communication channels. It is shown that at certain parameters of distribution there are two fashions which emergence was theoretically possible when using for the description of a dying down of four-parametrical distribution. For the solution of a problem of calculation of a noise stability in the channel with a dying down studying of likelihood characteristics of distribution that demands, in turn, attraction of the theory of special functions and, in particular, hyper geometrical functions is necessary. It is shown that mathematical representation of function of distribution is possible in two options: integrated representation and representation through Laurichell's hyper geometrical function. Ratios for the initial moments of the distribution considered in article are received. It is shown that the initial moments are expressed through Gauss's hyper geometrical function. At the heart of the solution of a problem of a noise stability representation of probability of a symbolical (bit) mistake for multiitem alarm designs in a communication channel with additive white Gaussian noise through Owen's special function that allows to receive the common decision of a task lies. The analytical formulation of the partial task which decision is a basis for the solution of the general problem of calculation of a noise stability in a communication channel with a dying down described by TWDP model is presented.