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# Determination of probability of a discrete signal recognition in presence of additive noise for N information channels

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I.I. Troitskiy - Ph.D. (Eng.), Associate Professor, Information Security Department, Bauman Moscow State Technical University. E-mail: iitroitskiy@mail.ru M.A. Basarab - Dr.Sc. (Phys.-Math.), Professor, Information Security Department, Bauman Moscow State Technical University. E-mail: bmic@mail.ru V.A. Matveev - Dr.Sc. (Eng.), Professor, Head of the Faculty of Informatics and Control Systems, Head of Information Security Department, Bauman Moscow State Technical University, Honored Scientist of Russian Federation, Laureate of the State Prizes of USSR and RF, Laureate of the Russian Government Prize in Science and Education

The method for discrete signal recognition in the presence of additive noise, with the use of N information transmission channels con-taining both discrete signals and noises, is proposed. The method is based on the correlation of noises in the transmission channels. For noise compensation, the linear correlation function between the signals and noses in the channels is chosen and its parameters are determined on the basis of the maximum of the signal-to-noise ratio. In general, it is not possible to determine these parameters analytically by solving a system of quadratic equations, so the problem is solved by numerical methods. Analytical expressions for the parameters can be obtained when the problem of the use of N channels is reduced to the problem of using two channels, or when special cases of the normalized correlation matrix are considered. For a composition of normal noises, the probability of correct recognition of a discrete signal after the compensation for the case of N channels is defined.
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