Instruments and Systems: Monitoring, Control, and Diagnostics Annotation << Back Detection of a signal with a random phase against the background of noise using a characteristic function YU.M. VESHKURTSEV, N.D. VESHKURTSEV, D.A. TITOV A new solution of the classical problem of detecting a signal with a random phase against the background of noise is presented using the Neumann-Pearson criterion and the characteristic likelihood, to obtain which the characteristic function of A.Lyapunov is used. The obtained results are compared with the knowh basic vesearch data, it is found that the reliability of the detection of a signal with a random phase was twice higher, and the probability of a “false target” is zero with a signal/noise ratio of one or more. Keywords: additive mixture, signal detection, characteristic function, characteristic likelihood, Neumann – Pearson criterion, signal – to – noise ratio. Contacts: E-mail: vym1940@mail.ru Pp. 48-55.