Corresponding author: Shakhtarin Boris I., Bauman Moscow State University, Moscow, 105005, Russian Federation
E-mail: shakhtarin@mail.ru

Received on May 25, 2016
Accepted on June 01, 2016

Questions of analysis of the statistical characteristics of the radioautomatic systems, in particular, the phase-locked loops (PLL), refer to the classical problems of the statistical communication theory. The Costas loop was proposed by John Costas in the middle of the previous century, but despite this it has been studied insufficiently. Currently, this radioautomatic system finds wide application in the telecommunication devices, global positioning systems (GPS, GLONASS), medical implants, and mobile communication systems. In contrast to the classic approaches PLL Costas loop simultaneously solves the problem of recovery of the suppressed carrier and demodulation of the input signal. This article presents Markov mathematical model of the Costas loop in the form of the stochastic differential equations with the additive effects of harmonic interference and white Gaussian noise, which takes into account the impact of the loop arm low-pass filters on the data modulation. The statistical properties of the loop phase error in the linear approximation are considered. The cumulant analysis of the Costas loop in the Gaussian approximation is offered. These results can be used for the engineering analysis of the noise immunity of the system in the presence of harmonic interference and Gaussian noise, which is typical for communication and navigation systems in difficult noise conditions caused by the industrial broadband and narrowband interferences. The resulting model and the considered linear and Gaussian approximation can also be used for the spectral analysis of the phase noise of the system.

Keywords: phase locked loop, Costas loop, quadrature loop, carrier recovery, phase error, linearization, cumulant analysis

For citation:
Neusypin K. A., Sizykh V. V., Shakhtarin Б. I., Shevtsev V. A. Cumulant Analysis of the Costas Loop with Additive Effects of the Harmonic Interference and Broadband Noise, Mekhatronika, Avtomatizatsiya, Upravlenie, 2016, vol. 17, no. 9, pp. 621—632.

DOI: 10.17587/mau.17.621-632

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