Probability Distribution Density of Error Signal in the Continuous and Discrete Phase-Locked Loops in the Presence of Jamming

Methods for calculation of the probability distribution density of an error signal in the continuous and discrete synchronization systems in the presence of jamming are considered. An equation defining the probability distribution density for the continuous phase-locked loop and its solution in the presence ofjamming are given. For the same conditions, determination of the probability distribution density of an error signal using the approximate Galerkin methodfor the case of the discrete phase-locked loop is shown. The sinusoidal form of nonlinearity of the phase discriminator characteristic was used in calculations for both continuous and discrete phase-locked loops. Plots of the probability distribution densities of the error signal are constructed for the continuous and discrete phase-locked loops and their comparative analysis is performed. A conclusion is drawn on the impact of jamming upon the system of the continuous and discrete phase-locked loops, when different values of the signal-to-noise ratio and jam-to-signal ratio were taken for comparison.

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