Analysis and Simulation of a PN Synchronization System

This paper analyzes the synchronization error which results when a pseudonoise synchronization signal in a coherent communication link is degraded by both additive white Gaussian noise and amplitude jitter produced by the reference carrier phase error. A synchronization system similar to a phase-locked loop is presented and simulated on a digital computer in order to find the distribution of the synchronization error. It is shown that the error is made up of two Gaussian components: one produced by the additive noise and one produced by the amplitude jitter. An approximate solution is also derived by appropriately bounding the reference phase error. The results are shown to be applicable to several similar systems found in the literature.