The problem of acquiring and maintaining synchronization of a pseudonoise code, particularly at low signal-to-noise ratios, is analyzed to determine the mean time to acquisition and the mean time to lose lock. An analysis procedure is developed which explicitly considers the search/lock strategy and the transition from search to lock. A practical example is included to demonstrate the technique.

The probability of error in a binary communication system using pseudonoise (PN) modulation to spread the transmitted spectrum is influenced by noise, bandlimiting, and synchronization errors. In this paper the average probability of error is determined, using a series expansion of the characteristic function of the intersymbol interference. It is shown that the effects of intersymbol interference are reduced by spreading and that local code synchronization errors become the dominant factor in the probability of error when the system bandwidth is large.