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Radar, communications, and ranging systems can use pseudonoise modulated carriers. The extraction of information from the carrier requires the synchronization of a pseudonoise waveform at the receiver for correlation detection. For initial synchronization, the receiver must examine all possible time positions of the incoming pseudonoise waveform. In serial search the time difference between the pseudonoise modulation on the carrier and the pseudonoise waveform generated at the receiver is linearly varied. A continuous decision process determines when synchronization has been achieved. With additive white normal noise interference, the probabilities of false alarm and false dismissal during synchronization for coherent and incoherent detection are computed. The results are dependent on carrier power, noise per unit bandwidth, and search rate.