Performance of a tracking status detector for a digital delay lock loop

A lock detector for providing precise time synchronization in a satellite-earth communication system is proposed and analyzed. The detector is operated on the principal that the instantaneous phase error determines the loop tracking status. The proposed detector is analyzed by a Markov random walk model. Two sets of probabilities were determined: the probability of detecting the out-of-lock condition given that the loop was out of lock, and the probability of exceeding the threshold given that the loop was in lock. It was found that at a signal-to-noise ratio of 6 dB, a 0.9999 probability of out-of-lock detection is attainable. The probability of one or more false alarms in one year was less than 1/100,000. The frequency drift estimator is also discussed.