Symbol synchronization for digital signals with multisegment trajectory: digital data transition tracking loop

The symbol synchronizer presented is an all-digital data transition tracking loop which permits simple implementation and voltage control of the loop bandwidth. The equivalent loop integration constant is changed by changing the threshold level of a comparator at the output of the loop phase error detector. Phase error probability distribution function, its variance, and the average probability of cycle slipping are analyzed analytically for the general case. The theory of finite Markov chains is used to analyze statistical properties of the tracking error, primarily with regard to the phase error distribution and its variance, the average probability of the cycle slipping, the synchronizer time response, and bandwidth. As an example, numerical results for generalized tamed frequency modulation (GTFM with B=0.62 and r=0.36) are presented and discussed.