Optimization of the Performance of a Digital-Data-Transition Tracking Loop

The steady-state behavior of a data-transition tracking loop, used as a bit synchronizer in a phase-coherent receiver, is considered. Optimization of mean-square phase noise and mean time to first cycle slip is performed when the average power of the reference cross-correlating signal is constrained. It is shown that by adjusting the quadrature channel gain along with the integration interval, a significant improvement in phase noise and cycle slip performances can be achieved over that system which integrates in the quadrature channel over the full symbol period. All the results are derived for a first-order loop filter merely to indicate the approach to the problem and the relative value of optimizing the system.