A discrete phase state bit-synchronization loop is proposed for synchronization and detection of a binary nonreturn-to-zero (NRZ) process. The general loop model is developed for 11 and 17 phase states with optional sequential loop filter. Loop performance is considered in terms of the phase error density function, rms phase error, and mean time to bit slippage. It is shown that satisfactory loop performance can be achieved at -3 dB SNR through use of sequential loop filters.

A discrete receiver structure is introduced that consolidates the problems of bit detection and bit synchronization to provide optimal estimates of bit values without explicit knowledge of the transition epoch. Equations are developed for the propagation of the discrete a posteriori density function on an interval-by-interval basis. The general model is developed for a signal corrupted by additive and multiplicative noise, and the receiver structure is shown to be equivalent to a synchronous discrete receiver. The model is applied to on-off-keyed (OOK) modulation in the presence of multipath.