Adaptive PLL performances analysis for digital transmission context

The adaptive phase locked loop are used in digital communication systems to recursively estimate phase introduced by carrier's misadjustments and all time varying channel, allowing thus a better synchronization between the transmitter and the receiver. A rigorous analysis of PLL performances is difficult due to the non-linearity of the equation that govern the PLL. In this paper through the finite alphabet approach dedicated to the digital communication context, we generalize the 1/sup st/ order development of the adaptive PLL behavior for a higher order.