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^st order development of the adaptive PLL behavior for a higher order.