Bridging the gap between Kalman filter and Wiener filter in carrier phase tracking

Data-aided carrier recovery based on Phase-Lock Loop (PLL) is a popular scheme for tracking the phase of an incoming carrier affected by phase noise. Optimum tracking is achieved by a Kalman filter, that, with multilevel Quadrature Amplitude Modulation (QAM), is implemented by a PLL with variable loop gain. The paper shows that a PLL with fixed gain achieves a performance that is close to the optimal one provided that the phase detector is optimized. Monte Carlo simulations for the mean-square phase error and the symbol error rate of a 256-QAM constellation are provided to validate the analysis.