On Models, Bounds, and Estimation Algorithms for Time-Varying Phase Noise

In this paper, first, a new discrete-time model of phase noise for digital communication systems, which is a more accurate model compared to the classical Wiener model, is proposed based on a comprehensive continuous-time representation of time-varying phase noise, and statistical characteristics of this model are derived. Next, the non-data-aided (NDA) and decision-directed (DD) maximum-likelihood (ML) estimators of time-varying phase noise, using the proposed discrete-time model are derived. To evaluate the performance of the proposed estimators, the Cramer-Rao lower bound (CRLB) for each estimation approach is derived and by using Monte-Carlo simulations it is shown that the mean-square error (MSE) of the proposed estimators converges to the CRLB at moderate signal-to-noise ratios (SNR). Finally, simulation results show that the proposed estimators outperform existing estimation methods as the variance of the phase noise process increases