On models, bounds, and estimation algorithms for time-varying phase noise

In this paper, a new discrete-time model of phase noise for digital communication systems, based on a continuous-time representation of time-varying phase noise is derived and its statistical characteristics are presented. The proposed phase noise model is shown to be more accurate than the classical Wiener model. Next, using the this model, non-data-aided (NDA) and decision-directed (DD) maximum-likelihood (ML) estimators of time-varying phase noise are derived. To evaluate the performance of the proposed estimators, the Cramér-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.