Near Optimum Low Complexity Smoothing Loops for Dynamical Phase Estimation—Application to BPSK Modulated Signals

This correspondence provides and analyzes a low complexity, near optimum, fixed-interval smoothing algorithm that approaches the performance of an optimal smoother for the price of two low complexity sequential estimators, i.e., two phase-locked loops (PLLs). Based on a linear approximation of the problem, a theoretical performance evaluation is given. The theoretical results are compared to some simulation results and to the Bayesian and hybrid Cramer-Rao bounds. They illustrate the good performance of the proposed smoothing PLL (S-PLL) algorithm.