Analysis of non-data-aided carrier frequency recovery with Luise-Reggiannini estimators applied to M-PSK schemes

Luise and Reggiannini introduced a data-aided feedforward estimator for carrier frequency recovery in an all-digital receiver. For M-PSK as a modulation scheme, the concept is easily extended to the non-data-aided case. In this context, a closed-form solution for computation of the jitter variance is provided, which agrees with the simulation results for medium-to-high SNR values and frequency offsets representing a smaller fraction of the operational range. In the sequel, the analytical result is used for comparison purposes and parameter optimisation.