Generalized method of moments for blind near efficient carrier phase acquisition

A blind carrier phase estimator based on a suitably weighted phase histogram of the received signal samples is phrased as a particular case of the GeneralizedMoments Method (GMM). More in general, in this contribution, we point out that the estimation of a shift parameter by means of the GMM can be realized using a fast, DFT based, computationally efficient, coarse-to-fine estimation procedure. Furthermore, we develop the statistical analysis needed to extend the estimator to the optimally weighed GMM estimator, i.e. the weighted estimator achieving the minimum estimate variance. The theoretical analysis of the optimally weighted estimator performances is carried out in close form. Finally, the theoretical weighted estimator performances are compared with those of the unweighed estimator, of a state-ofart estimator and of the Cramèr-Rao lower bound. The performance improvement due to the optimal weighting is clearly appreciated, since, at medium to high SNR, it approaches the Cramèr-Rao lower bound on all constellations.