Generalized method of moments estimation of location parameters: Application to blind phase acquisition

In this paper, we address the problem of location parameter estimation via a Generalized Method of Moments (GMM) approach. The general framework for the GMM estimation requires the minimization of a suitable, generally nonconvex, elliptic norm. Here we show that, if the estimandum is a shift parameter for a suitable statistic of the observations, a fast, DFT-based, computationally efficient procedure can be employed to perform the estimation. Besides we discuss the relation between the GMM estimation and the maximum likelihood (ML) estimation, showing that the GMM estimation rule provides a closed form ML estimator for shift parameters when the observations are multinomially distributed. As a case study, we analyze a GMM blind phase offset estimator for general quadrature amplitude modulation constellations. Simulation results and theoretical performance analysis show that the GMM estimator outperforms selected state of the art estimators, approaching the Cramer-Rao lower bound for a wide range of signal-to-noise ratio values.