Optimal blind nonlinear least-squares carrier phase and frequency offset estimation for burst QAM modulations

This paper introduces a novel family of blind feedforward nonlinear least-squares (NLS) estimators for joint estimation of the carrier phase and frequency offset of quadrature amplitude modulations (QAM). An optimal or "matched" nonlinear estimator that exhibits the smallest asymptotic variance within the family of envisaged NLS-estimators is developed. A class of computationally efficient monomial estimators is also proposed. The asymptotic performance of these estimators is established in closed-form expression and compared with the Cramèr-Rao lower bound corresponding to an unmodulated carrier. Finally, computer simulations are presented to corroborate the theoretical performance analysis.