Non-Data-Aided Feedforward Carrier Frequency Offset Estimators for QAM Constellations: A Nonlinear Least-Squares Approach

Abstract

This paper performs a comprehensive performance analysis of a family of non-data-aided feedforward carrier frequency offset estimators for QAM signals transmitted through AWGN channels in the presence of unknown timing error. The proposed carrier frequency offset estimators are asymptotically (large sample) nonlinear least-squares estimators obtained by exploiting the fourth-order conjugate cyclostationary statistics of the received signal and exhibit fast convergence rates (asymptotic variances on the order of, where stands for the number of samples). The exact asymptotic performance of these estimators is established and analyzed as a function of the received signal sampling frequency, signal-to-noise ratio, timing delay, and number of symbols. It is shown that in the presence of intersymbol interference effects, the performance of the frequency offset estimators can be improved significantly by oversampling (or fractionally sampling) the received signal. Finally, simulation results are presented to corroborate the theoretical performance analysis, and comparisons with the modified Cramér-Rao bound illustrate the superior performance of the proposed nonlinear least-squares carrier frequency offset estimators.