A Robust Data-Aided Frequency Offset Estimator for Single-Frequency Signals

This paper presents a data-aided frequency offset estimator for a single complex sinusoidal signal corrupted by complex additive white Gaussian noise (AWGN). Kay [4] developed a maximum likelihood (ML) estimator based on differential phase measurements which achieves Cramer-Rao lower bound (CRLB) at high signal-to-noise ratios (SNRs); however, it exhibits large outliers at SNRs lower than 10-15 dB. In this paper, we propose an idea to divide the observation vector into adjacent segments. The samples within the same segment are then added together to produce a new sample. The closed-form of the proposed estimator is derived by applying the ML estimation over the new set of samples in the same way as of Kay´s estimator. Simulation results show that with the proposed estimator, the threshold reduces 3-4 dB as the segment length is doubled. The estimation variance remains close to the CRLB even at SNR values as low as 0 dB. The proposed estimator is also compared with another family of frequency estimators that exploits the sample correlations.