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.