Frequency offset estimation for differential OFDM

This paper proposes a novel frequency offset (FO) estimator for differential orthogonal frequency division multiplexing. By separating the normalized FO into integral and fractional parts, our FO estimation is carried out in two successive stages. In the first stage, we take advantage of differential coding and the finiteness of signal constellation to derive a channel-independent cost function whose minimization leads to an accurate estimate of the fractional part. It is proved that under certain mild assumptions, the identifiability of the fractional part can be guaranteed with probability one. After compensating the fractional part, the second stage estimates the remaining integral part with the aid of a judiciously designed initial block of differential coding. Combining these two stages, the proposed estimator is shown capable of offering full-range FO estimation without relying on any training or virtual subcarriers. Furthermore, unlike some existing estimators, the proposed estimator is applicable in both frequency-flat and frequency-selective fading channels. Another salient feature of the proposed estimator is that accurate FO estimation can be achieved with two received data blocks only, making it very attractive especially for short-burst communications. The merits of our FO estimator have been confirmed by theoretical analysis as well as corroborating simulations.