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We present a novel approach for carrier frequency offset estimation in OFDM systems. Before they enter the OFDM system, the information bearing symbols are segmented into blocks so that each even indexed block shares one common symbol with the previous block. This redundancy allows for the frequency offset estimation at the receiver, without the need of pilot symbols. The offset is obtained based on cross-correlations of successive received blocks, and is decoupled from the channel estimate. With the proposed approach, offset estimation is achieved with very small reduction of rate of the OFDM system, as opposed to higher reduction caused by other existing approaches.