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We study the problem of frequency offset due to the Doppler velocity of orthogonal frequency division multiplexing (OFDM) systems. A regular OFDM has an IFFT at the transmitter and an FFT at the receiver. The proposed parallel algorithm employs an FFT at the transmitter and an IFFT at the receiver. The regular OFDM samples, which are generated by the IFFT, are transmitted as the first block, and the FFT outputs are transmitted as the second block. At the receiver, the results of the first output generated by the FFT are combined with the second output generated by the IFFT. This combined operation forms a parallel intercarrier interference (ICI) cancellation scheme for mitigating frequency offsets of OFDM systems. It provides: (1) a robust OFDM system in the presence of relative velocity, also known as Doppler frequency offset; (2) high signal to ICI ratio (7 dB better than that of the linear self-cancellation algorithms at N=1024 and ΔfT≤1% of subcarrier frequency spacing); (3) backward compatibility with the existing OFDM system; (4) better BER performance in both additive white Gaussian noise (AWGN) and fading channels.