An inter-carrier interference (ICI) occurs in an orthogonal frequency division multiplexing (OFDM) system when a channel is rapidly time-varying. The proposed scheme employs a polynomial cancellation code (PCC) to suppress this ICI, and uses a linear complex field (LCF) code as a transmit-diversity technique to make the transmission rate compatible up n(T) / (n(T) + 1), where n(T) is the number of transmit antennas used. The conventional orthogonal code (OC), such as the Alamouti code, with accompanying PCC cannot achieve this rate. Both analysis and simulation results verify that the proposed scheme can achieve higher channel capacity as well as lower bit error rate (BER) than the other schemes in rapidly time-varying channels, even with a linear receiver and inaccurate channel estimation.