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Orthogonal frequency division multiplexing (OFDM) is widely recognized as the key technology for the next generation broadband wireless communication (BWC) systems. Besides high spectral efficiency, reliable performance over fast fading channels is becoming more and more important for OFDM-based BWC systems, especially when high speed cars, trains and subways are playing an increasingly indispensable role in our daily life. The time domain synchronous OFDM (TDS-OFDM) has higher spectral efficiency than the standard cyclic prefix OFDM (CP-OFDM), but suffers from severe performance loss over high speed mobile channels since the required iterative interference cancellation between the training sequence (TS) and the OFDM data block. In this paper, a fundamentally distinct OFDM-based transmission scheme called time-frequency training OFDM (TFT-OFDM) is proposed, whereby every TFT-OFDM symbol has training information both in the time and frequency domains. Unlike TDS-OFDM or CP-OFDM where the channel estimation is solely dependent on either time-domain TS or frequency-domain pilots, the joint time-frequency channel estimation for TFT-OFDM utilizes the time-domain TS without interference cancellation to merely acquire the path delay information of the channel, while the path coefficients are estimated by using the frequency-domain grouped pilots. The redundant grouped pilots only occupy about 3% of the total subcarriers, thus TFT-OFDM still has much higher spectral efficiency than CP-OFDM by about 8.5% in typical applications. Simulation results also demonstrate that TFT-OFDM outperforms CP-OFDM and TDS-OFDM in high speed mobile environments.