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Large-scale orthogonal frequency division multiplexing (OFDM) multiple-input multiple-output (MIMO) is a promising candidate to achieve the spectral efficiency up to several tens of bps/Hz for future wireless communications. One key challenge to realize practical large-scale OFDM MIMO systems is high-dimensional channel estimation in mobile multipath channels. In this paper, we propose the time-frequency training OFDM (TFT-OFDM) transmission scheme for large-scale MIMO systems, where each TFT-OFDM symbol without cyclic prefix adopts the time-domain training sequence (TS) and the frequency-domain orthogonal grouped pilots as the time-frequency training information. At the receiver, the corresponding time-frequency joint channel estimation method is proposed to accurately track the channel variation, whereby the received time-domain TS is used for path delays estimation without interference cancellation, while the path gains are acquired by the frequency-domain pilots. The channel property that path delays vary much slower than path gains is further exploited to improve the estimation performance, and the sparse nature of wireless channel is utilized to acquire the path gains by very few pilots. We also derive the theoretical Cramer-Rao lower bound (CRLB) of the proposed channel estimator. Compared with conventional large-scale OFDM MIMO systems, the proposed TFT-OFDM MIMO scheme achieves higher spectral efficiency as well as the coded bit error rate performance close to the ergodic channel capacity in mobile environments.