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In this paper, a new semiblind spectrally efficient channel estimation method is presented for fast fading orthogonally coded multiple-input multiple-output orthogonal frequency-division multiplexing (MIMO-OFDM) systems. The proposed method benefits from both the available training symbols inserted in the data frame structure of wireless standards as LTE and WiMAX and the redundancy introduced in the space-time code to enhance channel estimation quality. Our method offers a closed-form solution and performs channel estimation in the time domain in two consecutive steps. First, the subspace containing the true channel vector is estimated from the extended covariance matrix of the received data in a fully blind fashion, and then, the true channel vector is recovered from the obtained subspace using available training symbols. The parsimonious channel characterization that we use decreases the number of parameters required to be estimated. On the one hand, it results in a performance improvement as compared to the frequency domain channel estimation methods by coherent processing over all subcarriers. On the other hand, the bandwidth efficiency is enhanced by training overhead reduction as compared to the pure training-based approaches. Moreover, the proposed method is able to eliminate all nonscalar ambiguities inherent in blind channel estimation techniques in two practically important cases, the systems involving single-antenna receivers and the systems involving rotatable codes.