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By combining multiple-input-multiple-output (MIMO) communication with block transmission using a cyclic prefix (CP), MIMO block transmission systems can not only achieve high data rates but also simplify channel estimation and equalization. In this paper, to provide a bandwidth-efficient solution for channel estimation in MIMO block transmission systems with a CP, we present a framework for blind channel estimation based on a general non-redundant precoding. Using this framework, we propose a blind estimator exploiting a simplified non-redundant precoding that is robust against overestimates of a true MIMO channel order. Furthermore, in the case with the number of transmit antennas greater than that of receive antennas, we show under specific system conditions that the proposed blind algorithms can be used for estimation of the MIMO channel without oversampling the received signals. With the simplified precoding conditions established in this paper, the proposed method does not impose the strict identifiability conditions on the MIMO channel, which are required for the existing methods. Furthermore the proposed estimator achieves accurate channel estimation with a small number of symbol blocks. In addition, we derive a simplified precoder that is optimized in the sense of minimizing the impact of unknown additive noise. We discuss the tradeoff between channel estimation accuracy and bit error rate performance associated with the simplified precoder. Finally, we develop a technique for resolving the channel ambiguity in the proposed blind estimator to create a semi-blind channel estimator relying on only a few known symbols.