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The multiple input multiple output (MIMO) channel results from the use of multiple transmit and multiple receive antennas, which allows to achieve high spectral efficiency by spatial multiplexing. The high number of coefficients in the channel response (number of TX antennas by number of RX antennas by delay spread) allows to achieve high diversity and to improve the outage capacity, but at the same time represents a challenge for channel estimation as it imposes the use of a longer training sequence (TS) leading to a rate loss. In this paper, we augment the TS artificially by including the blind part (unknown symbols) information and the non pure training information, this allows to reduce the TS length needed for channel estimation and hence to save rate. We use semiblind approaches that exploit both training and blind information. These techniques have a complexity not immensely much higher than that of training based techniques. For the flat channel case, the technique we present achieves the Cramer-Rao bound. In the frequency-selective channel case we use a quadratic semiblind criterion that combines a training based least-squares criterion with a blind criterion based on linear prediction.