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In this paper, the problem of channel estimation in spatially correlated multi-input multi-output (MIMO) channel is investigated. We consider minimum mean square error (MMSE) criterion which requires accurate knowledge about second order statistics of the channel and noise. In our method, the output of the least square estimator is exploited to estimate the channel correlation matrix and noise variance using the same training sequences. Advantages of this method over methods that ignore correlation among sub-channels will be demonstrated in the sense of mean square of estimation error and bit-error rate.