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We consider a point-to-point, correlated and block fading multiple antenna channel where the receiver has a noisy channel estimation and the transmitter has the statistics of the channel. Although very high rates are promised when the receiver knows the channel perfectly, the capacity is not known when the receiver has a noisy channel estimation. In this paper, we will derive an upper bound to the capacity of the system that we consider, and analyze the tightness of this bound and previously derived lower bounds with respect to block length and total average power. We observe that the lower and upper bounds converge with increasing block length, however there is a non-vanishing difference between the bounds with increasing total average power.