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We investigate the fading multiple-antenna channel. The decoder is assumed to possess imperfect channel fading information. A modified nearest neighbor decoder with an innovative weighting factor is introduced and an expression for the generalized mutual information (GMI), the achievable rate, is obtained. We show that under certain conditions the achievable rate is equivalent to that of a fading multiple-antenna Gaussian channel where fading is known to the receiver and is equal to the channel estimation, and where noise is due to both the channel noise and the channel estimation error. We show that for our communication scheme, the minimum mean square error (MMSE) channel estimator is optimal in the sense that it achieves the highest value of GMI, and hence the highest communication rate. Additionally, a training based multiple-input multiple-output (MIMO) scheme in a block-fading channel is investigated and it is shown that the number of degrees of freedom depends on the signal-to-noise ratio (SNR).