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The potential for capacity increase in multiantenna wireless communication systems has drawn considerable attention to space-time codes. However, most of the existing space-time code construction methods have assumed ideal channel models: either quasi-static fading of fast fading. In this work, we derive the performance criteria for space-time coded wireless communications systems taking into account both spatial and temporal channel correlation. We show that if the space-time correlation matrix is of full rank, the space-time code design problem for fast fading channels can be reduced to the code design problem for fast fading channels. Some simulation results are also presented to support the theory.