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In this paper, the space-time correlation (STC) functions of multiple-input multiple-output (MIMO) fading signals are derived for both frequency-flat and frequency-selective channels in macrocell and microcell environments. To avoid large computation load in calculating the exact STC, we recommend the concept of effective scatterers and provide simplified expressions of STC functions. The STC functions are used to calculate the coefficient matrices that are necessary for generating MIMO channels, when the vector autoregressive method is used. The analytical results are verified by Monte Carlo simulations. Finally, we use the generated channels to investigate MIMO capacities under various channel parameters and to evaluate the bit-error-rate performance of downlink wideband code-division-multiple-access system with transmit and receive diversity.