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Space-time correlation functions between the links of MIMO Rayleigh fading channels are derived using a new three-dimensional (3-D) cylinder scattering model. Closed form, mathematically tractable formulas are obtained for the space-time correlation functions for general MIMO systems where the base station and mobile station antennas may be arranged in 3-D space. It is shown that the correlation functions computed by the 3-D cylinder model are of significant difference than those of the conventional 2-D Clarke's isotropic scattering model for vertically placed antennas. The general formulas of the correlation functions includes the 2-D Clarke's model and the 3-D SIMO, MISO models as special cases.