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This paper' deals with the modeling, analysis, and simulation of multiple-input multiple-output (MIMO) narrowband fading channels for mobile-to-mobile communications. A stochastic MIMO mobile-to-mobile reference channel model is derived from the geometrical two-ring scattering model under the assumption that both the transmitter and the receiver are surrounded by an infinite number of local scatterers. Using a wave propagation model, the complex channel gains are derived and their statistical properties are studied. General analytical solutions are provided for the three-dimensional (3-D) space-time cross-correlation function (CCF). We show that this function can be expressed as the product of two 2D space-time cross-correlation function (CFs), called the transmit and receive CF. From the non-realizable reference model, a stochastic and a deterministic simulation model are derived using a double sum of complex exponential functions. It is shown how the parameters of the simulation model can be determined for any given distribution of the angle of departure (AOD) and angle of arrival (AOA). In case of isotropic scattering, we present a closed-form solution for the parameter computation problem and illustrate some numerical results concerning the transmit CF. The proposed procedure provides an important framework for designers of future mobile-to-mobile communication systems to verify new transmission concepts employing MIMO techniques under realistic propagation conditions.