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A three-dimensional (3-D) geometrical propagation model for wideband multiple-input multiple-output (MIMO) mobile-to-mobile (M-to-M) communications is proposed. Based on the geometrical model, a 3-D parametric reference model for wideband MIMO M-to-M multipath fading channels is developed. From the reference model, the corresponding space-time-frequency correlation function is derived for a 3-D non-isotropic scattering environment. It is shown that the time and frequency dispersion of a wide sense stationary uncorrelated scattering channel cannot be treated independently, contrary to common practice. From the space-time-frequency correlation function, the space-Doppler power spectral density and the power space-delay spectrum are derived and compared with measured data. Finally, a new sum-of-sinusoids based simulation model for wideband MIMO M-to-M Ricean fading channels is proposed. The statistics of the simulation model are verified by simulation. The results show that the simulation model is a good approximation of the reference model.