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This paper deals with the modeling and analysis of narrowband multiple-input multiple-output (MIMO) mobile-to-mobile (M2M) fading channels in relay-based cooperative networks. Non-line-of-sight (NLOS) propagation conditions are assumed in the transmission links from the source mobile station to the destination mobile station via the mobile relay. A stochastic narrowband MIMO M2M reference channel model is derived from the geometrical three-ring scattering model, where it is assumed that an infinite number of local scatterers surround the source mobile station, the mobile relay, and the destination mobile station. The complex channel gains associated with the new reference channel model are derived and their temporal as well as spatial correlation properties are explored. General analytical solutions are presented for the four-dimensional (4-D) space-time cross-correlation function (CCF), the three-dimensional spatial CCF, the two-dimensional (2-D) transmit (relay, receive) correlation function (CF), and the temporal autocorrelation function (ACF). Closed-formed expressions for different CCFs under isotropic scattering conditions are also provided in this paper. The proposed reference channel model can be used as a starting point to develop stochastic and deterministic channel simulators. Such channel simulators are not only important for analyzing the dynamic behavior of the MIMO M2M channel capacity but also for the development of future MIMO M2M cooperative communication systems.