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This paper proposes a new space-time-frequency (STF) correlation model based on the two-ring model with both single- and double-bounced rays for miltiple-input multiple- output (MIMO) mobile-to-mobile (M2M) multicarrier ricean fading channels in a non-isotropic scattering environment. The proposed model allows us to study the correlation functions (CFs) between any two sub-channels with different carrier frequencies of MIMO M2M Ricean fading channels. The derived STF CF and the corresponding space-Doppler-frequency (SDF) power spectral density (PSD) have generic closed-form expressions including many existing CFs and PSDs as special cases. Based on the derived SDF PSD, the resulting doppler PSD is investigated in more detail in terms of some important parameters. Our numerical evaluations show the impacts of different parameters of the propagation environment on the doppler PSD. More importantly, we find that the shapes of the Doppler PSD are completely different according to single- or double-bounced rays for M2M channels, while they are exactly the same for fixed- to-mobile (F2M) channels. Finally, it is worth mentioning that some interesting observations obtained from these numerical results can be considered as the guidance for further proposing more realistic M2M channel models and building up future measurement campaigns.