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The synergetic integration of heterogeneous terrestrial and aerospace networks will play an important role in the evolution of wireless communications systems. In this direction, high-altitude platforms (HAPs) could act as relay stations in the stratosphere transferring information from an uplink to a downlink channel. This paper presents a novel transmission scheme for the delivery of mobile-to-mobile (M-to-M) services and proposes a three-dimensional (3-D) reference model for multiple-input multiple-output (MIMO) M-to-M via stratospheric-relay (MMSR) channels in amplify-and-forward (AF) networks. This model considers both line-of-sight (LoS) and non-line-of-sight (NLoS) propagation conditions and assumes that the scatterers in the vicinity of the mobile stations are non-uniformly distributed within two separate cylinders. From this model, the four-dimensional (4-D) space-time correlation function (STCF) is derived and numerical results are provided.