In recent years, the increasing demand for high data rates and the limited available bandwidth have motivated the investigation of wireless systems that efficiently exploit the spatial dimension. An interesting trend in wireless communications that is spatially efficient employs multiple antennas at both transmitter and receiver. This trend is called multiple-input multiple-output (MIMO) communications. The application of antenna arrays for wireless cellular systems has received much attention, as they improve the coverage and capacity of such systems by combating interference and fading. Also, by exploiting antenna arrays at both the transmitter and receiver, the capacity of wireless channels can be increased significantly. In order to design high performance multiple-input multiple-output (MIMO) wireless systems, and to predict the impact of random multipath propagation on fading, it is necessary to have accurate and reliable MIMO channel models. In this thesis, we have derived cross-correlation function (CCF) between the space-time-frequency (STF) transfer functions of two sub-channels of an outdoor non-isotropic environment with non-omnidirectional antennas, using the plane wave propagation model, when the moving system (MS) has a constant speed. Most MIMO channel models employ certain geometries for the scatterers around the receiver to describe non-isotropic propagation. Alternatively, in this thesis we have described and simulated such a channel with analytical-stochastic approach, using Von Mises probability distribution function to describe the non-isotropic propagation. The CCF is expressed in a closed and easy-to-use form, as a function of propagation environment and antenna arrays parameters. This cross-correlation function is comprised of two terms, either of which represents the impact of the wireless channel around the transmitter, the receiver, and along the channel, in terms of time, carrier frequency, and location of the antenna arrays elements. Finally, in order to examine the description and study the effects of the propagation and antennas parameters, as well as, the motion of the receiver on the CCF, the expression for the stationary channel power spectral density function is calculated and illustrated. Keywords: MIMO channel models, Cross-correlation function (CCF), Non-omnidirectional antenna array, Power Spectrum Density function (PSD), Von Mises distribution function