A cross-correlation model for non-isotropic scattering with non-omnidirectional antennas in MIMO propagation channels

We present a cross-correlation model for multiple-input multiple-output (MIMO) Rayleigh fading channels in a two-dimensional (2D) multipath random media when energy is non-uniformly received/transmitted to/from the receiver/transmitter along propagation directions. We investigate the impact of non-omnidirectional propagation pattern of antennas along with the impact of non-uniform distribution of the scatterers in the propagation environment which introduces non-isotropic wave propagation, at both transmitter and receiver ends. The non-isotropic propagation is described by non-uniform probability density functions (pdf) for the direction-of-departure (DOD) and the direction-of-arrival (DOA) of the outgoing/incoming propagating waves from/to stations. The propagation patterns of antenna elements (and the effect of mutual coupling between them) are also described by the Fourier series expansion of antenna propagation patterns. The expression of the cross-correlation function (CCF) turns out to be a linear expansion of a number of Bessel functions of the first kind. The coefficients of this expansion are given by linear convolution of the Fourier series coefficients (FSC) of the corresponding antenna patterns and the FSCs of the corresponding pdf of the non-isotropic propagation directions. The Fourier analysis on the CCF shows impacts of non-isotropic environment and non-omnidirectional antennas on the spectrum of the received channel process while the maximum Doppler frequency shift remains invariant with variations of beam-patterns and the pdf of propagating waves.