A cross-correlation MIMO channel model for non-isotropic scattering environment and non-omnidirectional antennas

We present a cross-correlation model for multiple-input multiple-output (MIMO) Rayleigh fading channels in a two-dimensional (2D) space. In particular, we investigate the impact of non-omnidirectional antennas at both transmitter and receiver ends and the non-uniform distribution of the scatterers in the random media which introduces non-isotropic wave propagation. The non-isotropic propagation is described by general non-uniform probability density functions (pdf) for the direction-of-departure (DOD)/direction-of-arrival (DOA) of the outgoing/incoming propagating waves from/to stations. The propagation pattern of each antenna element and the effect of mutual coupling between them are also described by their Fourier series expansion. The expression of the cross-correlation function (CCF) turns out to be a linear series expansion of a number of Bessel functions of the first kind. In particular the coefficients of the expansion of the CCF are described by linear convolution of the Fourier series coefficients of the antenna pattern, the Fourier series coefficients of the azimuth angular spread and the Fourier series expansion of the pdfs describing the non-isotropic environment. In fact, the Fourier-Chebyshev series expansion of proposed CCF is given in terms of the Fourier series coefficients of the involving distributions and patterns as well as other parameters of the environment