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Scattering encountered in many wireless communications scenarios is non-isotropic. Assumption of uniform distribution of Power Azimuth Spectrum (PAS) in a non-isotropic scattering environment introduces significant errors on the second order channel statistics which are the basis for the estimation of some important receiver parameters. Moreover, there are certain applications in communications that rely solely on the statistics of the channel. In this contribution, we use the well-known Jacobi-Anger expansion of the plane wave to develop a discrete-time generalized Rayleigh fading channel model that models the statistics of the channel in closed form in general, non-isotropic and isotropic, scattering environments. We compare the statistics of the channel for different commonly used non-isotropic scattering distributions, first, on the basis of autocorrelation, and, then, using a function (mutual information) of the correlational properties of the channel. In the latter case, through simulations, we observe the effect of varying different parameters like the angular spread, the block length of transmission and the mobile velocity which gives some interesting insights.