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We present a comprehensive cross-correlation model for a multiple-input multiple-output Rayleigh fading channel in an isotropic scattering environment. The scattering environment is assumed to be a microcellular media with sufficient number of scatterers. This implies uniformly distributed angle of departure and angle of arrival either at the transmitter or at the receiver. Simple and reasonable assumptions are made for various relevant physical parameters, such as exponential or normal time-delay distribution and uniform phase change in the receiving waveform. A novel method of modeling is suggested to consider a geometry for the local scatterers. This approach establishes a mathematical relation between the time-delay and the channel gain associated to each dominant propagation path, and uses appropriate probability density function (pdf) for the time-delay profile. This flexible method allows us to characterize a wide range of propagation environments. Cross-correlation function between channels appears to be a multiplication of tow Bessel functions, and two other multiplicative terms. Bessel functions represent the Doppler effect, the carrier frequencies, and the spatial separation, either at the transmitter or at the receiver. The effect of the carrier frequencies also appears on the other terms. Interestingly, the last two terms are η/2-order derivative of the moment generating function of the delay profile at two carrier frequencies, respectively, where η is the environment pathloss exponent. Overall, the model has a closed form and is a generalization of the Clark model.