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Diversity techniques for various communication and MIMO systems exploit the spatial and temporal diversity attributes to mitigate the ill effects of the fading channels. To evaluate these techniques, a method to generate multiple correlated fading channels is crucial. We propose a unified approach capable of generating correlated flat-fading envelope processes with the desired auto-correlation functions, cross-correlation functions, and probability density functions (pdfs). The proposed approach utilizes the Gaussian vector autoregressive process and the inverse transform sampling techniques. Comparing to the past research focusing on generating fading channels of the same family, the novelty of the proposed approach is its capability to generate fading processes of heterogeneous pdfs. Three examples are demonstrated. In the first example, the autocorrelated Nakagami channel is generated. The second example is designed to generate correlated 2x2 MIMO Rayleigh channels. In the third example, the proposed approach generates three correlated channels having Nakagami, Rician, and Rayleigh pdfs. The settings of the first two examples are adopted from previously published results, which are intended to verify the effectiveness of our proposed approach to tackle previously known problems. The third example demonstrates the novelty of the proposed approach to generate correlated channels of heterogeneous pdfs.