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A complete statistical characterization of correlated Nakagami channels is either their joint probability density function or their joint characteristic function (CHF), which is indispensable to many applications in wireless communications. The classical correlated multivariate Nakagami model in current use is subject to a restriction that the fading parameters must be identical. We derive a generic correlated Nakagami fading model, in the form of a multiple CHF, allowing for an arbitrary covariance matrix and distinct real fading parameters. The application of the new model to wireless communications is also presented.