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Exact outage-probability analysis for optimum combining of arbitrarily faded signals in the presence of correlated Rayleigh-faded interferers is not available in the literature. In this paper, we show that the conditional probability density of the reciprocal of the instantaneous signal-to-interference ratio (SIR), given the signal vector, can be represented as the higher order derivative of a simple exponential function in signal power whereby generic formulas for the outage probability and probability density function related to SIR can be determined. The new formulas take simple closed form in terms of the characteristic function of the signal vector. They are, therefore, widely applicable, leading to various results for correlated Rayleigh-, Rician-, and Nakagami-faded signals. Numerical examples are also presented for illustration.