A general outage formula for optimum combining of arbitrarily faded signals with correlated Rayleigh interferers

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. 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 (PDF) related to SIR can be determined. The new formulas take a 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.