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Sums of fading envelopes arise in several wireless communications applications, such as equal-gain combining, outage probability, signal detection, etc. In this paper, based on the intricate task of evaluating the exact statistics of such sums, accurate approximations for the outage probability of equal-gain receivers subject to arbitrary independent cochannel interferers are proposed. In our analysis, an M-branch_N-interferer system subject to an alpha-mu fading scenario is considered. The results are obtained in terms of a singlefold integral, which replaces the M times N nested integrals required in the exact solution. The accuracy of our formulation is checked by comparing it with Monte Carlo simulation results. It is shown that approximate and simulated curves are practically indistinguishable from each other.