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The effects of incoherently combining on dual-branch equal-gain combining (EGC) receivers in the presence of correlated, but not necessarily identical, Nakagami-m fading and additive white Gaussian noise are studied. Novel closed-form expressions for the moments of the output signal-to-noise ratio (SNR) are derived. Based on these expressions, the average output SNR and the amount of fading are obtained in closed-form. Moreover, the outage and the average bit error probability for binary and quadrature phase-shift keying are also studied using the moments-based approach. Numerical and computer simulation results clearly depict the effect of the carrier phase error, correlation coefficient, and fading severity on the EGC performance. An interesting finding is that higher values of the correlation coefficient results to lower irreducible error floors.