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An approach to the performance analyses of dual selection combining (SC) diversity receiver over correlated alpha-mu fading channels with the arbitrary parameters is presented. Fading between the diversity branches and interferers is correlated and distributed with alpha-mu distribution. Infinite series expressions are obtained for the output SIR's probability density function (PDF), cumulative distribution function (CDF) and an important measure of the system's performances, the outage probability (OP). An average error probability is efficiently evaluated for coherent and non-coherent modulation schemes such as coherent frequency-shift keying (CFSK), coherent phase-shift keying (CPSK), binary frequency-shift keying (BFSK) and binary differentially phase-shift keying (BDPSK). Numerical results are presented to show the effects of various parameters such as fading severity, input SIR unbalance and the level of correlation between received desired signals and interferences on system's performances.