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Motivated by the suitability of the Weibull distribution to model multipath fading channels, the performance of L-branch selection combining (SC) receivers, with non-identical statistics, is presented. Deriving a useful expression for the probability density function of the SC output signal-to-noise ratio (SNR), important performance metrics are studied. More specifically, a closed-form expression is derived for the moments of the combiner output SNR, which is used to study the average output SNR and the amount of fading. The average symbol error probability for several coherent and non-coherent, binary and multilevel modulation schemes is also obtained in closed-form.