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We derive a comprehensive analytical framework for the ED over generalized, extreme, and non-linear fading conditions which addresses the topic completely. This is carried out for both conventional and diversity receptions and it is based on the area under the ROC curve (AUC), which is an efficient performance measure that is widely used in physical sciences and engineering. This differentiates the considered methodology from the aforementioned routine approaches and additionally providesdoi:10.1109/tvt.2017.2692278 fatcat:hgalcromu5fgfftu53fztxpmsi