A unified MGF based approach to the analysis of area under the ROC curve of energy detection over generalized fading channels

The performance of energy detection, in terms of the area under receiver operating characteristic (AUC), is investigated. By using its contour integral representation, the generalized Marcum Q-function is reformulated as an analytically attractive exponential integral, which in turn allows for a unified moment generating function (MGF) based approach to the AUC analysis of energy detection in an arbitrarily fading channel. The proposed MGF approach is then modified to include square-law combining (SLC) diversity and is further extended to address partial AUC with SLC.