  This work is devoted to the analysis of the performance of energy detection
based spectrum sensing in the presence of enriched fading conditions which are
distinct for the large number of multipath components and the lack of a
dominant components. This type of fading conditions are characterized
efficiently by the well known Nakagami${-}q$ or Hoyt distribution and the
proposed analysis is carried out in the context of the area under the receiver
operating characteristics (ROC) curve (AUC). Unlike the widely used probability
of detection metric, the AUC is a single metric and has been shown to be rather
capable of evaluating the performance of a detector in applications relating to
cognitive radio, radar systems and biomedical engineering, among others. Based
on this, novel analytic expressions are derived for the average AUC and its
complementary metric, average CAUC, for both integer and fractional values of
the involved time-bandwidth product. The derived expressions have a tractable
algebraic representation which renders them convenient to handle both
analytically and numerically. Based on this, they are employed in analyzing the
behavior of energy detection based spectrum sensing over enriched fading
conditions for different severity scenarios, which demonstrates that the
performance of energy detectors is, as expected, closely related to the value
of the fading parameter $q$.
