A Simple Analytical Expression of Average AUC with Diversity over Composite Fading

In the realm of cognitive radio networks, spectrum sensing stands out as a practical approach to efficiently utilize unoccupied portions of the spectrum. Among the various methods within cognitive radio, energy detection emerges as a straightforward technique to detect primary user signals in the spectrum. However, this method encounters challenges in scenarios involving composite fading effects on the communication channel. The mathematical derivation of the average area under the receiver operating characteristic curve (AUC) is achieved by employing Gaussian-Hermite integration (GH-I) over a shadowed Weibull distribution combined with maximum ratio combining reception (MRC). The accuracy of the derived mathematical expressions is verified through comparison with simulation results.