  In this paper, we investigate the performance of energy detection-based
spectrum sensing over F composite fading channels. To this end, an analytical
expression for the average detection probability is firstly derived. This
expression is then extended to account for collaborative spectrum sensing,
square-law selection diversity reception and noise power uncertainty. The
corresponding receiver operating characteristics (ROC) are analyzed for
different conditions of the average signal-to-noise ratio (SNR), noise power
uncertainty, time-bandwidth product, multipath fading, shadowing, number of
diversity branches and number of collaborating users. It is shown that the
energy detection performance is sensitive to the severity of the multipath
fading and amount of shadowing, whereby even small variations in either of
these physical phenomena can significantly impact the detection probability. As
a figure of merit to evaluate the detection performance, the area under the ROC
curve (AUC) is derived and evaluated for different multipath fading and
shadowing conditions. Closed-form expressions for the Shannon entropy and cross
entropy are also formulated and assessed for different average SNR, multipath
fading and shadowing conditions. Then the relationship between the Shannon
entropy and ROC/AUC is examined where it is found that the average number of
bits required for encoding a signal becomes small (i.e., low Shannon entropy)
when the detection probability is high or when the AUC is large. The difference
between composite and traditional small-scale fading is emphasized by comparing
the cross entropy for Rayleigh and Nakagami-m fading. A validation of the
analytical results is provided through a careful comparison with the results of
some simulations.
