Entropy and Energy Detection-Based Spectrum Sensing Over $\mathcal{F}$ -Composite Fading Channels

In this paper, we investigate the performance of energy detection-based spectrum sensing over $\mathcal {F}$ composite fading channels. To this end, an analytical expression for the average detection probability is first 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 the 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 differential entropy and cross entropy are also formulated and assessed for different average SNR, multipath fading, and shadowing conditions. Then, the relationship between the differential entropy of $\mathcal {F}$ composite fading channels and the corresponding ROC/AUC is examined where it is shown that the average number of bits required for encoding a signal becomes small (i.e., low differential entropy) when the detection probability is high or when the AUC is large. The difference between composite fading 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.