Optimality of the HDC rules in cooperative spectrum sensing for Cognitive Radio network

Cognitive Radio (CR) sensing has been widely considered as a spectrum scanning mechanism that allows secondary users (SUs) or cognitive radio users to use detected spectrum holes caused by primary user (PU) absence. Hard decision combining (HDC) schemes are proposed to combine the sensing decisions of the collaborated users to come out with a global binary decision on the presence or absence PUs. This paper presents an analytical study on the optimality of HDC rules at which the Bayes risk function is minimized. In this work, the sensing performance of energy detection (ED) is also evaluated in two cases; when the estimated noise power is perfectly known at the SU receiver and when noise uncertainty is present at the SU receiver. The sensing performance of the ED and likelihood ratio test (LRT) of local spectrum sensing (SS) is first compared. Then, the performance of cooperative spectrum sensing (CSS) employing k-out-of-N combining rule has been analyzed. A mathematical derivation of an optimal decision combining rule under low Bayes risk has been formulated. Computer results show that the sensing performance of the ED method slightly outperforms the LRT method within the lower range of probability of false alarm. However, the two methods exhibit almost similar sensing performance within the higher range of probability of false alarm. On the other hand, at lower values of probability of detection, the OR combining rule exhibits the best detection performance over the Majority and AND rules. Finally, it has been found that the optimal decision combining rule to achieve lower Bayes risk function is the Majority distributed decision rule.