## 5 Simulation Results
However, the entropy-based detector can still detect the PU signal under good SNR conditions, as shown in Figure 5 (d). The practical interest of MCRN is to determine the relationship between \(P_{m}\) or \(P_{d}\) and \(P_{f}\). Complementary receiver operation characteristic (ROC) curves can be obtained from the plot of \(P_{f}\) against \(P_{d}\) for a given average SNR and the time bandwidth product, \(TW\), with varying thresholds [27]. The complementary ROC curves at the land, sea state \(4\), sea state \(6\) and sea state \(7\), when using the energy detector and entropy-based detector with the optimal number of samples, \(N^{*}\), as local detectors, are shown in Figure 6. Here, we assumed that the average SNR of SU is \(-5\) dB. The result shows that the complementary ROC performance of the entropy-based detector with optimal \(N\) is better than that of the energy detector in the above-mentioned four cases. However, for sea state \(6\) and higher, it cannot detect  
Figure 6: Probability of detection _vs_. the probability of a false alarm at (**a**) the land network; (**b**) sea state 4; (**c**) sea state 6; and (**d**) sea state 7.  
the primary user with a high probability under low \(P_{f}\). Therefore, the cooperative spectrum sensing proposed in Section 4.3 helps to achieve better detection performance for higher sea states. The normalized throughput _versus_\(n\) and \(m\) for the detection constraint equal to \(\alpha_{G}=0.95\) is shown in Figure 7. It is evident from the Figure 7 that the choice of \(m\) and \(n\) has a huge impact on the throughput of MCRN. Moreover, there is a unique optimal point where the throughput of the MCRN is maximal. The optimal \(n\) and \(m\) to maximize the achievable throughput _versus_ the sea state are shown in Figure 8. For the simulations, \(\alpha_{G}\) and \(\beta_{G}\) are taken as \(0.9\) and \(0.1\), respectively. We found that for the different sea states, ranging from \(3\) to \(6\), majority rule is either optimal or near optimal. The complementary ROC curves for the land, sea state \(4\) and sea state \(6\) for the optimized \(m\)-out-of-\(n\) rule (discussed in Section 4.4), when using the energy detector and entropy-based detector with optimal \(N\) as local detectors, are shown in Figure 9. The proposed cooperative spectrum sensing scheme is used  
Figure 8: Optimal \(n\) and \(m\)_versus_ the sea state. Figure 3:0 Normalized throughput _versus_\(n\) and \(m\). with the sea state threshold \(\zeta=6.0\). There are a total of fifteen SUs participating in cooperation, and the SNRs of the SUs vary from -10 dB to 10 dB. The distance from the PU varies from zero to 20 km for each SU randomly. Figure 9(a) shows the ROC curves for the land environment in which the probability of detection is high for both the energy detector and entropy-based detector. Thus, our results indicated that both detectors with an optimized \(m\)-out-of-\(n\) fusion rule in cooperative spectrum sensing work reasonably well for the land environment. Figure 9(b) shows the ROC for the sea environment having sea state \(4\). The probability of detection is still good in the case of the energy detection and entropy-based detector with the same number of samples as the local detector. The complementary ROC for sea state \(6\) is shown in Figure 9(c). In the case of energy detection with the optimized \(m\)-out-of-\(n\) rule, the probability of detection for sea state \(6\) does not satisfy the requirement of IEEE 802.22, with the same number of samples as used for entropy-based detection. However, the entropy-based detector with the optimal number of samples, \(N^{*}\), works reasonably well under sea state \(6\).