## 4 Spectrum Sensing in Maritime Cognitive Radio Networks
### Cooperative Spectrum Sensing  
Cooperative spectrum sensing helps to improve the sensing performance with the increase in cooperative SUs. In order to get a cooperative decision, linear fusion rules are applied; the most commonly used fusion rules are AND, OR and majority rules. Upon applying a fusion rule, the fusion center forwards the cooperative decision to all individual SUs [7]. However, the reporting time increases with the increase in cooperative SUs, which results in lower network throughput. Therefore, the optimal number of cooperative SUs and the fusion rule are required to satisfy the detection performance constraints. Let the local decision of the \(ith\) SU be \(D_{i}\), which can be one or zero with respect to the presence or absence of PU, respectively. In the AND rule, the cooperative decision at the fusion center is made by performing the logical AND on all the local decisions reported by SUs. The cooperative decision about the presence of PU is made only when all SUs report the presence of PU, while the cooperative decision about the absence of PU is made when any one of the SUs report absence. In the OR rule, the logic OR is performed at the fusion center on all the local decisions made by SUs. The cooperative decision about the absence of PU is made only when all the SUs report the absence of PU, and the cooperative decision about PU presence is made when one of the SUs reports the PU presence. The majority rule requires at least half of the SUs to report the presence of PU to confirm the presence and _vice versa_. The generalized form of these simple rules uses \(m\)-out-of-\(n\) rules in which the fusion center declares a cooperative decision about PUs presence, if more than \(m\) SUs among \(n\) SUs report the PU presence. The global probability of false alarm and detection is the one which is calculated at the central entity by fusing the results of cooperative SUs. The global probability of detection, \(Q_{d}\), and the global probability of false alarms, \(Q_{f}\), for the \(m\)-out-of-\(n\) rule are given by [PERSON] _et al_. [23]:  
\[Q_{d}=\sum_{j=m}^{n}{n\choose j}P_{d}^{j}(1-P_{d})^{n-j}, \tag{12}\]  
\[Q_{f}=\sum_{j=m}^{n}{n\choose j}P_{f}^{j}(1-P_{f})^{n-j} \tag{13}\]  
where \(P_{d}\) and \(P_{f}\) are the probability of detection and the probability of a false alarm determined by each SU. The total number of SUs participating in cooperation is \(n\), and \(m\) determines the rule among AND, OR and majority. The flow of the proposed cooperative spectrum sensing algorithm for MCRN is shown in Figure 2. There are \(n\) SUs participating in the proposed cooperative spectrum sensing for MCRN. The central entity is capable of measuring the sea state and determining if the sea state is good enough to rely on the spectrum sensing results of the individual SUs. If the sea state is greater than the threshold, \(\zeta\), beyond which the spectrum sensing results are not reliable, the central entity will decide that the channel is not available without considering the spectrum sensing results of individual SUs. However, if the sea state is less than the threshold, \(\zeta\), the optimized \(m\)-out-of-\(n\) will be applied in order to determine the presence or absence of PU. The entropy detector is targeted to find the number of cooperative SUs, \(n\) and \(m\), under the constraint of the global probability of detection, \(\alpha_{G}\), the constraint of the global probability of a false alarm, \(\beta_{G}\), and the sea state to maximize throughput in MCRN. Let \(C_{0}\) be the throughput of an SU operating in the absence of the PU. The practical throughput of an SU without cooperation is calculated [24]. Let \(Th\)  
Figure 2: Proposed cooperative spectrum sensing for the maritime cognitive radio network. denote the practical throughput in the case of cooperative spectrum sensing.