## 2 System Model
### Sensing Result Classification  
The classification patterns of the received signal energy range and the residual energy of the SU node are given in Figure 3a,b, respectively. The \(H_{0}\) hypothesis on the PU's received signal is classified into \(k\) discrete regions, \(reg_{n}\), by using \(k\) reliability thresholds, \(\lambda_{n}=\{P_{dn},P_{fn}\}\), where \(n=1,2,...,k\). The region under hypothesis \(H_{1}\) can be considered a single class in which the SU does not execute transmission. The threshold for which \(n=k\) defines the boundary between the \(H_{1}\) and \(H_{0}\) hypotheses. Let the residual energy of the SU node be denoted by \(E_{r}\). The residual energy of the node is also classified into \(j+1\) discrete regions by using thresholds \(\alpha_{m}\), where \(m=1,2,...,j\), as shown in Figure 3b. The objective is to choose the transmission power of the SU node based on the energy level of the sensed PU signal and the residual energy in the SU node's battery. The higher the sensed energy level, the lower the transmission power of the SU node. In contrast, the higher the residual energy in the SU node's battery, the higher the transmission power of the SU node. The reason is that the higher sensed energy means a higher probability of the PU's presence, and hence, lower transmission power should be selected to reduce interference with the PU signal by the SU, because it can be a missed detection where the SU node did not detect the presence of the PU. The selection of lower transmission power when the residual energy of the SU node is low increase the energy efficiency of the system, and thus, increase the capacity. The simulation results verify these statements by achieving higher throughput under the proposed scheme, compared to conventional systems where only two classes are considered, i.e., \(H_{0}\) and \(H_{1}\). The total number of classes is obtained using \(k\) regions of the received signal energy and \(j\) discrete levels of the battery. The classification obtained by dividing the received signal energy into five regions (including the region under hypothesis \(H_{1}\)), i.e., \(k=4\), and quantizing the residual energy of the SU node into four levels, i.e., \(j=3\), is given in Table 1. The \(L_{i}\) for \(i=1,2,3,4\) and \(reg_{i}\) for \(i=1,2,...,5\) represent the discrete residual energy levels and quantized received signal energy levels, respectively. \(Ci\) is the output class of the classifier categorized based on the residual energy and received signal energy. \(C_{0}\) is the class when the SU node does not transmit. In \(reg_{5}\) of the received signal energy, the SU does not transmit irrespective of the residual energy in the SU node's battery; refer to Table 1. This region is considered under the hypothesis \(H_{1}\) where the detection probability of PU is high. For regions of the received signal energy other than \(reg_{5}\), the SU node selects transmission power \(P_{T\bar{i}}\) according to the output class, \(Ci\), of the classifier, which is based on the residual energy of the SU node. Class \(C_{1}\) refers to the scenario in which the SU node selects the lowest transmission power, \(P_{T1}\). Similarly, transmission power \(P_{T2}\), chosen in case of \(C_{2}\), is comparatively higher than \(P_{T1}\) and lower than \(P_{T3}\) (selected under \(C_{3}\)). The highest value of transmission power, \(P_{T4}\), is selected when the classifier gives output of \(C_{4}\), the class in which the received signal energy is in the lowest region but the residual energy is at the highest level. The four values of transmission power, \(P_{T\bar{i}}\) for \(i\in\{1,2,3,4\}\), respective to each output class, i.e., \(Ci\) for \(i\in\{1,2,3,4\}\), are predefined by the system. The SU node selects one of the four values according to the output of the classifier. The selection of transmission power values is also critical to improving the performance of the system.