## 2 System Model  
The flowchart of the proposed scheme is shown in Figure 1. First, the statistical features are extracted from the received signal, as shown in Figure 1a. The probability of detection (\(P_{d}\)) or the probability of false alarm (\(P_{f}\)) is obtained from the input signal simultaneously. The input signal is sorted into various classes based on \(P_{d}\) (or \(P_{f}\)) and the residual energy values ranging from 0% to 100%. After classification, the feature observations that were extracted from the received signal are labeled, as explained in next subsection. The training dataset is obtained in the same way. In the testing phase, the features are extracted from the input test signal, and the residual energy of the node is added as the fourth element of observation. These observations are then given as input to the trained classifier for classification. The classifier provides output in the form of a single value corresponding to the label of the observation class.  
The system model considers a pair of SUs operating within the range of PU transmitter, as shown in Figure 2. The bold line represents the signal of the SU channel, whereas the dashed line denotes the PU signal. For simplicity, a single channel is assumed on which both the PU and the SU operate. The SU senses the channel and extracts the features from the input signal, then concatenates the residual energy as a percentage. The trained SVM puts the observation into one of the predefined classes. The SU transmission decision, along with the transmission power, is selected based on the output of the SVM. If the decision is for no transmission, the SU will wait for the next time slot to start sensing the channel again.  
Figure 1: Flowchart of the proposed scheme: (**a**) the training phase; and (**b**) the testing phase.  
Figure 2: System model considering a pair of secondary users (SUs) operating in the range of primary users (PUs).  
The sensing result under hypotheses \(H_{0}\) and \(H_{1}\) is given as follows:  
\[\left\{\begin{array}{l}H_{0}:x_{i}=n_{i},\\ H_{1}:x_{i}=s_{i}+n_{i},\end{array}\right. \tag{1}\]  
where \(s_{i}\) and \(n_{i}\) for \(i=1,2,...,M\) represent the received PU signal and the additive white Gaussian noise at the \(i\)th sample, respectively, and \(M\) is the total number of sensing samples in one observation obtained in a sensing slot. \(H_{0}\) and \(H_{1}\) denote the hypotheses in which the PU is absent and is present, respectively. The local observation of a SU node is given as  
\[Y=\sum_{i=1}^{M}|x_{i}|^{2}. \tag{2}\]  
For a large value of sensing samples per observation, for instance \(M\geq 300\), the received signal energy can be approximated as a Gaussian distribution, given as follows:  
\[Y\sim\left\{\begin{array}{l}N(M,2M),\qquad\qquad\qquad\qquad\qquad H_{0},\\ N(M(1+\gamma_{p}),2M(1+2\gamma_{p}),\qquad H_{1},\end{array}\right. \tag{3}\]  
where \(\gamma_{p}\) denotes the SNR of the PU signal. The probability of false alarm, \(P_{f}\) (the probability of falsely detecting the PU's presence when the PU is not present), and the probability of detection, \(P_{d}\) (the probability of detecting the PU's presence when the PU is actually present), for given energy threshold, \(\lambda\), of sensing signal are given as follows:  
\[\begin{array}{l}P_{f}=P(Y>\lambda|H_{0})=Q\left(\frac{\lambda-M}{\sqrt{2M}} \right),\\ P_{d}=P(Y>\lambda|H_{1})=Q\left(\frac{\lambda-M(\gamma_{p}+1)}{\sqrt{2M(2 \gamma_{p}+1)}}\right),\end{array} \tag{4}\]  
where \(Q(.)\) is the complementary cumulative distribution of a standard Gaussian, defined as \(Q(x)=\int_{x}^{+\infty}e^{-t^{2}/2}dt\Big{/}\sqrt{2\pi}\).