## 3 Simulation Results  
Simulations are performed using MATLAB (R2017a, The MathWorks Inc., Natick, MA, USA, 2017). A dataset for each training and testing phase, having 500 and 2000 observations, respectively, is generated using Equation (1). First, the activity of PU was generated with a 50% probability of the PU's presence. Then, the PU's signals were generated for each of the generated activity of PU. The percentage residual energy values of the node are generated randomly from 0 to 100 with a uniform distribution. Finally, each observation was labeled based on the probability of detection obtained from the sensed signal and the residual energy of node. This means that, in each training and testing dataset, the distribution of observations over the five classes was not fixed and were obtained randomly. The observations in training dataset, which is consisted of the three features (given in Table 3) extracted from input received signal concatenated with the residual energy of the node, are labeled as classes \(C_{0}\) to \(C_{4}\), as shown in Figure 1. In testing phase, the harvested energy is added with a Poisson distribution to the residual energy of SU node in each iteration. After updating the residual energy, the received signal is classified again using the updated residual energy of SU node. The recent classification result of SVM obtained using the updated observation is then used to obtain the channel capacity. In this way, the throughput of the channel is obtained for each iteration. The simulation steps are summarized as follows: the SVM-based classifier is trained in a _one-versus-rest_ approach using training dataset consisting of 500 labeled input observations. Each observation is obtained by concatenating the three statistical features extracted from received signal and the residual energy of the node as the fourth feature. The testing dataset of 2000 unlabeled observations is used to analyze performance. Table 4 lists the values of simulation parameters assumed in the experiment. The performance of the classifier is analyzed using accuracy, defined as the ratio of correct classifications to the number of total test observations. Figure 4 shows the accuracy comparison of three separate classifiers trained with three kernel functions (linear, RBF, and polynomial) applied in proposed multi-hypothesis scheme of spectrum sensing versus the SNR of the PU, \(\gamma_{p}\), ranging from \(-25\) dB to \(0\) dB. The classifiers trained with the RBF and the polynomial kernel function always performed better than the linear kernel function, which attained accuracy between 60% and 65%, irrespective of \(\gamma_{p}\). The former mentioned two classifiers followed a similar trend of improving accuracy with an increase in \(\gamma_{p}\). The minimum accuracy of 72% was achieved for \(\gamma_{p}=-25\) dB with the RBF kernel. The accuracy varied slightly when \(\gamma_{p}\) increased to \(-12\) dB. Further increases \begin{table}
\begin{tabular}{c} \hline \hline \(X_{1}=10\times\left(\frac{1}{M}\sum\limits_{i=1}^{M}s_{i}\right)^{10}\). \\ \(X_{2}=\frac{1}{M}\sum\limits_{i=1}^{M}s_{i}^{2}\). \\ \(X_{3}=\sqrt{\left(\sum\limits_{i=1}^{q}s_{i}\right)^{3}}\); \(q\leq M\), \(s_{i+1}\geq s_{i}\). \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Features extracted from received signal of PU. in \(\gamma_{p}\) rapidly increased accuracy to 95% to 96% for \(\gamma_{p}=-5\) dB. Additional raise in \(\gamma_{p}\) from \(-5\) dB does not affect the performance of the classifier considerably. The polynomial kernel-based classifier followed a trend similar to that of the RBF kernel, although the accuracy ranged from 75% to 80% for \(\gamma_{p}=-25\) dB \(\sim-12\) dB. The better performance of polynomial kernel function-based classifier, compared to the counter two kernel functions-based classifiers, at a low \(\gamma_{p}\), lets it be used for further simulations, although it achieved comparable accuracy at higher \(\gamma_{p}\) to the RBF kernel function-based classifier.