## 3 Simulation Results
Figure 5 shows the achievable average throughput versus the total battery capacity of the SU node. Based on the output of the classifier, transmission power varied in each iteration. Then, the corresponding throughput was calculated according to Equation (9). The term average refers to the calculation in two phases. In the first phase, the average value of the throughput was calculated as the ratio of total achieved throughput (obtained by a single node in 10,000 iterations) to the number of opportunities for transmission. The result was then averaged on the total number of observations, which is 2000. The resultant values were used to obtain Figure 5. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Name** & **Symbol** & **Value** \\ \hline One Slot Duration & \(T\) & 100 ms \\ Sensing Time & \(\tau_{S}\) & 3 ms \\ Bandwidth & \(W\) & 1 MHz \\ Sensing Samples & \(M\) & 300 \\ Training Observations & & 500 \\ Testing Observations & & 2000 \\ Prob. of Detection of Reliability Thresholds & \(P_{d1},P_{d2},P_{d3},P_{d4}\) & 0.95, 0.9, 0.85, 0.8 \\ Residual Energy Classification Thresholds & \(\alpha_{1},\alpha_{2},\alpha_{3}\) & 25, 50, 75(\%) \\ Reference Energy & \(E_{ref}\) & 20 Packets \\ Energy Difference & \(E_{diff}\) & 5 Packets \\ Kernel Function & & Polynomial \\ k-fold Cross-validation & & 4 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Simulation Parameters. Figure 4: Comparison of the accuracy of the support vector machine (SVM)-based classifiers trained with linear, radial-basis function (RBF), and polynomial kernel functions applied in proposed scheme. The throughput was achieved for two values of \(\gamma_{p}=-15\) dB and \(\gamma_{p}-5\) dB. The results of the proposed algorithm are compared to conventional two-class spectrum sensing (\(H_{0}\) and \(H_{1}\)) in two scenarios. First, the max transmission power (the transmission power for \(C_{4}\)) in the proposed scheme is used for transmission in \(H_{0}\) sensing result, labeled as _Max Tx Power_ in the figure. Secondly, the minimum transmission power (used for \(C_{1}\)) in the proposed scheme is used for transmission in conventional two-class spectrum sensing when PU is sensed absent, labeled as _Min Tx Power_. Note that a similar classifier with similar characteristics and matching sizes of training and testing datasets is used in all scenarios. _Min Tx Power_ outperformed _Max Tx Power_ in terms of throughput for a limited battery capacity because of a higher number of transmission attempts. However, we can see from the figure that the proposed scheme achieves efficient performance compared to the other two scenarios. In all cases the throughput follows an almost constant trend when battery capacity is increased from 1500 packets in SU node. The reason is the usage of energy harvesting equipped-SU node and the fixed 10,000 number of iterations for SU to sense and transmit. When the battery capacity is low, the battery is emptied with a few number of transmission executions. Then the SU node waits to store enough residual energy for transmission using energy harvesting function. With increase in the battery capacity (such as above 1500 packets), there is low chances of SU to be out of battery. At these higher battery capacity values, the throughput is affected by the number of attempts of transmissions rather than the battery capacity. The theoretical results of the proposed scheme are also given in the Figure 5. In the paper, theoretical results in machine learning mainly deal with a type of inductive learning called supervised learning. In supervised learning, an algorithm is given samples that are labeled in some useful way. To get a theoretical performance of the proposed scheme, which can be considered as \"upper bound\" of the performance the proposed scheme, we utilize the following steps: First, a vector containing the activity of PU (\(H\)) is generated with a 50% probability of the PU's presence. Then, the PU's signals are generated for each of the activities of PU.