## 3 Cognitive Radio Engine Platform Usage Scenario
### Available Channel Extraction Method via Conducting the Reasoning Engine
#### 3.4.1 Reasoning from the PU Traffic Reference Model
This paper considers the case-based reasoning approach to extract a group of available channels for a cognitive radio node operating in a tactical sensor network. For this objective, inspection of the histogram representing the channel usage pattern of a PU is initially conducted using the learning engine. During the second step, the resulting histogram is matched with reference traffic models previously stored in the learning engine; this step is to determine which traffic model is highly similar. During the third step, as the final step in the case-based reasoning process, the group of channels is extracted. To provide some insight into the procedure for matching the PU traffic pattern, Table 3 delivers a few examples that highlight the feature of characterizing the shape of the histogram in terms of the mean, variance, skewness, and kurtosis. There are nine reference traffic models, which can be distinguished from each other by analyzing these intrinsic signatures that determine the shape of the histogram. In Table 3, the first traffic model in the leftmost column has the lowest mean value, and the mean value gradually increases toward the ninth traffic model. Thus, the first traffic model indicates the situation of low PU activity for every channel, whereas the ninth traffic model corresponds to high PU activity. In this work, the PU traffic models stored up to the previous reasoning period are regarded as reference PU traffic models. The reasoning process determines which traffic model among the reference PU traffic models matches the newly-acquired histogram constructed by the recently-observed samples that are relevant to the PU traffic. In this case, to assess the degree of similarity, the mean and the second, third, and fourth central moments can be utilized to match the traffic models [21; 22]. The mean value of \(P_{on}^{n}\) is denoted as the central moment associated with the histogram representing the distribution of the frequency of the PU occupancy probability value. The \(k\)th central moment is defined as in Equation (9), \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**PU Traffic Model** & **1** & **2** & **3** &... & **9** \\ \hline Mean (\(\mu\)) & 0.1 & 0.2 & 0.3 &... & 0.9 \\ Variance (\(\mu_{2}\)) & 0.025 & 0.052 & 0.069 &... & 0.025 \\ Skewness (\(\gamma_{1}\)) & 2.888 & 1.569 & 0.850 &... & \(-\)2.776 \\ Kurtosis (\(\gamma_{2}\)) & 9.540 & 1.792 & 0.308 &... & 9.505 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Examples of the reference PU traffic models. \[\hat{\mu}_{k}=\frac{1}{N}\sum\limits_{n=1}^{N}\left(P_{on}^{n}-P_{on}^{Arg}\right) ^{k}. \tag{9}\]  
Furthermore, the relationships introduced in Equation (10) describe how to generate the second moment through the fourth moment, i.e.,  
\[\hat{\mu}_{2} =m_{2}-\mu^{2}, \tag{10}\] \[\hat{\mu}_{3} =m_{3}-3\mu_{2}+2\mu^{3},\] \[\hat{\mu}_{4} =m_{4}-4\mu m_{3}-6\mu^{2}m_{2}-3\mu^{4}\]  
where \(\mu=P_{on}^{Arg}=\frac{1}{N}\sum\limits_{n=1}^{N}P_{on}^{n}\), the second central moment becomes the variance of \(P_{on}^{n}\), and the third and fourth central moments are used to achieve the skewness and the kurtosis. With the help of Equation (10), the skewness \(\gamma_{1}\) and the kurtosis \(\gamma_{2}\) are calculated by Equation (11):  
\[\gamma_{1}=\frac{\hat{\mu}_{3}}{\hat{\mu}_{2}^{3/2}}\,,\quad\gamma_{2}=\frac{ \hat{\mu}_{4}}{\hat{\mu}_{2}^{3}}-3\,. \tag{11}\]  
The mean, variance, skewness, and kurtosis corresponding to the \(i\)th traffic model, which is one of \(I\) models comprising the overall PU reference traffic model structured for the previous reasoning period, are calculated based on recently-acquired samples.