# A Correlation-Based Sensing Scheme for Outlier Detection in Cognitive Radio Networks
## 4 Numerical Evaluation  
In this section, we numerically evaluate the performance of the proposed scheme considering the parameters given in Table 1.  
To verify the effectiveness of the proposed scheme, we considered three scenarios. In the first scenario, we considered the only existence of the OMU with the normal SUs in the network. The OMUs are very sensitive to the performance of the network. Figure 3 shows the simulation results when the outlier behaves as an OMU. It can be observed that the normal SUs lie in the range of the lower and the upper quartile limits defined by the box-whisker plot, whereas the OMU lies outside the limits. These lower and upper quartiles define the boundary of the normal SUs in the network. Table 2 presents the values of the SNRs, the quartile, IQR and the lower and the upper quartile limits of the SUs in the network. In the second scenario, we considered only the existence of the ROMU and the normal SUs in the network. The ROMU behaves randomly with the probability \(p\) and appears as a normal SU with the probability 1-\(p\). Figure 4 shows the simulation results in this scenario. The upper and lower quartile limits are defined in Table 3. It can be shown from Figure 4 that the box-whisker plot defines the limits of the lower and upper quartiles for the normal SUs and the proposed scheme can easily classify the normal SUs in this limit, whereas the ROMU response is different from the normal SUs, and easily identified in the system, which shows the effectiveness of the proposed scheme. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Values** \\ \hline Number of SUs & 10 \\ Number of OMUs & 1 \\ Number of ROMUs & 1 \\ Signal-to-noise ratio (SNR) [dB] & \(-\)30 to \(-\)20 \\ Number of iteration & 10,000 \\ Samples in each sensing interval & 270 \\ Sensing time & 1 ms \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Simulation parameters. Figure 3: Correlation vs. signal-to-noise ratio (SNR), when an opposite malicious user (OMU) exists in the network. In the third scenario, we considered the existence of both the OMU and ROMU in the network. Table 4 defines the upper and the lower quartile limits for the normal SUs. Figure 5 shows the simulation results, when both the OMU and the ROMU are equally distributed. From Figure 5, we can observe that the normal SUs lie within the range of the upper and lower limits, whereas the OMU and ROMU are not in the range of the limits set by the box-whisker plot. Figure 5 shows that the detection results of the OMU were more negative compared to the ROMU. The ROMU behavior was closer to that of the normal SUs and more sensitive care was required for the detection of such outliers or of the MUs. In Figure 6, we show the receiver operator characteristics (ROC) comparison of the proposed scheme with other existing schemes when the MU was present in the network, and when the MU did not exist in the network. Figure 6 demonstrates that when no scheme was applied, the probability of detection decreased and the probability of false alarm \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**SNR (dB)** & **Min** & **Q1** & **Median** & **Q3** & **Max** & **IQR** & **Lower Limit** & **Upper Limit** \\ \hline \(-30\) & \(-0.11872\) & \(0.027923\) & \(0.029733\) & \(0.033575\) & \(0.036673\) & \(0.005652\) & \(0.019445\) & \(0.042053\) \\ \(-28\) & \(-0.11368\) & \(0.024431\) & \(0.029003\) & \(0.032603\) & \(0.038683\) & \(0.008172\) & \(0.012172\) & \(0.044861\) \\ \(-26\) & \(-0.1143\) & \(0.023746\) & \(0.026274\) & \(0.033884\) & \(0.043767\) & \(0.010139\) & \(0.008538\) & \(0.049092\) \\ \(-24\) & \(-0.13541\) & \(0.028492\) & \(0.035867\) & \(0.040777\) & \(0.041255\) & \(0.012285\) & \(0.010063\) & \(0.059205\) \\ \(-22\) & \(-0.14429\) & \(0.03397\) & \(0.040021\) & \(0.042547\) & \(0.045457\) & \(0.008577\) & \(0.021104\) & \(0.055413\) \\ \(-20\) & \(-0.17651\) & \(0.04133\) & \(0.048643\) & \(0.052537\) & \(0.061966\) & \(0.011206\) & \(0.024521\) & \(0.069346\) \\ \hline \hline \end{tabular}
\end{table}