# A Correlation-Based Sensing Scheme for Outlier Detection in Cognitive Radio Networks
## 4 Numerical Evaluation

Table 2: Box-whisker plot data of the correlation results under OMU users only. Figure 4: Correlation vs. SNR, when a random opposite malicious user (ROMU) exists in the network. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**SNR** & **Min** & **Q1** & **Median** & **Q3** & **Max** & **IQR** & **Lower Limit** & **Upper Limit** \\ \hline \(-30\) & \(-0.04204\) & \(0.004687\) & \(0.00771\) & \(0.013285\) & \(0.020143\) & \(0.008598\) & \(-0.00821\) & \(0.026181\) \\ \(-28\) & \(-0.04186\) & \(0.006307\) & \(0.009428\) & \(0.011756\) & \(0.016341\) & \(0.005449\) & \(-0.00187\) & \(0.019929\) \\ \(-26\) & \(-0.05041\) & \(0.003967\) & \(0.010962\) & \(0.01545\) & \(0.021564\) & \(0.011483\) & \(-0.01326\) & \(0.032674\) \\ \(-24\) & \(-0.0499\) & \(0.01026\) & \(0.01173\) & \(0.013742\) & \(0.018565\) & \(0.003482\) & \(0.005036\) & \(0.018966\) \\ \(-22\) & \(-0.05722\) & \(0.007603\) & \(0.013448\) & \(0.017124\) & \(0.022818\) & \(0.009521\) & \(-0.00668\) & \(0.031406\) \\ \(-20\) & \(-0.06726\) & \(0.009589\) & \(0.017555\) & \(0.019618\) & \(0.021469\) & \(0.010028\) & \(-0.00545\) & \(0.03466\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Box-whisker plot data of the correlation results under ROMU users only. and probability of misdetection increased. Furthermore, when the proposed scheme was applied in the presence of MU, the performance was better than other existing schemes. Tabular and graphical results show that the proposed scheme was effective in detecting the outliers or MUs in CSS environments. The proposed scheme had the ability to identify \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**SNR (dB)** & **Min** & **Q1** & **Median** & **Q3** & **Max** & **IQR** & **Lower Limit** & **Upper Limit** \\ \hline \(-30\) & \(-0.1233\) & \(0.01559183\) & \(0.02097\) & \(0.023847249\) & \(0.025981888\) & \(0.008255\) & \(0.003209\) & \(0.03623\) \\ \(-28\) & \(-0.12418\) & \(0.01502566\) & \(0.02049\) & \(0.02298377\) & \(0.03319715\) & \(0.007903\) & \(0.003172\) & \(0.034782\) \\ \(-26\) & \(-0.12967\) & \(0.01767262\) & \(0.02225\) & \(0.0264105\) & \(0.02960883\) & \(0.008738\) & \(0.004566\) & \(0.039517\) \\ \(-24\) & \(-0.14605\) & \(0.02419445\) & \(0.02566\) & \(0.030521757\) & \(0.031995221\) & \(0.006327\) & \(0.014703\) & \(0.040013\) \\ \(-22\) & \(-0.15155\) & \(0.01600466\) & \(0.02709\) & \(0.031661185\) & \(0.035777566\) & \(0.015657\) & \(-0.00748\) & \(0.055146\) \\ \(-20\) & \(-0.1768\) & \(0.0300924\) & \(0.03288\) & \(0.033382178\) & \(0.038434105\) & \(0.00329\) & \(0.025158\) & \(0.038317\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Box-whisker plot data of the correlation results under both OMU and ROMU users. Figure 5: Correlation vs. SNR, when both the OMUs and ROMUs exist in the network. Figure 6: ROC curve of the proposed in comparison with other schemes. and classify both types of outliers, i.e., the OMU and the ROMU. By utilizing the box-whisker plot, an SU was classified as an outlier by the FC if its result lay above the upper quartile limit or below the lower quartile limit. Through the simulation results, we have shown that the proposed scheme can easily detect the outlier of OMU and ROMU in nature.