## 3 Simulation Results
### Multiple-Target Environment
In order to more intuitively demonstrate the advantages of KLQVI-CFAR in detection performance in multiple-target environments, the detection probabilities of various detectors are shown in Figure 6.  
From Figure 6a-c, KLQVI(6,3) consistently exhibits the best detection performance, indicating that KLQVI-CFAR has stronger detection capability and robustness compared to detectors such as VIHECMOS-CFAR and KLQ-CFAR. For different CFAR detectors, the lower SNR when the detector reaches the same detection probability, the better its detection performance. In order to analyze the performance of the detectors in a multiple-target environment, four interferences are added to \begin{table}
\begin{tabular}{c c c c c c} \hline  & **Sum of Squares** & **Degree of Freedom** & **Mean Square** & **F** & **P** \\ \hline Between groups & 6.9 \(\times\) 10\({}^{-4}\) & 2 & 3.5 \(\times\) 10\({}^{-4}\) & 618.5880 & 2.812 \(\times\) 10\({}^{-23}\) \\ Within group & 1.5 \(\times\) 10\({}^{-5}\) & 27 & 5.6 \(\times\) 10\({}^{-7}\) & & \\ Total & 7.1 \(\times\) 10\({}^{-4}\) & 29 & & & \\ \hline \end{tabular}
\end{table} 
Table 7: ANOVA in multiple-target environments when there is one interference in each of the leading windows and lagging windows. Figure 5: Environmental misjudment probabilities when (**a**) there are three interferences in the leading window, (**b**) there are four interferences in the lagging window, (**c**) there is one interference in each of the leading windows and lagging windows. Figure 6: The detection probability of various detectors when (**a**) there are three interferences in the leading window, (**b**) there are four interferences in the lagging window, (**c**) there is one interference in each of the leading window and lagging window. the reference window, and _Pd_ is set as 0.5. The SNR required for each detector to meet the detection probability is shown in Table 8.  
From Table 8, CA detection method cannot meet the detection requirement of _Pd_ = 0.5. Furthermore, when _Pd_ = 0.5 dB, the SNR required for KLQVI (6,3) is 2.22 dB lower than that required for VIHCEMOS, and 0.09 dB lower than that required for KLQ (6,3). Therefore, KLQVI(6,3) has better detection performance than VIHCEMOS and KLQ(6,3), and the designed KLQVI-CFAR is effective and reasonable. In order to illustrate the superiority of the anti-interference ability of KLQVI-CFAR in multiple-target environments, the number of interferences is increased from 0 to 5, and the detection probability of various CFAR detectors at SNR = 20 dB are shown in Table 9.  
As shown in Table 9, when the number of interferences is less than or equal to 3, the detection probability of KLQVI-CFAR is similar to that of KLQ-CFAR, IBQ-CFAR, and VIHCEMOS-CFAR. However, when the number of interferences exceeds 3, the detection probability of KLQVI-CFAR outperforms all other compared detectors. Thus, it can be seen that KLQVI-CFAR has better anti-interference ability than VIHCEMOS-CFAR in multiple-target environments. The Receiver Operating Characteristic (ROC) curve is commonly used to evaluate the performance of CFAR detectors, illustrating the relationship between false alarm probability and detection probability for each detector under a fixed SNR. A higher detection probability at the same false alarm probability is associated with better detector performance. Four interferences are added to the reference window, SNR is set as 15 dB, and the ROC curves of various detectors in a multiple-target environment are shown in Figure 7.  
As shown in Figure 7, the ROC curves from top to bottom are KLQVI(6,3), KLQ(6,3), IBQ(6,3), OS(28), VIHCEMOS and CA, respectively. Therefore, it can be seen that KLQVI-CFAR has stronger robustness to the detection results and shows better detection performance. When there are interferences in the reference window, the detection threshold of the detector will unexpectedly increase, which will result in a lower observed false alarm probability \(P_{fa}\) than the pre-set false alarm probability \(P_{FA}\).