## 3 Simulation Results
### Homogeneous Environment  
Comparative analysis experiments on detection performance are conducted in a homogeneous environment. The average detection probability of each detector in a homogeneous environment with _SNR_ ranging from 10 dB to 25 dB is shown in Table 4. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Leading Window** & **Lagging Window** & **Different Means?** & **VI-CFAR Adaptive Threshold** & **Equivalent** \\
**Variable?** & **Variable?** & **Means?** & **Adaptive** & **CFAR** \\ \hline No & No & No & \(T_{N}\cdot(\sum X_{A}+\sum X_{B})\) & CA \\ No & No & Yes & \(T_{F}\cdot FOSTA(k_{F})\) & FOSTA \\ No & Yes & - & \(\tau h_{KLQ}(X_{e})\) & KLQ \\ Yes & No & - & \(\tau h_{KLQ}(X_{e})\) & KLQ \\ Yes & Yes & - & \(\tau h_{KLQ}(X_{e})\) & KLQ \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The selection rules for the detection algorithm in KLQVI-CFAR. In Table 4, KLQVI(6,3) denotes KLQVI-CFAR with \(r_{1}=6\) and \(r_{2}=3\), OS(28) denotes OS-CFAR with the ordinal value \(k=28\), KLQ(6,3) denotes KLQ-CFAR with \(r_{1}=6\) and \(r_{2}=3\), and IBQ(6,3) denotes IBQ-CFAR with \(r_{1}=6\) and \(r_{2}=3\). Table 4 shows that KLQVI-CFAR achieves an average detection probability that is 1.47% higher than KLQ-CFAR, 2.93% higher than OS-CFAR, and 1.31% higher than IBQ-CFAR. This indicates that KLQVI-CFAR exhibits superior detection performance in homogeneous environments compared to the other three methods. Moreover, the higher average detection probability of KLQVI-CFAR compared to VIHCEMOS-CFAR suggests that the incorporation of the FOSTA detection algorithm improves the detector's robustness across diverse background scenarios. To assess the significance of performance differences between KLQVI-CFAR, KLQ-CFAR, and VIHCEMOS-CFAR, Analysis of Variance (ANOVA) is employed. ANOVA is used to test whether there are significant differences in the means of different groups. \(F\) represents the ratio of between-group variance to within-group variance, with a larger \(F\) indicating greater between-group differences. \(P\) is used to determine whether the differences between groups are statistically significant, and \(P\) less than 0.05 indicates that the differences are significant. The ANOVA results for KLQVI-CFAR, KLQ-CFAR, and VIHCEMOS-CFAR are shown in Table 5.  
As shown in Table 5, in homogeneous environment, the sum of squares between groups for KLQVI-CFAR, KLQ-CFAR, and VIHCEMOS-CFAR is 8.1 \(\times\) 10\({}^{-4}\), the sum of squares within groups is 3.5 \(\times\) 10\({}^{-4}\), \(F\) is 30.8367, and \(P\) is 1.0671 \(\times\) 10\({}^{-7}\). Since \(P\) is less than 0.05, it indicates that the differences between groups are statistically significant. The environmental misjudgment probability refers to the probability that the current environment is incorrectly classified as another environment by the detector. When environmental misclassification occurs, detection algorithms that are unsuitable for the current environment may be selected by traditional detectors, leading to a deterioration in detection performance. Therefore, the environmental misjudgment probability is considered a critical metric closely associated with the performance of the detector. This probability is calculated by performing 10\({}^{4}\) Monte-Carlo experiments at each SNR level and recording the frequency of incorrect environment classifications made by the detector. VIHCEMOS-CFAR and KLQVI-CFAR use the same environmental classification method, so their environmental misjudgment probabilities are the same, as shown in Figure 3.  
From Figure 3, the average probability of misjudging a homogeneous environment as a clutter edge environment is as high as 9.89%; as a result, the detection performance of VIHCEMOS-CFAR is worse than that of CA-CFAR in a homogeneous environment. In comparison, the FOSTA detection algorithm is used in KLQVI-CFAR in a clutter edge envi