# Adaptive Constant False Alarm Detector Based on Composite Fuzzy Fusion Rules
## 5 Simulation Experiment Results and Analysis
### CFKLQ-CFAR Detection Performance
#### 5.1.2 Statistical Test  
To test the difference in the average detection probability between CFKLQ-CFAR and ASKLQ-CFAR, paired \(t\)-tests, and ANOVA are performed using SPSS26.0 software. First, a \begin{table}
\begin{tabular}{l c} \hline \hline
**Weight Distribution** & **Average Detection Probability** \\ \hline \([0.25,0.25,0.25,0.25]\) & 55.41\% \\ \([0.4,0.1,0.1,0.4]\) & 55.60\% \\ \([0.5,0.1,0.1,0.3]\) & 55.42\% \\ \([0.3,0.1,0.1,0.5]\) & 55.70\% \\ \([0.1,0.1,0.1,0.7]\) & 55.90\% \\ \([0.1,0,0.0,9]\) & 56.02\% \\ \([0.08,0,0,0.92]\) & 55.93\% \\ \([0,0,0,1]\) & 55.96\% \\ \([0.12,0,0.08]\) & 55.98\% \\ \([0.15,0,0,0.85]\) & 55.97\% \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The average detection probability of CFKLQ-CFAR with different weights. \begin{table}
\begin{tabular}{l c c c c c c} \hline \hline
**Environment** & **KLQ (6, 3)** & **MAXKLQ** & **MINKLQ** & **APKLQ** & **ASKLQ** & **CFKLQ** \\ \hline Homogeneous environment & 56.40\% & 57.42\% & 56.38\% & 56.40\% & 57.43\% & 57.45\% \\ One interference in the leading window & 54.11\% & 55.64\% & 54.15\% & 54.35\% & 56.74\% & 56.78\% \\ Three interferences in the leading window & 52.33\% & 53.98\% & 52.41\% & 52.68\% & 55.02\% & 55.04\% \\ One interference in both windows & 53.26\% & 54.81\% & 53.26\% & 53.50\% & 55.96\% & 56.02\% \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The average detection probability of each detector in different environments. paired \(t\)-test is performed. The selected data, CFKLQ-CFAR and ASKLQ-CFAR, are tested 10 times in two environments: a homogeneous environment and three interferences in the leading window. Two groups of paired \(t\)-tests are performed. In a homogeneous environment, the results of the paired \(t\)-test on CFKLQ-CFAR and ASKLQ-CFAR are as follows:  
As shown in Table 5, the average detection probability of ASKLQ-CFAR is 57.4241%, and that of CFKLQ-CFAR is 57.4509%. The average of CFKLQ-CFAR is 0.0268% higher than that of ASKLQ-CFAR. This shows that the detection performance of CFKLQ-CFAR with the composite fusion rule has been improved in a homogeneous environment. In order to further compare whether the detection performance of the two detectors has reached the statistical difference level, paired \(t\)-tests are performed for ASKLQ-CFAR and CFKLQ-CFAR. The average value is \(-\)0.02685, the standard deviation is 0.0052781, the standard error mean is 0.0016691, the 95% confidence interval for the difference is \([-\)0.0306257, \(-\)0.02300743], the t-value is \(-\)16.087, the degree of freedom is 9, and the \(p\)-value is 6.1364 \(\times\) 10\({}^{-8}\). As can be seen from the above data, the T value of the paired \(t\)-test of the average detection probability of ASKLQ-CFAR and CFKLQ-CFAR is \(-\)16.087. The \(p\) value is 6.1364 \(\times\) 10\({}^{-8}\), which is less than 0.05 at the significance level of 0.05. Therefore, it is believed that there is a significant difference between the detection performance of ASKLQ-CFAR and CFKLQ-CFAR in a homogeneous environment. The same data were used for the following ANOVA. In the ten sets of ASKLQ-CFAR data, the mean is 57.42405, the standard deviation is 0.0039803, and the 95% confidence interval of the mean is [57.421203, 57.426897]. In the ten sets of CFKLQ-CFAR data, the mean is 57.45008, the standard deviation is 0.0054558, and the 95% confidence interval of the mean is [57.446177, 57.453983]. From these data, it can be seen that the average detection probability of CFKLQ-CFAR is 0.02603 higher than that of ASKLQ-CFAR. According to the confidence intervals of the two sets of data, it can be seen that the two sets of data are quite different. It can be considered that CFKLQ-CFAR improves detection performance.The ANOVA is shown in Table 6.  
As shown in Table 6, the sum of squares between groups is 0.003, and the sum of squares within groups is 0.00041. The F value of the sum of squares between groups is 148.5259, and the significant \(p\) value is 3.9252 \(\times\) 10\({}^{-10}\), which is less than the significant level of 0.05.