# Adaptive Constant False Alarm Detector Based on Composite Fuzzy Fusion Rules
## 5 Simulation Experiment Results and Analysis  
### CFKLQ-CFAR Detection Performance  
#### 5.1.1 Monte Carlo Simulation Experiment  
In order to test the detection performance of CFKLQ-CFAR, comparative simulation experiments are carried out. The simulation experiment is carried out on MATLAB R2022b software. The Monte Carlo method is used to simulate and compare the performance of CFAR detectors in homogeneous environments and multiple-target environments. The number of simulations is \(10^{5}\) times; the environmental background consists of Gaussian white noise and clutter with an envelope that follows a Rayleigh distribution. After the envelope detector, clutter obeys the assumption of exponential clutter, and the target under \(H_{0}\) has a probability density function:  
\[f(x|H_{0})=\frac{1}{\mu}\exp(-\frac{x}{\mu}) \tag{10}\]  
where \(\mu\) is the scale parameter. Both the target and the interference are followed by Swerling II model fluctuation under \(H_{1}\). If the signal-to-clutter ratio (SCR) is denoted as S, the probability density function the target under \(H_{1}\) is given by [9]:  
\[f(x|H_{1})=\frac{1}{\mu(1+S)}\exp\biggl{[}-\frac{x}{\mu(1+S)}\biggr{]} \tag{11}\]  
In a multiple-target environment, the interference power is the same as the target power. Set \(P_{FA}=10^{-6}\), the number of reference cells is \(N=32\). Choose KLQ-CFAR [9], MAX-based fuzzy fusion rules KLQ-CFAR (MAXKLQ-CFAR), MIN-based fuzzy fusion rules KLQ-CFAR (MINKLQ-CFAR), algebraic product-based fuzzy fusion rules KLQ-CFAR (APKLQ-CFAR), algebraic sum-based fuzzy fusion rules KLQ-CFAR (ASKLQ-CFAR) and CFKLQ-CFAR as comparative methods for performance analysis. The \(r_{1}\) and \(r_{2}\) of KLQ-CFAR are set to 6 and 3. Several experiments have shown that when the weight distribution is [0.1, 0, 0, 0.9], CFKLQ-CFAR has the best detection performance. The simulation results of the target detection probability are shown in Figure 2.  
As shown in Figure 2, the performance of the KLQ-CFAR detector with fuzzy fusion rules is superior to that of the traditional KLQ-CFAR detector. After calculation, in Figure 2a, the average detection probability of CFKLQ is 57.45%, which is 1.05% higher than that of KLQ, 0.03% higher than that of MAXKLQ, 1.07% higher than that of MINKLQ, 1.05% higher than that of APKLQ and 0.02% higher than that of ASKLQ. In Figure 2b, the average detection probability of CFKLQ is 56.78%, which is 2.67% higher than that of KLQ, 1.14% \begin{table}
\begin{tabular}{c c c c c} \hline
**Leading Window** & **Logging Window** & **Different Means?** & **Background Environment** & **Strategy Selection** \\
**Variable?** & **Variable?** & & & \\ \hline No & No & No & Homogeneous environment & CA-CFAR \\ No & No & Yes & Clutter edge environment & GO-CFAR \\ Yes & No & / & Multiple-target environment. & CFKLQ-CFAR \\ No & No & / & Multiple-target environment. & CFKLQ-CFAR \\ Yes & Yes & / & Multiple-target environment. & CFKLQ-CFAR \\ \hline \end{tabular}
\end{table} 
Table 2: CFVI-CFAR algorithm. higher than that of MAXKLQ, 2.63% higher than that of MINKLQ, 2.43% higher than that of APKLQ and 0.04% higher than that of ASKLQ. In Figure 2c, the average detection probability of CFKLQ is 55.04%, which is 2.71% higher than that of KLQ, 1.06% higher than that of MAXKLQ, 2.63% higher than that of MINKLQ, 2.36% higher than that of APKLQ and 0.02% higher than that of ASKLQ. In Figure 2d, the average detection probability of CFKLQ is 56.02%, which is 2.76% higher than that of KLQ, 1.21% higher than that of MAXKLQ, 2.76% higher than that of MINKLQ, 2.52% higher than that of APKLQ, and 0.06% higher than that of ASKLQ. The target detection method based on fuzzy fusion integrates the detection information of two sensors and achieves better performance than traditional binary decision-making approaches. CFKLQ-CFAR further combines the judgment results of four fuzzy fusion rules to obtain a composite judgment result with better performance.