## 3 Simulation Results and Interpretation
### Scenario 1: The Effect of Distance  
The choice of the parameters indicated in the following table is based on the studies of several researchers to bring our simulation closer to reality. In this scenario, we consider two targets with the parameters presented in Table 3 below.  
First, we simulated the two targets very close in distance (they are in the same resolution cell) and in the absence of clutter such that the OS-CFAR detector alone cannot distinguish them. In the second case, each target is simulated in a separate resolution cell. As shown in Figure 13, the target spot in red is shown on the panoramic display of our radar system (Plan Position Indicator PPI).  
The number of reference cells (N\({}_{\text{os}}\)) of the OS-CFAR detector is greater than 24, and the variable k is more significant than 3/4 of the number of N\({}_{\text{os}}\). These chosen parameters  
Figure 13: Position of radar targets displayed by the PPI.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameters** & **Symbols** & **Target 1** & **Target 2** \\ \hline Distance & R & 88 km & 80.5 km \\ \hline Azimuth angle & \(\theta_{\text{AZ}}\) & \(10^{\circ}\) & \(10^{\circ}\) \\ \hline Speed & \(\upsilon\) & 333.3 m/s & 333.3 m/s \\ \hline Altitude & Alt & 2200 m & 2200 m \\ \hline Hidden corner & \(\eta\) & 200\({}^{\circ}\) & 200\({}^{\circ}\) \\ \hline Radar cross-section & SER & \(1\) m\({}^{2}\) & \(1\) m\({}^{2}\) \\ \hline \hline \end{tabular}
\end{table}
Table 3: Target properties in scenario 1.  
prove to result in better performance in terms of the probability of detection and guarantee a minimum number of false alarms. The OS-CFAR detector configuration parameters are grouped into Table 4.  
In Figure 14, we have the OS-CFAR detector and the target amplitude where it can be observed that there is one target amplitude that goes above the limit of the detector at around 84 km, allowing the target to be detected. It goes along with the position of the target displayed by the PPI (Figure 13), showing the target at approximately the same position.  
The detector based on the Gabor transform (proposed detector) is characterized by 64 samples on the time axis and 8 samples on the frequency axis. The analysis window h(n) is 32 cells in width, and the degree of oversampling q equals 1. The configuration parameters of the Gabor-based detector are grouped in Table 5.  
Figure 15 shows the targets detected with the OS-CFAR method and those obtained using the proposed detector without clutter.  
We observe in Figure 15b that the proposed detection method easily finds the position of the targets at M = 36 for the first target and at M = 43 for the second target. Compared to the conventional OS-CFAR detector, which detects a single target in the 84 km range (see Figure 15a) and the second target is missed. The proposed detector has been able to detect the two targets simulated here, while the OS-CFAR method detected a single target.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Values** \\ \hline N\({}_{\text{os}}\) & 24 \\ \hline k & 24 \\ \hline N\({}_{\text{G}}\) & 2 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Conventional OS-CFAR parameters.  
Figure 14: Clutter-free targets detected with the conventional OS-CFAR detector.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Values** \\ \hline h(t) & Gaussian \\ \hline N\({}_{\text{h}}\) & 32 \\ \hline M & 64 \\ \hline N & 8 \\ \hline q & 1 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Configuration parameters of the Gabor-based detector.