## 3 Simulation Results and Interpretation
### Scenario 2: Effect on the Number of Targets
#### 3.2.3 Simulation with Clutter Model 3  
We performed a simulation of the three targets using clutter model 3 (targets drowned in cluttered normal distribution). The clutter follows a normal distribution with a standard deviation \(\sigma=400\), the temporal and frequency values of the Gabor transform are M = 128 and N = 8 for the first simulation then M = 256 and N = 2 for the second simulation. We observe in Figure 35 that we encountered a limitation with the proposed detector when using clutter model 3 with a standard deviation \(\sigma\) equal to 400. In both figures, we see that the proposed detector is not able to clearly distinguish the three targets and has several false alarms, which is the same for the OS-CFAR detector. Despite increasing the temporal value of the Gabor transform to M = 256 and decreasing the frequency value to N = 2, we still face challenges, and the proposed detector is still not able to distinguish the three targets from all the false alarms obtained (Figure 36). The simulation results for scenario No. 2 are summarized in Table 8 below. Knowing that Nfa represents the number of false alarms, at each detection limitation, for extreme clutter conditions, we adjusted the time and frequency parameters of the Gabor transform to enhance target detection. We therefore note that there is a possibility of detecting a target. On the other hand, for the Nos number of the OS-CFAR detector, we observed that reducing the Nos improved the ability of the proposed detector to distinguish targets. Figure 34: Targets simulated with clutter model 2 (b = 250) using (**a**) the conventional OS-CFAR detector and (**b**) the proposed detector (M = 128 and N = 8). Figure 33: Targets simulated with clutter model 2 (b = 200) are distinguished with the proposed detector (M = 128 and N = 8). We presented in each scenario several Monte Carlo simulations for the different types of clutter in order to show the performance of the proposed detector. The conventional detector (OS-CFAR) has not been able to clearly distinguish all the three targets used in the simulations; it could not separate existing targets from the clutter involved in the simulations, while the proposed detector has shown better performance by being able, in the cases of clutter free, clutter model 1, and clutter model 2, to distinguish the three targets used for the simulations. Additionally, we observed limitations of our detector in certain cases related to the clutter models. These cases occurred when we increased the frequency of the Gabor transform N from 8 to 32 for the Weibull distribution and when the time and frequency values of the Gabor transform were, respectively, M = 64 and N = 16 for the Rayleigh distribution, where target separation could not be improved. The same problem occurred when we had the standard deviation \(\sigma\) equal to 400. As anticipated, increasing the number of targets affects the efficiency of the proposed detection by decreasing the probability of detection and increasing the number of false alarms. The obtained results in the simulations helped to demonstrate the superior performance of the proposed detector compared to the OS-CFAR detector, even when the targets were very close in distance, azimuth, and speed. To better illustrate the difference and progress between the proposed method of this work and other methods that have been developed previously, a table of method comparisons (Table 9) has been established. Figure 35: Targets simulated with clutter model 3 (\(\sigma\) = 400) using (**a**) conventional OS-CFAR and (**b**) proposed detector (M = 128 and N =8). Figure 36: Simulated targets with clutter model 3 (\(\sigma\) = 400) using (**a**) conventional OS-CFAR and (**b**) proposed detector (M = 256 and N =2).