## 4 Simulation
### MATLAB Simulation  
Figure 9 shows the block diagram of the MATLAB simulation algorithm. The simulation environment was configured to closely match the real-world experimental setup,  
Figure 8: (**a**) Estimated Signal Padding applied twice (two targets) (**b**) FFT result. Figure 7: (**a**) Estimated Signal Padding applied twice (single target); (**b**) FFT result. as shown in Table 1. Table 1 lists the radar parameters that are identical to those used in the FMCW radar. Since the center frequency of the FMCW radar to be used is 24 GHz, the MATLAB simulation incorporated 24 GHz multipath fading and Additive White Gaussian Noise (AWGN). Through the above parameters, the FMCW waveform was generated from MATLAB. Table 2 presents the performance results at different target separations as a function of padding length. Besides identifying the number of targets, range accuracy--defined as how closely the estimated target positions match the actual positions--is also critical. Table 2a shows the performance results with an allowable range error of 0.1 m, which is a quarter of the original range resolution of 0.4 m. Table 2b shows the results with an allowable range error of 0.2 m, which is half of the original range resolution. The targets were located within a 2 m to 8 m range, and 1000 data samples were used for each scenario. The OS-CFAR algorithm was utilized for target detection, with the following parameters: False Alarm Rate: 1 \(\times\) 10\({}^{-4}\); Training Cells: 60; Guard Cells: 6; and Rank: 32. Figure 10 graphically represents the result of Table 2, confirming that the best performance was achieved with four times the padding. There is difference between the generated signal and the original signal. Since the generated signal is padded after the original signal, if the padding length is longer than a certain level, the performance of the proposed algorithm is limited. This is because the difference between the original signal and the regenerated signal increases as the padding length grows, which leads to reduced accuracy. This algorithm can confirm that the highest performance is when the padding length is 4 times. \begin{table}
\begin{tabular}{c c} \hline \hline Center Frequency & 24 GHz \\ Bandwidth & 300 MHz \\ Sweep Time & 6.8 us \\ Range Resolution & 0.4 m \\ Sampling Frequency & 300 MHz \\ Sample Point & 256 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: MATLAB simulation environment. Figure 10: Performance results graph by distance between targets according to padding length: (a) \(1/4\) error of existing range resolution; (b) \(1/2\) error of existing range resolution. Figure 9: MATLAB simulation block diagram of proposed algorithm. Table 3 presents the results of measurements assessing the maximum number of targets detectable at varying inter-target distances using a four-times padding configuration. Distances between 0.1 m and 0.3 m showed that the system struggled to distinguish between two targets. Consequently, measurements were only conducted for distances of 0.4m or more. Performance was evaluated using 1000 data samples, indicating that up to approximately four targets could be detected. In the process of generating the signal, an ideal signal is generated. This causes an error between the actual signal and the generated signal. Due to a signal error, the problem is that the images are not completely removed and new images are also generated. As a result, the proposed algorithm can detect four targets on average. Table 4 illustrates the performance results of various algorithms when the targets differ in size. When the size of the target was the same, the performance was evaluated using 1000 data samples in the same way as the performance result of Table 2. When the size of the target is not the same, the performance was evaluated using a total of 1000 data \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Range Resolution** & **Original Length** & **Twice** & **Four Times** & **Eight Times** \\ \hline \hline  & & **(a)** & & \\ \hline  
\hline \hline \end{tabular}
\end{table}