## 3 Proposed Algorithm
Figures 3-5 illustrate the proposed algorithm for a single target. Figure 3a shows the time-domain view of the original received signal, and Figure 3b presents the result of an \(n\)-point FFT. Figure 4a shows the signal after applying the proposed Estimated Signal. Padding twice to the original received signal, and Figure 4b displays the result of a \(2n\)-point FFT. Figure 5a shows the signal after applying the proposed Estimated Signal Padding four times, and Figure 5b presents the result of a \(4n\)-point FFT. Figure 3: (**a**) Original received signal from single target; (**b**) FFT result. Figure 2: Flowchart of the proposed algorithm. When a target is within the range resolution, many sidelobes are generated, as shown in Figure 3b, making it difficult to accurately determine the number of targets. In this case, by padding the original signal \(x[n]\) with Estimated Signal Padding to increase the sample points to \(2n\) and \(4n\), as shown in Figures 4a and 5a, and performing \(2n\)-point and \(4n\)-point FFTs, the results shown in Figures 4b and 5b are obtained. As the number of sample points increases, the ratio of the main lobe to the sidelobes increases, allowing for a more accurate determination of the number and location of targets. Figures 6-8 explain the proposed algorithm for multiple targets. Figure 6a shows the time-domain view of the original received signal, while Figure 6b presents the result of an n-point FFT. Figure 7a shows the signal after applying the proposed Estimated Signal Padding twice to the original received signal, with padding applied only for the first target. Figure 7b displays the result of a \(2n\)-point FFT. Figure 8a shows the signal after applying the proposed Estimated Signal Padding twice to both the first and second target signals, and Figure 8b presents the result of a \(2n\)-point FFT. Figure 4: (**a**) Estimated Signal Padding applied twice; (**b**) FFT result. Figure 5: (**a**) Estimated Signal Padding applied four times; (**b**) FFT result. Figure 6: (**a**) Original received signal from multi target; (**b**) FFT result. When the original received signal is processed with an n-point FFT, as shown in Figure 6b, the presence of many sidelobes makes it difficult to determine the number of targets. Figure 7a shows the original signal \(x[n]\) padded to \(2n\) points with the generated signal \(x_{a}[u]\) corresponding to the first target. The result of the \(2n\)-point FFT is shown in Figure 7b. Since Estimated Signal Padding was applied to the first target, the ratio of the main lobe to the sidelobes for the first target increased, revealing that the second target was previously obscured by the sidelobes. Figure 8a shows the signal after padding the original received signal \(x[n]\) with both the generated first target signal \(x_{a}[u]\) and the second target signal \(x_{a+1}[u]\) up to \(2n\) points. The result of the \(2n\)-point FFT is shown in Figure 8b. As the ratio of the main lobe to the sidelobes for the second target increases, the number and location of the targets can be determined more accurately. With the target existing within the range resolution, the signals of the \(n\)-th target may not be detected due to the image generated by the largest target signal rather than the effect of noise. This algorithm generates and extends the dominant target signal to improve range resolution to reduce the images generated at the first target. This makes it possible to detect the previously invisible \(n\)-th target signal.