## 3 Proposed Algorithm  
In this paper, we propose an algorithm to improve radar range resolution by increasing the number of FFT points through signal extension in the time domain. Figure 1 presents the block diagram of the proposed algorithm. In Figure 1, the red sections represent parts added to the existing FMCW radar signal processing, and the yellow sections represent modified parts [30; 31]. The signal transmitted from the radar's TX section is reflected by the target and received by the RX section. The received signal undergoes an AFE process, resulting in data \(x[n]\), where n denotes the sample point. The signal \(x[m]\) is obtained by zero-padding \(x[n]\) from \(n\) to \(m-1\) points. The degree of range resolution improvement depends on \(m\), which is a flexible parameter. Performing an \(m\)-point FFT on \(x[m]\) yields \(X[k]\), where \(k\) denotes the FFT bin number. The presence of a target is determined using a CFAR detector. In this study, an OS-CFAR is used for target detection [32; 33]. If a target is detected, the index with the maximum value in \(X[k]\) is identified. A signal corresponding to the detected target is then generated and added to \(x[m]\) from \(n\) to \(m-1\) points to produce a new signal \(x[m]\). Afterward, an \(m\)-point FFT is performed, and previously detected signals are excluded from the CFAR detection. During the first loop, since no signals have been detected yet, this exclusion process does not apply. The process repeats until the CFAR algorithm indicates no further targets. When the CFAR detects no targets, the loop ends, and the total number of targets and their positions are determined. Figure 2 shows a flowchart of the proposed algorithm. Up to the CFAR detector, the process is the same as described in Figure 1. If the CFAR algorithm detects a target, a signal corresponding to that target is generated for signal extension. The index of the maximum value in \(X[k]\) corresponds to the target's location, and the signal for the \(a\)-th target is denoted as \(x_{a}[u]\). By adjusting the phase and amplitude, the signal \(x_{a}[u]\) can be generated, with the phase and amplitude being derived from \(X[k]\). \[M[k]=\left|\frac{X[k]}{N_{fft}}\right| \tag{9}\]  
\[\theta[k]=angle(X[k]) \tag{10}\]  
\[xa[u]=M[imax(a)]e^{i(2\pi f_{a}t+\theta[imax(a)])} \tag{11}\]  
The signal \(x_{a}[u]\) is generated using Equations (9)-(11). The magnitude of the generated signal \(M[k]\) is obtained using Equation (9), where \(X[k]\) is the result of a flexible-point FFT after zero-padding the original signal, and \(N_{fft}\) is the number of FFT points. For convenience, the flexible point number is denoted as \(m\). The phase of the original signal \(\theta[k]\) is calculated using Equation (10). By utilizing Equations (9) and (10), the signal \(x_{a}[u]\) is obtained as shown in Equation (11), where \(i_{max(a)}\) is the index with the maximum value in \(X^{\prime}[k]\) during the ath loop, and fais the frequency corresponding to \(i_{max(a)}\). Once \(x_{a}[u]\) is obtained, it is padded from \(n\) to \(m-1\) points in \(x[n]\) to create a new signal \(x^{\prime}[m]\). After signal extension, \(a\) is incremented by \(1\), and a flexible-point FFT is performed again. The previously detected targets are excluded from CFAR detection by setting \(i_{max(1)}\) through \(i_{max(a-1)}\) to zero, creating a new signal \(X^{\prime\prime}[k]\). The CFAR detector checks for the presence of  
Figure 1: Block diagram of the proposed algorithm. targets, and if any are found, the process repeats. If no targets are detected, the loop ends, and the total number of targets is determined. The proposed algorithm detects and removes targets one by one, starting from the target with the strongest power. It operates through a feedback loop, reusing resources during each iteration. The computational power increases proportionally with the number of detected targets as the same hardware resource is used, but the loop continues until the final target detection is completed.