# A Waveform and Velocity Ambiguity Resolution Method for Corner Radar
## 4 Simulation Experimental Verification
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **LRR (A Wave)** & **LRR (B Wave)** \\ \hline Center frequency & 76.5 GHz & 76.5 GHz \\ Frequency bandwidth & 430 MHz & 430 MHz \\ Chirp upward period & 29 us & 29 us \\ Chirp decline period & 4 us & 5 us \\ Chirp cycle & 36 us & 40 us \\ Chirp number & 512 & 512 \\ Sample frequency & 20 MHz & 20 MHz \\ Sample duration & 25.6 us & 25.6 us \\ Number of transmitting/receiving antennas & 4/4 & 4/4 \\ Range FFT points & 512 & 512 \\ Velocity FFT points & 512 & 512 \\ Range resolution & 0.395 m & 0.395 m \\ Maximum unambiguous velocity & \(-\)27.2–27.2 m/s & \(-\)24.5–24.5 m/s \\ Ambiguous multiple & \(-\)1:1 & \(-\)1:1 \\ Chirp total length & 18.432 ms & 20.480 ms \\ Velocity resolution & 0.11 m/s & 0.096 m/s \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Simulation waveform parameters. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Name** & **Parameter** & **Range/m** & **Velocity/ms\({}^{-1}\)** & **Azimuth\({}^{c}\)** \\ \hline T\({}_{1}\) & 160 & 0 & 30 \\ T\({}_{2}\) & 105 & \(-\)30 & 10 \\ T\({}_{3}\) & 60 & 75 & \(-\)15 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Simulation target parameters. Comparison with Actual B-Wave Output: The actual output of \(R_{B}\) (range) and \(V_{B}\) (velocity) from the B-wave CFAR is compared with the predicted range \(R^{\prime}{}_{A}\) of the A wave. If the difference between \(R_{B}\) and \(R^{\prime}{}_{A}\) is less than 2 range bin, it is initially considered to correspond to the same target. 5. Velocity Comparison and Adjustment: Subsequently, the velocities of each fuzzy multiple corresponding to \(V_{B}\) are calculated and compared with \(V_{A}\). If the difference between the two velocities is less than 4 doppler bin, it is considered the true velocity corresponding to the B-wave target point, and the fuzzy multiple \(k_{B}\) is the output. 6. Iteration for Unmatched Points: If the above conditions are not met, a re-match is performed with other points until all points that meet the conditions are found. The corresponding \(k_{B}\) for all points is then output, concluding the B-wave disambiguation process. Figure 6: Peak index of AB wave. (**a**) Peak index of A wave. (**b**) Peak index of B wave. Figure 7: Range Doppler spectrum of AB wave. (**a**) Range Doppler spectrum of A wave. (**b**) Range Doppler spectrum of B wave. According to Table 4, in the B wave, the target T\({}_{2}\) corresponds to the target point in the A wave when the velocity ambiguous multiple of T\({}_{2}\) is \(-1\). Similarly, when the ambiguous multiple of T\({}_{3}\) is 2, it can be successfully matched with the one in the A wave. The ambiguous multiple \(k\) of the corresponding velocity with the unambiguous velocity is output after the target is successfully matched. When performing target matching based on the current frame, the threshold value can be set slightly larger than that of the previous frame when the target is matched to prevent matching omission. The final AB wave deblurring simulation results are shown in Figure 9.  
When simulating the velocity disambiguation algorithm in this article, only the waveform of LRR mode was used for simulation to simplify the description of the algorithm. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**ParameterTarget** & **T\({}_{1}\)** & **T\({}_{2}\)** & **T\({}_{3}\)** \\ \hline R\({}_{A}\) (m) & 159.079 & 105.395 & 61.5789 \\ V\({}_{A}\) (m/s) & 0 & \(-30.2685\) & 75.2504 \\ R\({}^{\prime}\)A (m) & 159.079 & 103.882 & 65.0916 \\ R\({}_{B}\) (m) & 159.079 & 104.211 & 64.7368 \\ V\({}_{B}\) (m/s) & 0 & 18.7654 & \(-22.5756\) \\ k\({}_{B}\) (\(-1/0/1\)) & 0/0/0 & \(-30.23/18.76/67.77\) & \(-71.58/-22.58/26.58/75.58\) (k = 2) \\ Th\({}_{R1}\) (m) = 0.79 (2 range bin), Th\({}_{V1}\) (m) = 0.384 (4 doppler bin) & \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Simulation result of AB wave matching. Figure 8: CFAR spectrum of AB wave. (**a**) CFAR spectrum of A wave. (**b**) CFAR spectrum of B wave. Figure 9: Velocity after disambiguation.