# A Waveform and Velocity Ambiguity Resolution Method for Corner Radar
## 4 Simulation Experimental Verification  
To design the AB waveform to expand the maximum velocity after meeting the velocity resolution and calculate the \(V_{max}\) and \(\Delta V\) of the A and B waves, simulation follows these steps:  
Designing the AB waveform: Determine the waveform parameters, such as bandwidth, frame length, and modulation scheme, to meet the requirements for expanding the maximum velocity while ensuring sufficient velocity resolution. Calculating \(V_{max}\) and \(\Delta V\): Use the designed waveform parameters to calculate the maximum unambiguous velocity (\(V_{max}\)) and velocity resolution (\(\Delta V\)) for both the A and B waves. To simulate the waveform parameters in LRR mode with a frame period of 50 ms, the configured parameters are detailed in Table 2.  
Simulation targets are as follows. T\({}_{1}\): Positioned at 160 m to simulate the maximum detection distance for corner radar in LRR mode. T\({}_{2}\): Set at 105 m, slightly beyond the detection range of 100 m for MRR mode. Its velocity is positive, indicating proximity to the radar. T\({}_{3}\): Placed at 60 m, representing the maximum detection distance for SRR mode. Its velocity is negative, indicating movement away from the radar. Figure 5: AB wave matching flowchart. The velocity ambiguous multiples are set to 0, 1, and 2. To mitigate the impact of velocity on observations at the ambiguous boundary, they are adjusted to 1.1 times and 2.2 times the maximum unambiguous velocity. The specific parameters of distance, velocity, and azimuth for the simulation targets are shown in Table 3. These targets are strategically positioned at the intersection of different distance modes to simulate critical points where signal processing complexities are often encountered. This approach allows for a comprehensive evaluation of radar data processing performance. In accordance with Figure 4, a frame of the A wave and a frame of the B wave are transmitted, respectively. Combined with the target parameters in Table 2, the echo signal is generated. Subsequently, the two frames of chirp are processed, and before disambiguation, the AB wave was plotted. Figure 6 shows the peak index, Figure 7 shows the distance velocity map, and Figure 8 shows the CFAR map, (a) shows A wave, and (b) shows B wave. Velocity ambiguity does not occur in T\({}_{1}\), whereas velocity ambiguity is observed in the two frames of T\({}_{2}\) and T\({}_{3}\) in the AB waveform. The process can be decomposed into the following solution steps:  
1. [label=0., ref=0]
2. Ambiguous Multiple Determination: Based on the successful disambiguation of the A wave in the previous frame of wave B, the corresponding ambiguous multiple k\({}_{\rm A}\) is the output. For T\({}_{1}\), T\({}_{2}\), and T\({}_{3}\), the ambiguous multiples are 0, \(-\)1, and 1, respectively. 3. Velocity Derivation in A Wave: Utilizing the indexes of the target parameters in the Constant False Alarm Rate (CFAR) of frame A, the velocities of the three targets (T\({}_{1}\), T\({}_{2}\), and T\({}_{3}\)) in the A wave are derived as 0 m/s, \(-\)30.2685 m/s, and 70.254 m/s, respectively. 4. Range Prediction in the B Wave: The ranges of the targets in wave B are predicted based on the velocities derived in the A wave. For T\({}_{1}\), T\({}_{2}\), and T\({}_{3}\), the predicted ranges are 159.079 m, 103.882 m, and 65.0916 m, respectively.