# A Waveform and Velocity Ambiguity Resolution Method for Corner Radar
## 3 AB Wave Velocity Ambiguity Resolution Method  
If \(N\) groups of chirp repetition periods are denoted as [T1, _T2_, _T3_,..., _TN_], the repetition frequency PRF can be represented as {\(F1\): \(F2\): \(F3\): \(\ldots\): \(FN\)} = {\(K1\): \(K2\): \(K3\): \(\ldots\): \(KN\)}, where \(K1\), \(K2\), \(K3\), \(\ldots\), \(KN\) are mutually prime positive integers. The target Doppler frequencies of different repetition cycle waveforms can be derived from Equation (2) as  
\[f_{D}=f_{d1}+k_{1}\cdot F_{1}\cdot F_{1},\ f_{D}=f_{d2}+k_{2}\cdot F_{2},\cdots \cdot f_{D}=f_{dN}+k_{N}\cdot F_{N} \tag{7}\]  
where \(k_{1}\), \(k_{2}\), \(k_{3}\), \(\ldots\), \(k_{N}\) represent the ambiguous multiples corresponding to different cycles. According to the Chinese Remainder Theorem, the maximum ambiguous multiples that \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **SRR** & **MRR** & **Parking Mode** \\ \hline Center frequency & 76.5 GHz & 76.5 GHz & 77 GHz \\ Frequency bandwidth & 860 MHz & 600 MHz & 2500 MHz \\ Chirp cycle & 36 us & 36 us & 36 us \\ Chirp number & 512 & 512 & 256 \(\times\) 2 \\ Chirp total length & 18.432 ms & 18.432 ms & 18.432 ms \\ Up/Down duration & 30/4 μs & 30/3 μs & 14/2 μs \\ ADC sample rate & 20 MHz & 20 MHz & 40 MHz \\ Range resolution & 0.204 m & 0.293 m & 0.0656 m \\ Velocity resolution & 0.096 m/s & 0.096 m/s & 0.096 m/s \\ Maximum ambiguous velocity & \(-\)24.5–24.5 m/s & \(-\)24.5–24.5 m/s & \(-\)24.5–24.5 m/s \\ \hline \hline \end{tabular}
\end{table} 
Table 1: 4T4R corner radar waveform parameters. Figure 3: Chirp parameter design process. can be resolved for these N sets of waveforms is the product of \(k_{1}\), \(k_{2}\), \(k_{3}\), \(\ldots\), \(k_{N}\). In this paper, two different repetition period waveforms are considered, as depicted in Figure 4.  
The repetition frequency of the AB waveform, denoted as FA: FB = TB: TA = KA: KB, aligns with a machine cycle based on MMIC chips set at 50 ms. Consequently, the frame length is also set to 50 ms. The method employed for velocity ambiguity resolution involves alternating between frames, disambiguating the next frame based on the unambiguous velocity information obtained from the preceding frame, and continuing this process alternately. In contrast to the TI energy matching method, this approach hinges on the successful matching of target parameters estimated by the AB waveform to establish relationships for eliminating velocity ambiguity. The detection set of the AB waveform in detecting the target is represented by TarsetA and TarsetB, comprising data such as range, velocity, azimuth, and signal-to-noise ratio. TarsetA is further divided into TarsetA_S (points successfully matched) and TarsetA_F (points failed to match), while TarsetB undergoes similar division into TarsetB_S and TarsetB_F. The maximum unambiguous velocities corresponding to the Doppler frequency of the AB wave are denoted as \(V_{maxA}\) and \(V_{maxB}\), respectively. The ambiguous multiple, denoted as \(k\), ranges from \(-m\) to \(m\), where m represents the maximum ambiguous multiple. The true velocity of the target, denoted as \(V^{\prime}\), is expressed as  
\[V^{\prime}=V+k\cdot V_{max},k\in[-m,m] \tag{8}\]  
At a given moment t, where wave A represents the previous frame and wave B denotes the current frame, the points detected in frame B are categorized into TarsetB_S if they are successfully matched with the points from frame A. Conversely, if the points fail to match, they are grouped into TarsetB_F. Similarly, frame A also consists of two subsets: TarsetA_S and TarsetA_F, following the disambiguation process of the preceding frame. The current disambiguation process is as follows:  
Perform range prediction for the points in TarsetA. After TarsetA is disambiguated by the previous frame, yielding the ambiguous multiple \(k_{A}\), the original ambiguous velocity \(V_{A}\), and the range \(R_{A}\), the range \(R^{\prime}_{A}\) of the target in the next frame is predicted, and the subset is updated accordingly.