## 4 Numerical Examples
### Waveform Parameters Impacts
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline Slot & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 \\ \hline Designed waveform & 3 & 0 & null & 13 & null & null & 13 & 13 \\ \hline Uniform waveform & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ \hline Slot & 8 & 9 & 10 & 11 & 12 & 13 & 14 & 15 \\ \hline Designed waveform & 12 & null & null & 0 & 13 & 11 & null & null \\ \hline Uniform waveform & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ \hline Slot & 16 & 17 & 18 & 19 & 20 & 21 & 22 & 23 \\ \hline Designed waveform & 3 & 1 & 0 & null & null & 1 & 0 & 0 \\ \hline Uniform waveform & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ \hline Slot & 24 & 25 & 26 & 27 & 28 & 29 & 30 & 31 \\ \hline Designed waveform & null & 1 & null & 13 & 12 & null & 0 & null \\ \hline Uniform waveform & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ \hline Uniform waveform & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ \hline Slot & 32 & 33 & 34 & 35 & 36 & 37 & 38 & 39 \\ \hline Designed waveform & 13 & 13 & null & 0 & null & 1 & 0 & null \\ \hline Uniform waveform & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ \hline Slot & 40 & 41 & 42 & 43 & 44 & 45 & 46 & 47 \\ \hline Designed waveform & 1 & 0 & null & 0 & null & null & 3 & 1 \\ \hline Uniform waveform & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ \hline Slot & 48 & 49 & 50 & 51 & 52 & 53 & 54 & 55 \\ \hline Designed waveform & 0 & null & null & 5 & 3 & 3 & null & null \\ \hline Uniform waveform & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ \hline Slot & 56 & 57 & 58 & 59 & 60 & 61 & 62 & 63 \\ \hline Designed waveform & 5 & 4 & 3 & null & 3 & 2 & null & 0 \\ \hline Uniform waveform & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ \hline Slot & 64 & 65 & 66 & 67 & 68 & 69 & 70 & 71 \\ \hline Designed waveform & null & null & 11 & 12 & 10 & null & 12 & 11 \\ \hline Uniform waveform & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ \hline Slot & 72 & 73 & 74 & 75 & 76 & 77 & 78 & 79 \\ \hline Designed waveform & null & 11 & null & 11 & null & 13 & 10 & null \\ \hline Uniform waveform & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Designed Waveform Timing. \[\text{SCNR}=10 lg\frac{tr[(a\omega_{f_{d}}\omega_{\tau})^{H}a\omega_{f_{d}}\omega_{ \tau}]}{tr(C^{H}C)+tr(N^{H}N)} \tag{24}\]  
The results are shown in Figure 9. Figure 9a,d represent the velocity dimension for \(N_{t}=4\) targets and the results for \(N_{t}=8\) and \(N_{t}=12\) targets are shown in Figure 9b, Figure 9e, Figure 9c, and Figure 9f, respectively. It can be seen from the figure that when the number of targets is not too large, the OMP and IAA methods can recover the velocity of the targets accurately, with a good suppression effect on the sidelobe. As the number of targets increases, the sparse recovery performance decreases. When the number of targets increases to 12, a small number of targets cannot be well recovered, and some spurious targets also appear. This is because the targets no longer satisfy the sparse characteristics for the designed waveform with only 48 OFDM symbols. Figure 8: Velocity ambiguity function. Figure 9: Velocity dimension with OMP and IAA for targets of different numbers. (**a**,**d**) \(N_{t}=4\). (**b**,**e**) \(N_{t}=8\). (**c**,**f**) \(N_{t}=12\).