# Joint Radar and Communications Waveform Design Based on Complementary Sequence Sets
## 4 Results
### Performance of the DR-JRC-CWG
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Figure** & **JRC Waveform** & \(Q\) & \(w\) & \(M_{c}\) & \(M\) & \(T_{p}\) & **PRI** & \(N\) \\ \hline Figure 6(a1,a2) & JRC-CWG-BPSK & 0 & - & 1 & 6 & 5 \(\upmu\)s & 20 \(\upmu\)s & 64 \\ Figure 6(b1,b2) & DR-JRC-CWG-BPSK & 1 & \(\mathbf{w}_{1}=[0.95,0.05]^{T}\) & 1 & 6 & 5 \(\upmu\)s & 20 \(\upmu\)s & 64 \\ Figure 6(c1,c2) & DR-JRC-CWG-BPSK & 1 & \(\mathbf{w}_{2}=[0.9,0.1]^{T}\) & 1 & 6 & 5 \(\upmu\)s & 20 \(\upmu\)s & 64 \\ Figure 6(e1,e2) & DR-JRC-CWG-16-PSK & 1 & \(\mathbf{w}_{2}=[0.9,0.1]^{T}\) & 1 & 6 & 5 \(\upmu\)s & 20 \(\upmu\)s & 64 \\ Figure 6(e1,e2) & OPP-BPSK & - & - & - & 6 & 5 \(\upmu\)s & 20 \(\upmu\)s & 64 \\ Figure 6(f1,f2) & LFM-BPSK & - & - & - & 6 & 5 \(\upmu\)s & 20 \(\upmu\)s & 64 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameters used in Figure 6.  
Figure 7: Relation curves between PSLR and Doppler frequency. In Table 2, the NA stands for not-applicable. It can be determined that if the PSLR of the JRC waveform is required to be lower than \(-35\) dB, the OPP-BPSK waveform and the LFM-BPSK waveform will not be applicable. To make sure the PSLR is lower than \(-35\) dB, the radial velocity \(v\) between the JRC platform and the target should satisfy that \(v<25.1\) m/s for JRC-CWG-BPSK, \(v<63.9\) m/s for DR-JRC-CWG-BPSK with \(\mathbf{w}=\mathbf{w}_{1}\), \(v<67.5\) m/s for the DR-JRC-CWG-BPSK with \(\mathbf{w}=\mathbf{w}_{2}\), and \(v<66.9\) m/s for the DR-JRC-CWG-16-PSK with \(\mathbf{w}=\mathbf{w}_{2}\), respectively. Hence, the designed DR-JRC-CWGs have better Doppler resilience than the designed JRC-CWGs. Compared with the DR-JRC-CWG-BPSK with \(\mathbf{w}=\mathbf{w}_{1}\), i.e., \(\tilde{w}_{1}=0.05\), and \(\mathbf{w}=\mathbf{w}_{2}\), i.e., \(\tilde{w}_{1}=0.1\), it can be observed that the Doppler resilience of the designed DR-JRC-CWG-BPSK will be improved when the weight \(\tilde{w}_{1}\) in \(\mathbf{w}\) is increased. Moreover, the designed DR-JRC-CWG-BPSK with \(\mathbf{w}=\mathbf{w}_{2}\) has a similar performance to the designed DR-JRC-CWG-16-PSK with \(\mathbf{w}=\mathbf{w}_{2}\). From Figure 7, we can see that the designed DR-JRC-CWG has better Doppler resilience than the OPP-BPSK waveform, the LFM-BPSK waveform, and the JRC-CWG. Moreover, the Doppler resilience of the designed DR-JRC-CWG satisfies the demand of automotive JRC systems, while that of other JRC waveforms does not. In Figure 7, compared with the designed JRC-CWG-BPSK, the PSLR of the designed DR-JRC-CWG-BPSK at \(f_{d}=0\) is larger. Moreover, the larger the weight \(\tilde{w}_{1}\) in \(\mathbf{w}\) is, the larger the PSLR of the designed DR-JRC-CWG-BPSK at \(f_{d}=0\) is. Specifically, the PSLR of the designed JRC-CWG-BPSK at \(f_{d}=0\) is \(-151.9\) dB. For the designed DR-JRC-CWG-BPSK with \(\mathbf{w}=\mathbf{w}_{1}\), and the DR-JRC-CWG-BPSK with \(\mathbf{w}=\mathbf{w}_{2}\), the PSLR at \(f_{d}=0\) is \(-98.5\) dB and \(-71.2\) dB, respectively. Note that in the multi-objective optimization problem (25), the Doppler resilience and the sidelobe level of SACF of the DR-JRC-CWG are jointly optimized, whereas in the optimization problem (9) only the sidelobe level of the SACF of the JRC-CWG is optimized. Hence, the PSLR of the DR-JRC-CWG may be higher than that of the JRC-CWG. Moreover, the larger the weight \(\tilde{w}_{1}\) in \(\mathbf{w}\) is, the higher the PSLR will be. From Figure 7, it can be seen that the DR-JRC-CWG has a worse sidelobe performance than the JRC-CWG at \(f_{d}=0\). In practice, the user can employ the DR-JRC-CWG at first to estimate the velocity of the target. Then, the JRC-CWG can be employed, since the Doppler shift can be compensated at the radar receiver by using the estimated velocity. Generally, an ITS often suffers serious clutter.