# Doppler Shift Tolerance of Typical Pseudorandom Binary Sequences in PMCW Radar
## 4 Comparative Performance Analysis
### Evaluation of Doppler Shift Distortion of Range Profiles
#### 4.2.2 Peak-to-Sidelobe Level Ratio  
Next, the simulated PSLR results for all PRBSs from Table 1 are shown in Figure 9. Those are validated by the measured PSLR results as functions of \(f_{\text{D}}/\Delta f\) presented in Figure 10 for all considered PRBSs. Figure 8: Simulated (**a**) and measured (**b**) PPLR as a function of \(f_{\text{D}}/\Delta f\). Except for the combination of complementary sequences Golay A and B (**-**), which achieves the same PPLR profile for all \(N_{\text{PRBS}}\) values, all other considered PRBSs listed in Table 1 (**a**) achieve the same result. For the measurement results, the mean PPLR values are shown as solid lines, and their standard deviations are indicated by the shading in the background. Figure 9: Simulated PSLR as a function of \(f_{\rm D}/\Delta f\) for the considered PRBSs with approximate PACF usable length of (**a**) \(N_{\rm PRBS,usable}=32\), (**b**) \(N_{\rm PRBS,usable}=64\), (**c**) \(N_{\rm PRBS,usable}=128\), (**d**) \(N_{\rm PRBS,usable}=256\), (**e**) \(N_{\rm PRBS,usable}=512\), (**f**) \(N_{\rm PRBS,usable}=1024\), (**g**) \(N_{\rm PRBS,usable}=2048\), and (**h**) \(N_{\rm PRBS,usable}=4096\). The considered PRBSs are m-sequence (\(\blacksquare\)), Gold sequence (\(\blacksquare\)), Kasami sequence (\(\blacklozenge\)), APAS (\(\blacktriangledown\)), ZCZ sequence (**a**), Golay A (\(\vartriangle\)), Golay B (\(\bigstar\)), and the combination of complementary sequences Golay A and B (\(\blacktriangleright\)). The correspondence between their \(N_{\rm PRBS,usable}\) and \(N_{\rm PRBS}\) values is listed in Table 1.  
Figure 10: Measured PSLR as a function of \(f_{\rm D}/\Delta f\) for the considered PRBSs with approximate PACF usable length of (**a**) \(N_{\rm PRBS,usable}=32\), (**b**) \(N_{\rm PRBS,usable}=64\), (**c**) \(N_{\rm PRBS,usable}=128\), (**d**) \(N_{\rm PRBS,usable}=256\), (**e**) \(N_{\rm PRBS,usable}=512\), (**f**) \(N_{\rm PRBS,usable}=1024\), (**g**) \(N_{\rm PRBS,usable}=2048\), and (**h**) \(N_{\rm PRBS,usable}=4096\). The considered PRBSs are m-sequence (\(\blacksquare\)), Gold sequence (\(\blacksquare\)), Kasami sequence (\(\blacklozenge\)), APAS (\(\blacktriangledown\)), ZCZ sequence (**a**), Golay A (\(\vartriangle\)), Golay B (\(\bigstar\)), and the combination of complementary sequences Golay A and B (\(\blacktriangleright\)). The correspondence between their \(N_{\rm PRBS,usable}\) and \(N_{\rm PRBS}\) values is listed in Table 1.  
Overall, very similar PSLR performance is achieved by most of the considered PRBSs, which also present relatively stable PSLR values over the considered \(f_{\text{D}}/\Delta f\) range. This can, e.g., be illustrated by the highest sidelobe level in the previously discussed Figures 6 and 7 for \(N_{\text{PRBS}}\approxeq 1024\). Among the exceptions are the ZCZ sequence with \(N_{\text{PRBS}}\in\{256,512,1024\}\), Golay A and Golay B sequences with \(N_{\text{PRBS}}=256\), Kasami sequence with \(N_{\text{PRBS}}=255\), and APAS with \(N_{\text{PRBS}}=256\), for which the PSLR degrades after reaching high \(f_{\text{D}}/\Delta f\) values. Among the aforementioned sequences, the ones with lower \(N_{\text{PRBS}}\) start suffering from observable PSLR degradation at lower \(|f_{\text{D}}/\Delta f|\) values compared to their counterparts with longer PRBS length \(N_{\text{PRBS}}\). This can be explained by the fact that the ratio \(f_{\text{D}}/\Delta f\) corresponds to a shift in samples in the discrete-frequency domain. Therefore, the same shift by \(f_{\text{D}}/\Delta f\) samples becomes relatively less relevant in comparison to the total number of samples \(N_{\text{PRBS}}\) as the PRBS length increases. With the increased relevance of Doppler shifts, the nearest sidelobe to the mainlobe, which is not significantly affected by Doppler shifts as depicted in Figures 6 and 7, does not dominate the PSLR trend anymore. Rather, sidelobes located far from the mainlobe may become stronger than the aforementioned one and degrade the PSLR performance.