# Doppler Shift Tolerance of Typical Pseudorandom Binary Sequences in PMCW Radar
## 4 Comparative Performance Analysis
### Evaluation of Doppler Shift Distortion of Range Profiles
#### 4.2.3 Integrated-Sidelobe Level Ratio  
Unlike in the PPLR and PSLR results, where nearly all PRBSs perform equally and only small differences are observed, more relevant changes in the ISLR are observed due to the fact that it considers the whole range of sidelobes associated with \(N_{\text{PRBS,usable}}\) as described in Section 3. This is observed, e.g., in Figures 6 and 7 for \(N_{\text{PRBS}}\approxeq 1024\), where significant differences in the degradation of the sidelobe patterns of the PACFs of different PRBSs are observed at \(|f_{\text{D}}/\Delta f|=0.5\) w.r.t. their counterparts at \(|f_{\text{D}}/\Delta f|=0\). The simulated and mean measured ISLR results are shown in Figures 11 and 12, respectively, and are in good agreement for all PRBSs from Table 1 and \(|f_{\text{D}}/\Delta f|\) values. The achieved results show that the oversampled PACFs of the complementary sequences Golay A and B achieved the highest ISLR values of all for \(|f_{\text{D}}/\Delta f|\) between around 0.2 and 0.3, which is due to the increase of the sidelobes that otherwise tends to be similar as in the ZCZ sequences and the reduction of the mainlobe power as described in Section 4.2.1. The next highest ISLR values compared to the remaining sequences of similar \(N_{\text{PRBS,usable}}\) over the whole considered \(|f_{\text{D}}/\Delta f|\) range are achieved by the oversampled PACFs of Gold and Kasami sequences. Apart from the two aforementioned sequences, APAS present the worst ISLR values for reasonable normalized Doppler shifts, i.e., \(|f_{\text{D}}/\Delta f|\leq 0.1\), being followed by m-sequences, Golay A and B sequences, and ZCZ sequences, all with very similar ISLR performances. If, however, higher normalized Doppler shift values are considered, the ISLR associated with oversampled m-sequence PACFs degrades rapidly and tends to yield close values to the ISLRs of the Gold and Kasami sequences. The second most severe ISLR degradation is experienced by Golay A and B sequences, which, however, still achieve ISLR values more than 3 dB lower than the ones achieved by m-sequences. Furthermore, APAS and ZCZ experience similar ISLR degradation. Finally, the achieved results show that ZCZ sequences achieve the lowest ISLR over the whole considered \(|f_{\text{D}}/\Delta f|\) range compared to the other PRBSs with similar \(N_{\text{PRBS,usable}}\) when there exists a ZCZ sequence for the given \(N_{\text{PRBS}}\) and \(N_{\text{PRBS,usable}}\) pair. Figure 11: Simulated ISR as a function of \(f_{\text{D}}/\Delta f\) for the considered PRBSs with approximate PACF usable length of (**a**) \(N_{\text{PRBS,usable}}=32\), (**b**) \(N_{\text{PRBS,usable}}=64\), (**c**) \(N_{\text{PRBS,usable}}=128\), (**d**) \(N_{\text{PRBS,usable}}=256\), (**e**) \(N_{\text{PRBS,usable}}=512\), (**f**) \(N_{\text{PRBS,usable}}=1024\), (**g**) \(N_{\text{PRBS,usable}}=2048\), and (**h**) \(N_{\text{PRBS,usable}}=4096\). The considered PRBSs are m-sequence (\(\oplus\)), 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 \(N_{\text{PRBS,usable}}\) and \(N_{\text{PRBS}}\) values is listed in Table 1.  
Figure 12: Measured ISLR 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**) \(N_{\rm PRBS,usable}=4096\).