# Doppler Shift Tolerance of Typical Pseudorandom Binary Sequences in PMCW Radar
## 4 Comparative Performance Analysis
### Evaluation of Doppler Shift Distortion of Range Profiles
In the null Doppler shift cases, it can be observed that ZCZ, APAS, and Golay sequences (both A, B, and their sum) yield sinc-shaped oversampled PACFs in their usable intervals, which is due to the band-limited nature of the considered SISO-PMCW radar system, the remaining sequences yield oversampled PACFs with somewhat different shapes. As for the other PRBSs, m-sequences yield nearly sinc-shaped oversampled PACFs for their whole length, whereas Gold and Kasami sequences present rather irregular sidelobe patterns. When the Doppler shift is increased to \(|f_{\text{D}}/\Delta f|=0.5\), all of the considered PRBSs suffer peak power loss and present irregular sidelobe patterns. Figure 4: Maximum unambiguous range \(R_{\text{max}}=N_{\text{PRBS,usable}}\Delta R\) for the considered (a) automotive and (b) gesture recognition scenarios. Figure 6: Normalized oversampled PACFs (\(t=20\)) under \(f_{\mathrm{D}}/\Delta f=0\) and \(|f_{\mathrm{D}}/\Delta f|=0.5\) of (**a**,**b**) m-sequence, (**c**,**d**) Gold sequence, (**e**,**f**) Kasami sequence, (**g**,**h**) APAS, and (**i**,**j**) ZCZ sequence. An with approximate length of \(N_{\mathrm{PRBS}}=1024\) was adopted for all PRBSs. The relevant PACF intervals described in Section 3 are highlighted in red. To accurately quantify the Doppler shift-induced degradation of the oversampled PACFs for different \(N_{\text{PRBS}}\) values, an analysis assuming the described parameters in Section 3 is carried out based on simulation and measurement results. The adopted setup for obtaining the proof-of-concept measurement results consists of a monostatic SISO-PMCW radar supporting all PRBSs listed in Table 1 and the radar target simulator (RTS) described in [36] and used in [37; 38; 39], both implemented on a Zynq UltraScale+ RFSoC ZCU111 from Xilinx, Inc. To avoid multiple reflections, coaxial cables are used to directly connect the DACs and analog-to-digital converters (ADCs) of the radar connected to the ADCs and DACs of the RTS, respectively. For the aforementioned measurements, a sampling rate of \(F_{\text{s}}=100\,\text{MHz}\) was used for the SISO-PMCW radar system and the aforementioned RTS was used to introduce the Doppler shifts that result in \(f_{\text{D}}/\Delta f\) values ranging from 0 to 0.5. Although a low sampling rate was adopted to keep the absolute Doppler shifts at reasonable values that can be supported by the RTS, it is recalled that the normalized Doppler shifts \(f_{\text{D}}/\Delta f\) drive the ultimate degradation of the PACF, which allows for predictor of the behavior of SISO-PMCW radar systems with other \(F_{\text{s}}\) values based on the presented results. Figure 7: Normalized oversampled PACFs (\(u=20\)) under \(f_{\text{D}}/\Delta f=0\) and \(|f_{\text{D}}/\Delta f|=0.5\) of Golay sequences (**a**,**b**) A and (**c**,**d**) B acting as ZCZ sequences, and (**e**,**f**) sum of the PACFs of the complementary Golay sequences A and B. An with approximate length of \(N_{\text{PRBS}}=1024\) was adopted for all PRBSs. The relevant PACF intervals described in Section 3 are highlighted in red.