# Doppler Shift Tolerance of Typical Pseudorandom Binary Sequences in PMCW Radar
## 5 Conclusions  
This article presented an analysis of Doppler shift tolerance of the oversampled PACFs of typically adoped PRBSs in PMCW radars, namely m-sequences, Gold sequences, Kasami sequences, APASs, ZCZ sequences, and Golay sequences. After a mathematical formulation of the problem of range estimation via correlation in PMCW radar systems under Doppler shifts, the need for evaluating oversampled PACFs to capture effects on targets that are not at distances that are exact multiples of the range resolution was discussed. Next, PSLR, ISLR, and PPLR parameters were adopted for measuring the Doppler shift-induced degradation of oversampled PACFs of the aforementioned PRBSs and consequently ultimately generated range profiles. Finally, a numerical analysis supported by simulation and measurement results was carried out. The achieved results showed that, to avoid unwanted high sidelobes, only a short section of the output range profiles from the correlation operation is used in PMCW radar systems based on ZCZ sequences, Golay A and B sequences (used as individual sequences in a similar manner as ZCZ sequences) without sum of their oversampled PACFs, and APASs. Consequently, these PRBSs yield the lowest maximum unambiguous range values compared with the remaining PRBSs of same length. Furthermore, if the oversampled PACFs of complementary Golay sequences are to be summed, then a multiplexing strategy has to be adopted. In this article, TDM was the chosen approach to keep the baseband PMCW signal binary, which leads to a higher transmission time for the samples associated with a single range profile and consequently lower tolerable relative radial velocities. As for the Doppler shift-induced degradation of oversampled PACFs, it was shown that all sequences yield the same PPLR results. The only exception is the sum of the oversampled PACFs of the complementary sequences Golay A and B, which is severely degraded for certain Doppler shift values due to non-coherent sum or accumulation of the complementary sequences. In terms of PSLR, most sequences present negligible degradation. An exception is the combination of the complementary sequences Golay A and B due to the main lobe degradation observed in the PPLR analysis. Furthermore, ZCZ sequences, Golay A and B sequences used as individual sequences, and Kasami sequences of low PRBS length also present PSLR degradation, which was of less than 4 dB for a Doppler shift range that yields relative radial velocities close to the maximum unambiguous one. Finally, the oversampled PACFs of the analyzed PRBSs in this article yielded distinct ISLR values and degradation over the considered Doppler shift range. If, however, only Doppler shift values below the one defined by the same criterion for maximum tolerable velocity in OFDM radars are considered, most PRBSs yield very similar ISLR values and negligible degradation. The only exceptions are APASs, which yield around 3 dB higher ISLR, and Gold and Kasami sequences, which yield ISLR values around 9 dB higher thanobserved in the oversampled PACFs of the remaining PRBSs. Consequently, if a hardware-efficient design of a PMCW radar system is sought, m-sequences appear as good candidates due to their good robustness to moderate Doppler shifts defined by the aforementioned criterion originally set for OFDM radars, and their possibility of generation with LFSRs instead of complex high-speed DACs. Conceptualization, L.G.d.O. ; investigation, L.G.d.O. ; methodology, L.G.d.O. ; measurement, L.G.d.O. and A.D.; software-based evaluation, L.G.d.O. ; validation, T.A., B.N., E.B., M.B.A. and Y.L. ; supervision, B.N., A.B. and T.Z. ; writing--original draft, L.G.d.O; writing--review and editing, T.A., B.N., E.B., A.B., A.D., M.B.A., Y.L., M.P. and T.Z. All authors have read and agreed to the submitted version of the manuscript. This research was funded by the Federal Ministry of Education and Research (BMBF), Germany under the project \"ForMikro-REGGAE\" (16 ES1061).