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What is the logical reason behind this? Why are P1,P2, P3, P4 codes unaffected by doppler shifts?

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  • $\begingroup$ Are you currently taking a course? Seems like some of the questions you're asking are given in basic radar signal processing books. If this is for work, we can suggest resources on basic radar signal processing. $\endgroup$
    – Envidia
    Jan 26 at 15:08
  • $\begingroup$ "Doppler Properties of Polyphase Coded Pulse Compression Waveforms," IEEE Transactions on Aerospace and Electronic Systems ( Volume: AES-19, Issue: 4, July 1983). $\endgroup$ Jan 26 at 19:02
  • $\begingroup$ @Envidia you gave an answer to my question previously where you said "You will read in literature that phase-coded waveforms are intolerant, and that is due to the discontinuities inherent to their phase modulation, which wreaks havoc once a Doppler-shift is induced." i just needed a more elaborate explanation to this statement $\endgroup$
    – user70596
    Jan 27 at 7:34

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The short answer of what makes a waveform "Doppler tolerant" is that a frequency shifted version of the waveform still has all of its non-linear phase (in the frequency domain) removed when matched filtered with the original waveform. You can work this out on paper quite easily with something like an LFM, and you will see that you end up with a linear phase (again, in the frequency domain) when you matched filter the Doppler-shifted waveform with the original. This linear phase affects a time-domain shift of the return, but does not affect the quality of the IPR (a small loss in power withstanding). Having quadratic, cubic, etc. phase terms leads to a drop in things like the ISLR, PSLR, and so on.

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  • $\begingroup$ so it's all about phase discontinuity right? like bi-phase has abrupt change in phase(as we go from +1 to -1, vice versa) and polyphase ensures phase continuity? $\endgroup$
    – user70596
    Jan 27 at 5:53
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    $\begingroup$ Polyphase waveforms have phase discontinuities, they just have smaller phase jumps on average than biphase codes. An example of a waveform that doesn’t have phase discontinuities is an LFM chirp. $\endgroup$
    – Baddioes
    Jan 27 at 22:49
  • $\begingroup$ @ian It's all about not having quadratic and higher order terms after waveform removal (which is often approximated using a matched filter). Discontinuities are synonymous with higher order terms -- think about how many terms of a Taylor series are needed to accurately represent, say, a square wave. Residual quadratic phase will blur the IPR (work it out on paper to convince yourself). Residual cubic phase leads to lopsided IPRs with highly elevated sidelobes. If you take the residual phase and inverse FT it, you will have the function that gets convolved with the error-free IPR. $\endgroup$ Jan 29 at 17:11

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