Create a Range Doppler Map using "Arbitrary" phase coded Waveforms

This is my first questions I am asking to this community!

I want to understand how to create a Range-Doppler Map (RDM) for a phase/frequency coded radar return using an arbitrary waveform generator (AWFG). This application is very similar to Barker codes.

In a linear frequency modulated (LFM) pulse-Doppler radar, a single pulse return with a target signal can be auto-correlated against a copy of the transmitted pulse (or multiplied in the frequency domain). This is called a matched filter and it can get you the rang bin of the target. To get Doppler or velocity information from the target, you need to send out multiple pulses. This data is often stored in a fast-time (range) slow-time (Doppler) matrix.

Now, this application of creating a RDM is not using a pulse-doppler radar but rather an AWFG. I am only sending out and receiving a single phase coded/ frequency coded pulse that I want to create a RDM of (not LFM not multiple pulses). It still uses a matched filter.

I am looking for any equations for a hypothetical phase coded/frequency coded pulse compressed waveform, and equations for the its Doppler shift or Doppler bins. How would you create a Range-Doppler Map using arbitrary waveforms similar to Barker codes? Is this process at all similar to how I described the RDM creation for a pulse-Doppler radar?

Sorry if this is off topic or not the appropriate place to be asking this question. I am looking to learn about this as a personal project.

• HI! There's no special formulas here, by correlation you still estimate the same as with chirps or barker codes; pulse compression doesn't really care about the waveform (as long as it's white enough). Commented May 31, 2021 at 7:27
• If you’re using arbitrary frequency and phase-coded pulses, it should actually be easier than LFM because you won’t have range-doppler coupling that requires you to do multi-pulse to resolve. As far as I know, your range bin width is still an inverse proportion to your bandwidth (kc/2B), and I believe your doppler bin width is going to be directly proportional to your bandwidth? I’ve never dealt with the latter. Commented May 31, 2021 at 16:06
• It seems that you have a few questions and concerns in your question. Are you wanting to know how to attempt to generate a RDM with an AWFG? Are you not comfortable with forming an RDM via any manner just because the waveform is no longer LFM? Or all of the above? Commented Jun 3, 2021 at 5:08
• @Keegs range-Doppler coupling can be ignored in most cases if the chirp rate/bandwidth are not too high. Phase-coded waveforms are not very Doppler-tolerant. They suffer significant SNR loss during matched-filtering if the return signal has some Doppler. No free lunch. Commented Jun 7, 2021 at 2:56