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.