CDR files are more generic in nature than that, meaning you can't arbitrarily add fields to them.
To achieve what you need is to extrapolate the information you want from the file itself.
Incoming calls should arrive to you from specific channels (Your Zap channels for example) and in specific contexts.
In elastix's case for example, you should see incoming calls arriving in the 'from-did-direct' context.
The context in which the call was handled is the fourth column in the CDR if memory serves me right, but you can check that out in a zip
Anyway I hope I helped