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Do you know a reference (book, article) which gives (with a proof) the theoretical BER in the CDMA protocol for a differential modulation?

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  1. CDMA is not a protocol. It's a multi-access scheme.
  2. A BER can't be generally given for a multi-access scheme. You'll need to define your access characteristics, SNR scenario, look at the specific multi-user detector for your specific modulation.

Hence, BlackMath is right: you'll need to go down the long route: Learn about CDMA's basics; do a lot of estimation theory, and apply it to the problem that you're looking at.

For many types of CDMA, detection probabilities are relatively easy to derive; things get a bit complicated because you'll need to define how the different users access the channel, in terms of occupation probability, and synchronity, as well as probability distribution of receiver powers.

Then you'd need to model how your multi-user detector deals with that. As you can see, this requires stochastic modelling of your scenario.

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