I have a communication with a DBPSK modulation. The communication is disrupted by a Doppler shift (due to movement) and Doppler spread (due to channel). At the reception, after Doppler shift compensation with a preamble and DBPSK demodulation, I have a problem with the phase of the symbols. To correct the phase error, I use a phase tracking loop. Here is the link on what I'm doing phase tracking loop.
Here are my questions:
1) How to choose the constant loop $K_c$?
2) We suppose the Doppler shift is perfectly compensated. In my Matlab code, if for example I take $K_c=0.01$, sometimes I find exactly the symbol sent and sometimes I have symbol errors. What is the reason for these errors?