demodulation - FFT window phase syncronising

I'm currently devising a solution for demodulating a DPSK signal in C#. So far I've got a working FFT with phase detection, BUT:

I now have an issue of aligning the window of the FFT to synchronise with each symbol transmitted on the audio stream - now I've done some manual testing and for a test transmission I rendered, and I have symbols with a window width of 19 samples.

I do understand that DPSK is designed to avoid a reference signal for demodulating the input signal but FFT window alignment is still needed.

Now the problem is that because this will be potentially used on amateur radio where transmission times are entirely random, the alignment of each symbol will have to be determined. The transmission I rendered has a clock timing header of 1024 symbols, but how can I be sure to get the alignment right?

For example, the header is like:

1 0 1 0 1 0 1 0 etc etc

and the phase of the sine wave rendered from this bit stream would be:

0, 90 0, 90, 0, 90 etc etc

How can I make sure that the receiver will determine the transmitted phase and not anything like

15, 105 ,15, 105, etc etc

as this would also introduce spurious phase calculations from the FFT detecting the higher-frequency harmonics due to the jump in phase.