The demodulation is done with a PLL, but detection of phase error and frequency is determined by stability of frequency, modulation rate , SNR, BER, cost all affect choices in design solutions.
ideal "matched receiver" might look like this
broken link removed
But the synchronization of the samples must consider freq error, phase error, phase symmetry and lock detection method.
Does the data have a sync. pattern for bit sync?
Does the data have DC ? or is it RLL encoded? or biphase (manchester)?
There is BPSK RF modulation as well as Biphase "baseband" modulation which makes it easier to separate clock from data transitions.
If NRZ, then data transitions can be used to sample VCO clock for phase correct. THIS can be done digitally or using analog sawtooth to correct VCO phase error, but then we must look at data PATTERN and WAIT for BIT sync pattern then BYTE SYNC, then FRAME SYNC pattern for a synchronous channel.
(Edit)
The analog data can be extracted by using integrate and dump (I&D) over the synchronized bit window to use all the energy of the bit.
Alternate I&D's can be used to prevent lost time during capacitor discharge. Also DSP's can be used to enhance features of a digital radio.
Digital detector might use counter to detect phase and frequency errors or type II phase/freq comparator
There is no one solution for all types
http://www.google.ca/search?q=bpsk+...2PnuxwIVRxaSCh34hg84&biw=1157&bih=635#imgrc=_