Real-time BPSK demodulation
In the implementation of a real receiver, you have to do what is called "streaming", or handing of samples from one block to the next in real time.

Matlab does not lend itself to working with streaming samples; you need a different tool.

For instance, GnuRadio is designed to work in real time with streaming samples. You can even design your demodulator using a visual tool with drag-and-drop of different modules.

It should also be possible to use Python, by setting up a pipe to read samples from your front-end and processing them in sequence.

If you want to use a DSP, I can recommend this book: http://amzn.com/0387748857 which describes the entire design of a streaming digital communications system using a DSP evaluation board.