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Confuse about Inphase and quadrature component BPSK signal.

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bacbac

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I did my Costas loop for BPSK signal in my project. Out put of the loop is BPSK code. I need the BPSK code for next correlator. I realize that from only one branch of the loop (Inphase or quad), I can take BPSK code by comparing with a threshod level.
On the internet I found some document talking about the correlator. They use both I and Q component from costas loop to correlate the code. I confuse if I miss something when I use only one component (for example Inphase)?
Again, I understood two components inside the Costas loop, but after costas loop, do I need two components to describe the BPSK code? Please help me,
Thank you!
 

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