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Demodulation of bpsk singal in c++

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FRB

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Hi there,

Q1. I am using bi-polar NRZ for mapping the signals and simply converting each bit in 1 or -1 and transmit or, due to BPSK I have to convert the these (-1, 1) bit to energy signal waves?
or Simply do I transmit 1 or -1?

Q2. Let suppose after passing awgn channel my signals corrupted and I have received corrupted signals which is representing by complex numbers like (1.2535, 0.2455). How BPSK demodulator demodulate it to 1 or 0.
suppose (1.2354,0.2355) to 1..
 

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