a(t) is the PRBS，sending it to transmitter to upconversion to BPSK modulated signal s(t)，r(t) represnet the receiving signal that pass throung real wireless channel. The receiver would downconversion the receving signal r(t) into I(t) and Q(t) signal. After that, taking a(t) and I(t)+jQ(t) to do cross correlation to get the channel impulse response.
Yet, there is still some point that I confused about：
As far as I know, BPSK modulate and demodulate only need one I(t) signal，why the receiver output I(t) and Q(t) two signal?
After downconversion r(t), we get I(t)、Q(t) baseband signal. I am wondering aoubt the form of I(t)、Q(t) signal if I represnet a(t)、s(t)、r(t) as follow.
the point that I got stuck in is that is I(t) Q(t) signal BPSK demodulated signal or not? Moreover, no matter I(t) Q(t) is demoudulated signal or not, I both have problem. I describe it as below
Case 1： if I(t) Q(t) is BPSK demoudulated signal
The channel would definitely caused delay which would make the signal with phase shift that system unknown, so how can receiver demodulate the signal accurately?
Case 2：no need to do demodultion at Rx
To the best of my knowledge, if I have PRBS a(t) and the receving PRBS a(t-delay),then, after cross correlation of two signal I can get the delay time. Howerver, what if the receiver didn't demodulate the signal, how can I get the delay time and channel impulse response? Say the problem in another way is that, why calculate corss correlation of a PRBS signal and a sinusoid(I+jQ) signal can get the channel impulse response?