QPSK RECEIVER

If we want to receive data 1 0 meaning Q= 1 and I = 0 then in trigonometric form, (-sin wct + cos wct)

• at the product detector for I channelI = (-sin wct + coswct)(sinwct)
                                                                = (-sin2wct + coswct sinwct)

but sin2A = ½(1 - cos 2A) and cos AsinB = ½[sin(A+B) +sin(A-B)]

note: A and B in this case are equal

so,
    I = -1/2 [ 1- cos2wct] + ½ [sin(wc+wc)t + sin(wc-wc)t}
    I = -1/2 -1/2cos 2wct +1/2 sin2wct

After the LPF,
    I =-1/2 or logic (0)

for the Q channel the process is the same but since we used cos wct for the product detector the resulting

Q = +1/2 or logic 1.

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