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I have to implement a complete receiver in digital communications. The transmitter gives me an output vector which has real and imaginary values. It uses 16psk for modulation.

How would I demodulate that signal?

I was assuming the output with constant amplitude with different phases, but the magnitude of the whole vector is variable and also when I plot the real and imaginary parts of that vector they are also variable.

I do not know what is happening in the transmitter because it is an executable file. So can anybody help me in understanding what is actually happening and how to demodulate that signal.

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Take a relatively lengthy snapshot of the signal and make the sample rate an integer multiple of the symbol rate. Work with the snapshot in Matlab or Octave and figure out how to demodulate it there. That will involve eliminating the carrier offset and phase, and finding the correct symbol timing.

Once you are able to do it by hand, you will be in much better shape to create a demodulator that can do it automatically. There will still be a lot of things that you will need to learn, but you will at least have a better grasp on what questions to ask.

This answer may help too.

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Try looking at (plotting) the phase angle or atan2() of the real and imaginary parts. You may need to subtract a constant slope, unwrap, and low pass filter.

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