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If we have given a signal and we know that is a modulated QPSK signal, can we recover the carrier if we know the carrier frequency fc.

Edit: A clarification, I do not have to do it in hardware, a matlab code is fine.

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  • \$\begingroup\$ If it's unmodulated, then isn't the signal you have already just the carrier? \$\endgroup\$
    – The Photon
    Jul 5 '19 at 0:09
  • \$\begingroup\$ @ThePhoton I want the carrier only what I have is the modulated carrier. \$\endgroup\$
    – Creator
    Jul 5 '19 at 1:01
  • \$\begingroup\$ "we know that is a unmodulated..." and "what I have is the modulated...". Which do you actually have? Please edit your question if it needs correction. \$\endgroup\$
    – TimWescott
    Jul 5 '19 at 3:30
  • \$\begingroup\$ @TimWescott Thank you The point is I have modulated signal and I need to get the carrier before unmodulation. \$\endgroup\$
    – Creator
    Jul 5 '19 at 4:54
  • \$\begingroup\$ With regard to the modulation: it is pretty standard for QPSK to be scrambled using a maximal length LFSR of sufficient length to provide a normal PSD distribution over short periods - is this the case here? \$\endgroup\$ Jul 5 '19 at 9:03
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Look at the FFT of the squared, fourth power of the raw complex data. You will then be able to verify the carrier.

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  • \$\begingroup\$ The squared fourth power = the eighth power? \$\endgroup\$
    – user253751
    Mar 23 at 9:55
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I guess you want to extract the carrier from a carrierless modulated QPSK signal. You want a circuit or other method to sync a VCO so that it outputs the nonexistent QPSK carrier.

Without knowing anything of the modulated data it's impossible. If you can assume the data is an uniformly distributed random stream and coded in such way that short enough sequences also look out uniformly distributed, you can use a QPSK Costas Loop to keep a VCO in sync with the average phase of the modulated signal. For faster synchronization the data stream can include a known sequence now and then and the VCO is resynced to make the detection result to match exactly with the known sync data.

Here's a link to a Wikipedia article which shows the QPSK Costas Loop: https://en.wikipedia.org/wiki/Costas_loop. Good luck for trying to simulate it in Matlab.

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