Can i track any frequency offset my increasing samples/symbol. For example if my symbol rate is 1Msps. If my sample rate is 10 Msps. Can my receiver correct upto 5 Msps carrier offset using FFT I can follow it by costas carrier recovery to further correct it before timing?
1 Answer
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Ok so there are a couple ways to deal with this. As you pointed out there are things like the Costas Loop and PLL but I think band edge recovery is more intuitive. You can also continually apply STFT and track the frequency offset though you have the problem of time vs frequency localization.
I'm not an expert but I would probably square the signal and find the FFT peak, afterward I would do timing recovery and then apply decision directed feedback or a PLL after demodulation to track the remaining offset.
The band-edge filter timing recovery is pretty intuitive though fred harris derivation ignores some important things/obscures them for some reason. EX he tries to argue maximum-liklihood as a way to derive it but his derivation ignores issues like symbols not being time limited so it hides lots of stuff,
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$\begingroup$ Oh to be clear, as long as your sample rate is fast enough(IE, you sample at twice the approximate bandwidth) you will be good. carrier offset will shift that frequency requiring a higher sample rate but in terms of reconstruction you will be fine. $\endgroup$ Dec 19, 2019 at 4:01
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$\begingroup$ So i can correct upto 5msps ( fs/2) using FFT and followed by carrier recovery. O r may be i can follow fft by timing then matched filter and lastly the timing recovery so in this way i can correct any offset irrespective of the symbol rate $\endgroup$– nancyDec 19, 2019 at 13:09
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$\begingroup$ The Matched Filter Output degrades as the frequency offset increases since each term in the sum gets rotated a little bit from the previous. But yes, apply DFT and find approximate center frequency, I'm not sure of the best way to do this since it's not clear to me the DFT peak will be at the center frequency. One way to potentially handle this is to take the absolute values of the FFT and apply a box correlation in the frequency domain where the box is the approximate width of the shaping pulses spectrum. This should peak at approximately the center frequency. $\endgroup$ Dec 20, 2019 at 0:48
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$\begingroup$ After frequency has been approximately corrected you can do timing recovery after the matched filter and then do fine frequency correction. I read someone said you could do timing correction prior to the matched filter but it will be more rough so what ever adaptive algorithm you have will need to be heavily dampened. $\endgroup$ Dec 20, 2019 at 0:53