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This is the phase detector of PLL of OQPSK modulation. Apparently, it introduces a self-noise labeled in red which can’t be offset. I simulate this algorithm in Matlab, it doesn’t perform as well as the PLL of BPSK or QPSK modulation does,since the error won’t be stable even in the situation without phase offset where $y(kT_s)$ and $x((k+1/2)T_s)$ won’t be zero as phase error goes zero,$1/T_s$ is symbol rate. It’ll even scatter clustered constellation points without phase offset. Despite not performing well, it can still correct the phase offset whenever it exists. But when I add frequency offset, the PLL can’t lock to the frequency like its counterpart does in BPSK and QPSK, which may be due to the self-noise introduced in phase detector. So I want to know if the PLL can be used in carrier frequency for OQPSK. If not, is there other high precision algorithms which can recover the carrier frequency? And will the self-noise affect the performance of TLL used for timing synchronization.

  • $\begingroup$ How good is your symbol rate estimate in comparison to how large your carrier frequency offset might be? A very lazy method might be delaying the real part relative to the imaginary part of your reception by half a symbol period and doing classical qpsk recovery on that. $\endgroup$ Commented Jan 9 at 3:26
  • $\begingroup$ I use Gardner TLL to do timing synchronization, theoretically it’s fine as long as the frequency offset is not up to 20% of symbol rate. But what I concern is if the OQPSK PLL can recover the carrier frequency. From results I got in Matlab simulation, it can’t, but BPSK and QPSK PLL can perform the task. And they can’t be used in my situation cause I’m trying to correct OQPSK frequency offset. $\endgroup$
    – Xiang Li
    Commented Jan 9 at 6:31
  • $\begingroup$ Exactly as I say: if you know the symbol timing, congratulations, you can convert your oqpsk to qpsk for purposes of frequency recovery, simply by delaying I against Q. $\endgroup$ Commented Jan 9 at 7:35


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