# Can I do FFT based Frequency offset Estimation of 16 QAM?

I am exploring the FFT based algorithms for frequency offset estimation. previously I done the frequency estimation for QPSK using FFT and it worked fine, can I do the same for 16 QAM. FFT- based frequency offset estimation algorithm the method in the answer of this question is what I'm using for QPSK.

following are the steps I used for QPSK

• Raise the signal to the Mth power.
• Take the FFT of the result.
• Find the frequency where the peak occurs. -That frequency will be M times the true frequency offset estimate, f=MΔf .
• Coarse estimate is then Δf= f \ M

so basically I'm stuck at the 1st part as in QPSK we raised the signal to the Mth power. what should I have to do in the case of 16 QAM? .

• Yes you can but I suspect it wouldn’t be as efficient as doing the frequency discriminator as the imaginary component of the complex conjugate product of adjacent samples (2 multipliers per sample). If you add details to your question as to what you want to do specifically and where you are stuck you may get further help Commented Aug 1 at 14:06
• You're abusing the tag:dsp-core tag. Please make sure you read the tag descriptions before using tags! Commented 2 days ago
• @MarcusMüller my bad. I'll keep that in mind in my next questions. Commented 2 days ago
• @MuhammadUmar thanks for the edit. I think it was clear you wanted to do a frequency estimate. The question that Dan asks here is more about for what kind of 16-QAM system and channel you're doing this – the problem is that it's probably really not the right approach to modify the squaring recovery that you would use for QPSK. The whole idea of that is based on the fact that it's QPSK; since you're not using QPSK, it's not something you can "slightly modify" to make work well (it works, badly, still, because ¼ of the constellation points in 16-QAM happen to be at the right angle, but it's bad) Commented 2 days ago
• Look at the bullet points you added: the first one! Sit down and raise QPSK each of the 4 constellation points of QPSK to the fourth power – what numbers do you get? Does the same work for 16-QAM? For which kind of constellations does this approach work? Commented 2 days ago