# Generalized Barker sequences

So we're doing a project where we've decided on QAM-n modulation. I've read up a little bit on synchronization and found Barker sequences, which supposedly has nice autocorrelation properties which makes them good for synchronization.

So one option is to use BPSK modulation only in the synchronization phase and then move onto QAM for the data. But to me, it's very unintuitive that we couldn't construct even NICER synchronization sequences (wrt autocorrelation peakedness etc) if we utilize more of the signal space. Maybe something like simultaneous Barker BPSK for both I and Q?

Is there a nice explanation for why it's generally best to use BPSK for the synchronization?

You may say to yourself, "I could just use the same 13-bit Barker sequence for both the I and Q." If you do that, though, you have made a BPSK constellation, only you've rotated it by $\frac{\pi}{4}$.