qpsk – Removing fixed phase offset noise

This feels like a real basic question but I’m struggling to find a clear answer.

I have PSK signal that subjected to a fixed phase shift noise, introduced between the transmitter and receiver – so the received signal has a constant phase shift from the expected signal without noise.

The question is how to compensate for this – on the constellation diagram in Matlab the constellations are rotated, but in the physical system I understand that there will be a Phase Locked Loop in the receiver. Won’t this simply lock onto the zero crossings in the phase shifted signal, effectively removing the phase offset noise.

What am I missing?

What other options are there for removing the fixed phase offset noise?

Thanks