When looking at carrier recovery, a PLL is often applied to correct the frequency offset between the local oscillator and the transmitter after down conversion.
I'm wondering what happens to the PLL if this frequency offset is small? Does the PLL break as the carrier tone isn't as obvious and the loop filter can't as easily differentiate the modulation noise from the carrier?
Wouldn't it be more advantageous to have a local oscillator down-convert the signal to an intermediate frequency and then have the PLL track that?