How does carrier synchronization work in digital receivers?

Carrier synchronization recovers carrier frequency and phase for coherent demodulation. Methods: Squaring loop (for BPSK, squares signal to remove modulation, PLL locks to 2x carrier), Costas loop (parallel I/Q processing, generates phase error independent of data), Decision-directed (uses symbol decisions to generate error signal, works after timing recovery). For suppressed carrier (PSK), these must be phase-ambiguity aware. Frequency acquisition uses frequency detector (at large errors) then phase detector. Loop bandwidth trades acquisition speed vs phase noise. Digital implementations use NCO and loop filters with configurable bandwidth.