## Carrier recovery for coherent PSK

In order to ensure that the local carrier phase is approximately 0°, it is necessary either to transmit a carrier phase reference alongside the data signal, or to derive the reference from the incoming data signal. The concept of a separate reference signal has been discussed already in Chapter 4 as a means of detecting and correcting for local oscillator error and Doppler shift in mobile radio systems.

A data-derived reference for BPSK can be implemented by realizing that if the binary PSK signal is squared, the 0o and 180o phase states can be forced to be modulo 2p, thereby removing the modulation. The process of squaring also doubles the frequency of the carrier component. This twice frequency term requires filtering (usually with a phase-locked loop), to remove channel noise, and then the frequency must be halved to yield the required coherent carrier term. |

For data systems using N different phase symbol states (N = 2 for binary-PSK), an Nth order non-linearity must be used to force the phase modulation to be modulo 2p. The remainder of the carrier recovery process remains the same except that a frequency 'divide-by-N' circuit is needed to obtain the correct carrier frequency.