Carrier recovery

[1] However, many modulation schemes make this simple approach impractical because most signal power is devoted to modulation—where the information is present—and not to the carrier frequency.

Non-data-aided/“blind” carrier recovery methods do not rely on knowledge of the modulation symbols.

[2] Closed-loop non-data-aided systems are frequently maximum likelihood frequency error detectors.

[4] In general, the modulation's order matches the nonlinear operator required to produce a clean carrier harmonic.

by squaring: This produces a signal at twice the RF carrier frequency with no phase modulation (modulo

phase is effectively 0 modulation) For a QPSK signal, we can take the fourth power: Two terms (plus a DC component) are produced.

The carrier frequency and phase recovery, as well as demodulation, can be accomplished using a Costas loop of the appropriate order.

[5] A Costas loop is a cousin of the PLL that uses coherent quadrature signals to measure phase error.

Costas loop carrier recovery may be used for any M-ary PSK modulation scheme.

[5] One of the Costas Loop's inherent shortcomings is a 360/M degree phase ambiguity present on the demodulated output.

The phase error between the received value and nearest/decoded symbol is calculated using arc tangent (or an approximation).

[2] In low SNR conditions, the symbol decoder will make errors more frequently.

Example of QPSK carrier recovery phase error causing a fixed rotational offset of the received symbol constellation , X, relative to the intended constellation, O.
Example of QPSK carrier recovery frequency error causing rotation of the received symbol constellation , X, relative to the intended constellation, O.