Carrierphase

Carrier phase refers to the instantaneous phase angle of a sinusoidal carrier wave used to transmit information. In modulated signals, the carrier’s phase is varied according to the data, either directly through phase modulation (PM) or by encoding information in the phase of the carrier in schemes such as PSK (phase-shift keying) or QAM, while frequency modulation (FM) causes the phase to evolve over time. The carrier phase provides the reference around which the modulation occurs.

Mathematically, a simple carrier can be written as s(t) = A cos(2π f_c t + φ(t)), where f_c is the carrier frequency and φ(t) is the time-varying carrier phase, including a reference phase and phase changes due to modulation. In complex baseband form, the carrier is represented by A e^{jφ(t)}. The instantaneous phase is the argument of the analytic signal and is central to coherent detection.

Carrier phase recovery is a key challenge in receivers. If the transmitter and local oscillator have a phase offset or experience phase noise, coherent demodulation requires estimating and tracking the carrier phase, typically with a phase-locked loop (PLL) or a Costas loop. Some systems use differential encoding or noncoherent detection to mitigate blind phase requirements. In binary schemes there can be a 0/π phase ambiguity; in higher-order schemes, phase ambiguities align with the constellation.

In navigation systems such as GPS, carrier-phase measurements determine the phase of the received carrier relative to the transmitter. These measurements are extremely precise but are subject to a 2π ambiguity (an unknown integer number of full cycles) that must be resolved for accurate positioning.