Phase is the position of a point within the cycle of a wave, expressed in degrees (0–360°) or radians (0–2π).1 Two waves of the same frequency can differ in phase, meaning one is shifted in time relative to the other — a quarter-cycle lag is a 90° phase difference. Together with amplitude and frequency, phase is one of the three carrier properties a transmitter can vary, and deliberately jumping it between fixed values is how digital radios send bits.
How it works
Phase is only meaningful relative to a reference — either another wave or a notional clock ticking at the carrier frequency. On the IQ plane, which is how radios represent a signal, a sample’s angle measured from the positive I axis is its phase, and its distance from the origin is its amplitude. A rotating point traces out the wave: constant frequency is steady rotation, and a sudden change of angle is a phase shift. This geometric picture is why the IQ representation is so powerful — amplitude and phase, the two independent quantities of a bandpass signal, become the polar coordinates of a single complex number.
Because phase can be changed instantly and read out precisely, it is prime real estate for carrying data. Phase-shift keying assigns bit patterns to discrete phase positions — BPSK uses two (0° and 180°), QPSK four spaced 90° apart — and the receiver decides which was sent by measuring the angle of each symbol. QAM goes further, using both phase and amplitude at once. Differential schemes such as π/4-DQPSK encode data in the change of phase between successive symbols, sidestepping the need to know the absolute phase reference.
In practice
- Carrier recovery. The receiver’s idea of “zero phase” must be locked to the transmitter’s, or the whole constellation rotates. A Costas loop or PLL estimates and removes this offset continuously.
- Phase noise. Real oscillators jitter, smearing each symbol’s angle into a fuzzy cloud (phase noise); too much of it collapses the margin between adjacent PSK points and forces errors.
- Ambiguity. With symmetric constellations the recovered phase can lock 90° or 180° off; differential coding or a known sync pattern resolves which rotation is correct.
Relevance to SDR
Tracking phase is essential to demodulating the PSK and QAM signals GopherTrunk handles. The π/4-DQPSK used by P25 Phase 1 and the four-level schemes of DMR and NXDN all live in the angle of the IQ samples, so GopherTrunk’s carrier-recovery loop estimates the incoming phase and rotates each symbol back onto the ideal constellation before slicing it to bits. Residual phase error, whether from oscillator drift or channel-induced intersymbol interference, directly raises the error-vector magnitude and, past a point, breaks the decode.
Sources
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Phase (waves) — Wikipedia, on the position within a wave’s cycle and phase difference. ↩