Field Guide · technology

Also known as: phase-shift keying, PSK, QPSK

Phase-shift keying (PSK) is digital modulation that switches a carrier’s phase between fixed angles while amplitude stays constant.1 Two phases is BPSK (1 bit/symbol); four is QPSK (2 bits/symbol); eight is 8PSK (3 bits/symbol). It is one of the most spectrally efficient and noise-robust digital modulations, which is why it dominates satellite and deep-space links.

IQ 01111000
PSK encodes bits in the carrier's phase; QPSK uses four phase points (2 bits each). P25 Phase 2 uses a PSK variant.

How it works

Each symbol is a phase angle, read as a point on the IQ plane by quadrature (IQ) modulation. BPSK places two points at 0° and 180°; QPSK places four at 45°, 135°, 225°, 315° so that adjacent points differ by one bit (Gray coding), which minimises the bit errors caused by a phase slip to a neighbouring point. Because all points sit at the same radius, PSK shares FSK’s constant-envelope-friendly behaviour up to a point — though the transitions between points pass through lower amplitude, so it is not perfectly constant-envelope unless the trajectory is shaped to avoid the origin.

The central challenge is carrier recovery. The receiver has no separate copy of the transmitter’s carrier phase, so it must regenerate it from the signal itself. A Costas loop does this by feeding back a phase error computed from the recovered symbols, locking the local oscillator so the constellation lines up on the decision axes.2 A subtlety is phase ambiguity: a squaring or Costas loop can lock at any of the symmetric phases (0°/90°/180°/270° for QPSK), so systems either send a known preamble to resolve the rotation or use differential encoding (differential decoding), where information rides in the change of phase between symbols rather than its absolute value — immune to a constant rotation at the cost of about 2–3 dB in noise performance.

Variants

  • BPSK — 2 phases, most robust, used by GPS C/A code and PSK31.
  • QPSK — 4 phases, doubles the rate at the same SNR as BPSK per bit; ubiquitous in satellite and cellular.
  • 8PSK — 8 phases, 3 bits/symbol, used by EDGE and DVB-S2.
  • π/4-DQPSK — π/4-DQPSK, a differentially encoded QPSK that never passes through the origin; carries TETRA and P25 Phase 2’s H-DQPSK inbound.
  • CQPSK — P25’s linear-simulcast QPSK, symbol-compatible with C4FM.

Higher-order PSK packs more bits but crowds the phase circle, so 16-PSK and beyond are rarely used — past 8PSK, QAM (which also uses amplitude) makes better use of the same SNR.

Relevance to SDR

P25 Phase 2 uses a π/4-DQPSK-derived PSK variant, and TETRA, most geostationary and LEO satellite downlinks, and digital broadcast (DVB-S) are PSK, so tracking phase accurately with a Costas or PLL is central to decoding them. On an SDR the recovered symbols cluster tightly when locked and smear into rings when the carrier loop is unlocked — a quick visual diagnosis. GopherTrunk handles the CQPSK/C4FM-symbol path of P25; the linear PSK physical layers of Phase 2 and TETRA are more demanding and are tracked in its status notes rather than fully claimed.

Sources

  1. Phase-shift keying — Wikipedia, for the definition and the BPSK/QPSK/8PSK variants. ↩

  2. Costas loop — Wikipedia, for carrier phase recovery and the phase-ambiguity that motivates differential encoding. ↩

See also

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