Also known as: QPSK, quadrature phase-shift keying
QPSK (quadrature phase-shift keying) is phase-shift keying with four carrier phases, so each symbol carries two bits.1 By using both the in-phase (I) and quadrature (Q) components of the carrier, QPSK doubles the throughput of BPSK in the same bandwidth while keeping the same bit-error performance — which makes it one of the most widely deployed digital modulations in the world.
How it works
QPSK can be seen as two independent BPSK streams: the I channel carries one bit and the Q channel the other, added in quadrature. The four resulting phases — typically at 45°, 135°, 225°, 315° — are usually labelled with a Gray code, so neighbouring points differ by a single bit and the most likely symbol error costs only one bit. Because a QPSK symbol packs two bits into the same energy that BPSK spends on one, QPSK carries twice the data in the same spectrum without losing noise margin, which is its defining advantage.
Demodulation is coherent: a Costas loop recovers the carrier so the received cloud lines up with the reference constellation, then the I and Q signs give the dibit. The carrier-recovery loop has a four-fold phase ambiguity, so systems use differential encoding or a known sync word to fix the absolute rotation. A drawback of plain QPSK is that a symbol transition can swing the phase by 180°, driving the envelope briefly through zero and stressing non-linear amplifiers.
Variants
Two refinements dominate in radio. Offset QPSK (OQPSK) staggers the I and Q bit transitions by half a symbol so the phase never jumps a full 180°, easing amplifier requirements. π/4-DQPSK rotates the constellation by 45° each symbol and encodes bits differentially in phase changes, again avoiding through-origin transitions; it is the modulation of P25 Phase 1’s CQPSK path, TETRA, and several cordless standards. CQPSK (compatible QPSK) is the linear-modulation twin of P25 C4FM, sharing the same over-the-air symbols so the two interoperate.
Relevance to SDR
QPSK and its variants are everywhere a link must be spectrally efficient yet robust: satellite downlinks, DVB, cable and cellular systems, and land-mobile radio. In P25, π/4-DQPSK/CQPSK is the linear cousin of C4FM at 4800 symbols/s; TETRA uses π/4-DQPSK at 18 000 symbols/s; P25 Phase 2 uses an H-DQPSK-family scheme. On a constellation display, QPSK shows four clusters at the diagonals; timing and carrier errors rotate or smear them.
GopherTrunk decodes P25 (whose symbols can be viewed through the QPSK/CQPSK lens) and TETRA, so QPSK-family demodulation is directly relevant to its decode chain, alongside the equivalent 4FSK view of the same land-mobile signals.
Sources
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Phase-shift keying — Wikipedia, for the QPSK definition, the two-bits-per-symbol constellation, and the OQPSK/π-4-DQPSK variants. ↩