What Is Quadrature Phase Shift Keying?

Quadrature phase shift keying (QPSK) is a digital modulation scheme in which information is encoded in the phase of a carrier sinusoid, with four distinct phase states separated by 90 degrees. Each symbol carries two bits, mapping the dibit pairs 00, 01, 10, and 11 to phases of 45, 135, 225, and 315 degrees respectively in the most common Gray-coded convention. Because four states fit within a single symbol period, QPSK achieves twice the spectral efficiency of binary phase shift keying (BPSK) while maintaining the same noise immunity as BPSK on a per-bit basis, a property that made it the modulation of choice for bandwidth-constrained links.

The scheme is formulated as two BPSK streams superimposed on orthogonal carriers. The in-phase (I) carrier transmits one bit of each dibit pair and the quadrature (Q) carrier, offset by 90 degrees, transmits the other. This decomposition means QPSK can be built from two independent BPSK modulators, which simplifies hardware design and provides an intuitive framework for analysis. The mathematical structure connects directly to quadrature amplitude modulation: QPSK is equivalent to 4-QAM with a fixed-amplitude constellation at the corners of a square.

Phase Encoding and Constellation

The four-point QPSK constellation places symbols at equal distance from the origin and at 90-degree intervals on the complex plane. The Euclidean distance between adjacent symbols is sqrt(2) times the constellation radius, the same as for BPSK with identical energy per bit, which explains why both schemes have identical bit error rate curves over an additive white Gaussian noise (AWGN) channel when expressed in terms of Eb/N0. At an Eb/N0 of 10 dB, QPSK achieves a bit error rate below 10^-5, which is adequate for many satellite and wireless channels. Research on OQPSK modem implementation published through IEEE Xplore illustrates how these constellations are realized in field-programmable gate array hardware, covering the filter chains, phase detectors, and timing recovery loops that a practical QPSK modem requires. Gray coding of the constellation ensures that adjacent symbols differ in only one bit, so most symbol errors produce only a single bit error, limiting the degradation of bit error rate relative to symbol error rate.

Variants: OQPSK, DQPSK, and pi/4-QPSK

Several QPSK variants address specific implementation constraints. Offset QPSK (OQPSK) delays the Q channel relative to I by half a symbol period, preventing transitions where both bits change simultaneously and eliminating the 180-degree phase reversals that cause power amplifier nonlinearities to regenerate out-of-band energy. This makes OQPSK preferable for nonlinear amplifier chains in satellite terminals. Differential QPSK (DQPSK) encodes each dibit as a phase change relative to the preceding symbol rather than as an absolute phase, removing the need for an absolute phase reference at the receiver. The pi/4-shifted DQPSK variant, used in the Digital European Cordless Telephone (DECT) standard and North American TDMA (IS-54) cellular systems, combines the benefits of differential detection with reduced envelope fluctuation. The Analog Devices QPSK glossary entry summarizes these variants and the trade-offs governing their selection.

Applications

Quadrature phase shift keying has applications in a wide range of disciplines, including:

• Satellite communications, where QPSK and its offset variant OQPSK are standard payload and telemetry modulation schemes for LEO and GEO spacecraft
• GPS and GNSS signal transmission, where QPSK and binary offset carrier modulations carry ranging codes on L-band frequencies as documented by NOAA's National Geodetic Survey
• IEEE 802.11b wireless LAN at 5.5 and 11 Mbps data rates, using complementary code keying modulated onto QPSK
• Cable modem upstream channels following DOCSIS specifications
• Deep-space communications links operated by NASA and ESA, where power efficiency is the dominant constraint