Phase Shift Keying (PSK)

Phase Shift Keying (PSK) is a digital modulation scheme in which the phase of a carrier wave is varied in discrete steps to encode digital data. Each phase state represents a distinct symbol or bit pattern. PSK enables bandwidth-efficient digital transmission, particularly in wireless and satellite communication.

Mathematical Representation

The general PSK signal is described by:

s(t) = A_c · cos(ω_c · t + φ_n)

Where:

• s(t) = Modulated signal (V)

• A_c = Carrier amplitude (V)

• ω_c = Carrier angular frequency (rad/s)

• φ_n = Phase corresponding to symbol n (rad)

• t = Time (s)

In BPSK (Binary PSK), only two phases are used:

• Bit 0 → phase 0

• Bit 1 → phase π

This results in:

• s(t) = A_c · cos(ω_c · t) for bit 0

• s(t) = –A_c · cos(ω_c · t) for bit 1

Common PSK Variants

BPSK (Binary PSK)

• 2 phases (0, π)

• 1 bit per symbol

• Constant envelope

• High robustness, low spectral efficiency

QPSK (Quadrature PSK)

• 4 phases (0, π/2, π, 3π/2)

• 2 bits per symbol

• Constant envelope

• Common in satellite and cellular systems

8-PSK and Higher-Order PSK

• More than 4 phases (e.g., 8-PSK: 45° steps)

• Higher data rates

• Reduced noise resilience

• Envelope not constant → may distort with nonlinear amplifiers

DPSK (Differential PSK)

• Phase difference encodes data (no absolute reference)

• Simplifies receiver design

• Used in short-range and legacy systems

π/4-QPSK

• Phase shifts in quarter rotations

• Reduces amplitude fluctuations

• Used in mobile radio to improve amplifier performance

Constellation and Signal Space

PSK modulation is often illustrated using constellation diagrams:

• BPSK: 2 points on the real axis

• QPSK: 4 points at 90° intervals

• 8-PSK: 8 points evenly spaced on a circle

Each point represents a symbol in the I/Q plane, enabling visual analysis of distance between symbols and error performance.

Bandwidth and Spectral Efficiency

PSK is more energy-efficient than Amplitude Shift Keying (ASK) and more spectrally efficient than Frequency Shift Keying (FSK). However, QAM surpasses PSK in spectral efficiency at higher orders, making it more common in modern broadband systems.

Demodulation

PSK requires coherent demodulation, where the receiver must track the carrier phase accurately. Differential variants like DPSK remove this requirement at the cost of error performance.

Applications

PSK is used across a range of communication technologies:

• Satellite systems (e.g., BPSK/QPSK in DVB-S)

• Cellular networks (e.g., QPSK in LTE uplink)

• RFID systems

• Wireless sensors and telemetry

• Optical networks (differential PSK formats)

Advantages and Limitations

Advantages

• Efficient use of power and bandwidth

• Constant-envelope (BPSK, QPSK) supports nonlinear amplification

• Scalable for moderate data rates

Limitations

• Higher-order PSK (e.g., 8-PSK) susceptible to noise

• Requires phase synchronization

• QAM preferred for high data rates and spectral efficiency