MPSK

M-ary Phase Shift Keying (MPSK) is a digital modulation technique that encodes data by varying the phase of a carrier signal while keeping the amplitude constant. It uses M distinct phase states evenly spaced around the unit circle, with symbol s_k = exp(j 2πk/M) for k = 0, ..., M−1. Each symbol carries log2 M bits.

In coherent demodulation, the receiver compares the received complex symbol to the closest constellation point and decides the corresponding symbol. The scheme requires carrier phase synchronization and a reference oscillator.

Performance and design tradeoffs: For additive white Gaussian noise (AWGN), the approximate symbol error probability is Pe ≈ 2 Q(√(2 Es/N0) sin(π/M)) for M ≥ 4, where Es is symbol energy and N0 is the noise spectral density. Bit error probability depends on the labeling; with Gray coding, Pb ≈ Pe/log2 M. Exact expressions involve integrals. MPSK offers a constant envelope, enabling efficient nonlinear power amplifiers, and has relatively simple demodulation. Increasing M raises spectral efficiency but reduces the minimum distance between constellation points, making the scheme more sensitive to phase noise and errors at the same Eb/N0. Phase synchronization becomes more challenging as M grows.

Common values and use: 4-PSK (QPSK), 8-PSK, and 16-PSK are widely used. MPSK is employed in various wireless and satellite communication links and is often combined with coding or differential encoding to improve robustness against phase ambiguities.

See also: BPSK, QPSK, PSK, QAM.