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Phase Shift Keying (PSK) encodes information in carrier phase: s(t) = A·cos(ωct + φ[n]) for symbol n. BPSK uses two phases (0, π), QPSK uses four phases at π/4, 3π/4, 5π/4, 7π/4, and M-ary PSK extends to M phases. Demodulation uses phase-locked loops or matched filters matched to each constellation point.
From quadrature modulation and IQ representation, you know that any bandpass signal can be described by its in-phase (I) and quadrature (Q) components — effectively a 2D coordinate in the IQ plane. You also know that multiplying a baseband signal by cos(ω_c t) shifts it to carrier frequency ω_c without altering its information content. Phase Shift Keying builds directly on this: instead of varying amplitude (as in ASK) or frequency (as in FSK), PSK encodes information by varying the phase angle of the carrier for each transmitted symbol.
In BPSK (Binary PSK), there are only two possible phases: 0 and π (i.e., 0° and 180°). A bit value of 0 sends A·cos(ω_c t); a bit value of 1 sends A·cos(ω_c t + π) = −A·cos(ω_c t). In the IQ plane, these two constellation points sit at (+A, 0) and (−A, 0) — they are diametrically opposite on the I-axis. The receiver decides which symbol was sent by determining which constellation point the received signal is closest to (a minimum distance decision). BPSK transmits 1 bit per symbol and has the largest possible separation between points for a given amplitude, making it the most noise-resistant PSK scheme.
QPSK (Quadrature PSK) uses four phases: π/4, 3π/4, 5π/4, and 7π/4. In the IQ plane, these four constellation points sit at the corners of a square — two bits are encoded per symbol, doubling the spectral efficiency without increasing the required bandwidth. The two bits (b₀, b₁) select one of the four phases via Gray coding: adjacent constellation points differ by only one bit, so a detection error (misidentifying a point as a neighbor) typically causes only a single-bit error rather than two, improving practical bit error rate. QPSK achieves 2 bits per symbol with the same bandwidth as BPSK — a factor-of-two efficiency gain.
M-ary PSK generalizes to M equally-spaced phases, transmitting log₂(M) bits per symbol. Each additional doubling of M (8-PSK, 16-PSK, ...) adds one more bit per symbol but shrinks the angular distance between constellation points, requiring higher SNR to maintain the same error rate. Beyond 8-PSK, engineers typically switch to QAM (Quadrature Amplitude Modulation), which uses both phase and amplitude variation to spread constellation points more efficiently in 2D space. Demodulation of PSK requires accurate carrier phase recovery (typically via a phase-locked loop) because the receiver must know the reference phase to make correct decisions — this is the central practical challenge of PSK systems and the reason coherent demodulation is essential.