ASK, FSK & PSK

Digital modulation maps bits onto a carrier's amplitude, frequency or phase. Learn ASK/OOK, binary and M-ary FSK (and GFSK/MSK), BPSK, QPSK and differential PSK; constellation diagrams; bandwidth; BER comparisons; coherent vs non-coherent detection; and where each is used.

Key fobs use OOK, Bluetooth uses GFSK, GPS and satellites use BPSK, and QPSK is everywhere from DVB-S to LTE control channels. Each trades complexity, bandwidth and robustness differently.

An analogy

ASK is changing loudness, FSK is changing pitch, and PSK is changing the timing of a beat — all to signal 0s and 1s.

ASK and OOK

Amplitude shift keying switches between amplitudes; on-off keying (carrier on = 1, off = 0) is the simplest — used in remote controls and optical links. Sensitive to noise and fading.

FSK

Different frequencies for 0 and 1; constant envelope; can be detected non-coherently (simple receivers). MSK and GFSK smooth phase transitions to narrow the spectrum — Bluetooth, DECT, many IoT radios.

PSK

BPSK uses 0°/180° phases — the most robust binary scheme. QPSK sends 2 bits per symbol (four phases) with the same BER per bit as BPSK but half the bandwidth. DPSK avoids needing an absolute phase reference.

Constellations and detection

Constellation diagrams plot symbols in the I/Q plane; distance between points sets noise immunity. Coherent receivers need carrier phase recovery (Costas loops); non-coherent ones are simpler but need ≈ 1–3 dB more power.

Formulas

• BPSK / QPSK BER: P_b = ½ erfc(√(E_b/N₀))
• Coherent BFSK BER: P_b = ½ erfc(√(E_b/2N₀))
• Non-coherent BFSK BER: P_b = ½ e^(−E_b/2N₀)
• Symbol rate: R_s = R_b / log₂ M
• PSK null-to-null bandwidth: B ≈ 2 R_s

Worked example: BER comparison at 9.6 dB

Given: E_b/N₀ = 9.6 dB

Find: BER for BPSK, coherent and non-coherent FSK.

• BPSK: 9.7 × 10⁻⁶
• Coherent FSK: 1.3 × 10⁻³
• Non-coherent FSK: 5.2 × 10⁻³

Answer: BPSK is ≈ 100× better at this Eb/N₀

Worked example: QPSK symbol rate

Given: 10 Mbps QPSK

Find: Symbol rate and bandwidth.

• R_s = 10/2 = 5 Mbaud
• B ≈ 2 × 5 = 10 MHz null-to-null (≈ 6.75 MHz with α = 0.35)

Answer: 5 Mbaud

Common mistakes

• Wrong: Assuming QPSK has worse BER than BPSK. — Right: Per bit, they're equal (Gray-coded).
• Wrong: Ignoring carrier recovery. — Right: Coherent PSK needs accurate phase tracking.

Applications

• Remote keys & RFID: OOK/ASK.
• Bluetooth, DECT, IoT: GFSK and FSK.
• Satellite, GPS, LTE: BPSK and QPSK.

Key takeaways

• ASK amplitude, FSK frequency, PSK phase.
• BPSK/QPSK most power-efficient binary schemes.
• R_s = R_b/log₂ M.
• Coherent vs non-coherent trade-offs.

Going further

• MSK/GMSK: Continuous-phase FSK with compact spectrum.
• Costas loop: Carrier recovery for PSK.
• OQPSK: Reduced envelope fluctuation.