Digital Modulation: ASK, PSK, FSK and QAM For students.

Digital modulation is how bits ride on radio waves: instead of wiggling a carrier with audio (like AM/FM), we switch the carrier's amplitude, frequency, or phase between fixed states, each state meaning a pattern of bits. Your Wi-Fi, phone calls, and satellite TV are all just carriers hopping between such states billions of times per second.

The four classics each exploit one property: ASK (amplitude-shift keying) switches the carrier on and off, FSK (frequency-shift keying) hops between two tones, PSK (phase-shift keying) flips the phase, and QAM (quadrature amplitude modulation) varies amplitude and phase together to pack in the most bits. Choosing among them is the central trade of wireless design: speed versus toughness.

Key Concepts

• ASK: 1 = carrier on, 0 = carrier off (also called on-off keying) — simplest, but any amplitude noise corrupts it.
• FSK: 1 = frequency f1, 0 = frequency f2 — constant amplitude, so it resists noise.
• PSK: bits map to phases, e.g. BPSK uses 0° and 180°; QPSK uses four phases (45°, 135°, 225°, 315°) to send 2 bits per symbol.
• QAM: combines amplitude and phase — 16-QAM has 16 distinct points, carrying 4 bits per symbol; 64-QAM carries 6.
• Symbol: one transmitted state; symbol rate (baud) = bit rate ÷ bits per symbol.
• Constellation diagram: the map of all states as points; wider spacing means tougher against noise.

Formulas

• Bits per symbol: k = log2(M) for M-ary modulation — BPSK: 1, QPSK: 2, 16-QAM: 4, 64-QAM: 6.
• Symbol rate: Rs = Rb/k baud, where Rb is the bit rate in bits/s.
• BPSK wave: s(t) = ±Ac cos(2πfct) — the ± is the 0°/180° phase flip.
• FSK tones: s(t) = Ac cos(2πf1t) or Ac cos(2πf2t); minimum tone spacing ≈ 1/(2T) Hz for orthogonality, T = bit time.
• Assumptions: the channel is narrow enough that symbols do not smear into each other (no intersymbol interference); real systems add pulse shaping.

Worked Example

A link must carry Rb = 200 kbps. Step 1: with BPSK (1 bit/symbol), Rs = 200/1 = 200 kbaud, needing ≈ 200 kHz of bandwidth. Step 2: with QPSK (2 bits/symbol), Rs = 200/2 = 100 kbaud — half the bandwidth for the same data. Step 3: with 16-QAM (4 bits/symbol), Rs = 200/4 = 50 kbaud — a quarter of the BPSK bandwidth, but the 16 constellation points sit much closer together, so the link needs a far cleaner signal (higher SNR) to avoid errors. Step 4: the bits 1011 in 16-QAM map to a single symbol — one point on the constellation — transmitted in 20 µs (1/50 kbaud). This is exactly why your Wi-Fi slows down at long range: it retreats from 1024-QAM to QPSK/BPSK as the signal weakens.

Common Misconceptions

• "Higher QAM is always better." Wrong: 256-QAM is fast but fragile — phones drop to QPSK at the cell edge because a weak signal cannot resolve 256 crowded points.
• "ASK is obsolete." Not quite: on-off keying still lives in fibre optics (light on/off) and cheap RF remotes where simplicity beats efficiency.
• "FSK and FM are the same." Close but different: FSK is FM with digital (two-level) input — the math overlaps, but FSK's discrete tones are designed for bit decisions.

Real-World Applications

• Wi-Fi and 4G/5G adapt between QPSK, 16-QAM, 64-QAM, and 256/1024-QAM as signal quality changes.
• Bluetooth Classic uses GFSK (a smoothed FSK); satellite TV uses QPSK/8PSK.
• Old dial-up modems sang FSK/PSK tones down phone lines.
• Deep-space probes use BPSK — the toughest, slowest option — because every decibel counts.

ASK shouts by switching on and off, FSK by changing tone, PSK by flipping phase, and QAM by doing amplitude and phase together. More bits per symbol means more speed in less spectrum — but only if the signal is clean enough to tell the crowded states apart. That single trade shapes every wireless standard you use.