PSK rotates a point around a circle; ASK slides it in and out. The last idea of this module does both at once: vary the amplitude and the phase, and you can put constellation points anywhere on the I–Q plane, not just on a ring. That is Quadrature Amplitude Modulation — QAM — the scheme that carries the overwhelming majority of the world’s wireless bits today, from WiFi to LTE to your cable modem.
The clean way to see QAM is to remember the I–Q picture from the last lesson: a symbol is a value of I on the cosine carrier and a value of Q on the sine carrier, and the two are orthogonal. QAM simply lets each of I and Q take several amplitude levels, independently. It is two multi-level amplitude signals (two PAM streams) riding orthogonal carriers that never interfere:
A square QAM constellation uses √M levels on each axis, giving an M-point grid. Because I and Q are independent, the bits split evenly between them: 16-QAM is a 4×4 grid carrying 2 bits on I and 2 on Q — 4 bits per symbol. 64-QAM is 8×8 — 6 bits. Each doubling of levels per axis adds two bits per symbol:
| Scheme | Levels / axis | Bits / symbol | Where you meet it |
|---|---|---|---|
| 16-QAM | 4 | 4 | WiFi (802.11n), LTE |
| 64-QAM | 8 | 6 | WiFi, LTE, DVB-T |
| 256-QAM | 16 | 8 | 802.11ac, LTE-Advanced |
| 1024-QAM | 32 | 10 | WiFi 6 (802.11ax) |
| 4096-QAM | 64 | 12 | WiFi 7 (802.11be), DOCSIS 3.1 |
A dense grid is only useful if a small slip is a small mistake. Gray coding assigns the bit patterns so that any two horizontally or vertically adjacent points differ in exactly one bit. Because QAM’s I and Q axes are independent, you simply Gray-code each axis on its own. Then the common error — noise nudging a symbol into the neighbouring cell — flips a single bit, no matter how many bits the symbol carries. Without it, a 12-bit 4096-QAM symbol could scramble several bits on one small slip; with it, the bit-error rate stays close to the symbol-error rate divided by log₂M.
If more points are better, why not 64-PSK? Because PSK is stuck on a circle: as you add points, they crowd together around the ring, and the minimum distance collapses. QAM spends the same average power filling two dimensions — a grid — so its points sit farther apart. At M = 16 the QAM grid already has a noticeably larger dmin than the 16-PSK ring, and the gap widens fast with M. That is why every high-order scheme in practice is QAM, and PSK stops at 8 points.
The bill comes due in the amplifier. Unlike BPSK, QPSK, and FSK, QAM is not constant-envelope — its symbols sit at different distances from the origin, so the signal’s power swings symbol to symbol. That high peak-to-average power ratio forces a linear power amplifier run with backoff (the same efficiency penalty ASK paid in Lesson 5.2), and makes QAM sensitive to phase noise, I/Q imbalance, and amplifier non-linearity. Denser constellations also need more SNR — roughly 6 dB per extra 2 bits/symbol (Lesson 5.3). More bits is never free.
Because the right constellation depends entirely on how clean the channel is, real systems don’t pick one and stick with it — they switch on the fly. Adaptive modulation and coding (link adaptation) measures the channel quality every few milliseconds and chooses the densest QAM the SNR can support: 4096-QAM when you are next to the WiFi 7 router, dropping to 64-QAM, then QPSK, then BPSK as you walk away. WiFi (up to 256-QAM in 802.11ac, 1024-QAM in WiFi 6, 4096-QAM in WiFi 7), LTE and 5G NR (up to 256-QAM), and cable modems (DOCSIS 3.1, up to 4096-QAM) all live on this ladder. Module 6 makes the rule precise with Shannon’s capacity theorem.
Module 5 complete. That closes Module 5: Digital Modulation — from why we went digital, through ASK/FSK/PSK and the constellation, to QAM. Next, Module 6 asks the question the whole ladder was climbing toward: how many bits per second a channel can carry at all.