QAM: packing more bits into every symbol

Once the waveform is chosen, the modulation decides how many bits ride on each symbol. QAM stacks more and more points on the same plane, trading robustness for speed.

1. DefinitionWhat is QAM?

A carrier wave has an amplitude and a phase. Quadrature amplitude modulation varies both, by adding two carriers that are 90 degrees apart. They are called I (in-phase) and Q (quadrature). Every choice of I and Q is one point on a plane, a constellation, and one point is one symbol that carries a fixed number of bits.

• BPSK has two points (1 bit per symbol), QPSK four (2 bits; it is the same as 4-QAM), 16-QAM sixteen (4 bits), and so on.
• A square constellation with M points carries log₂(M) bits per symbol: 64-QAM carries 6, 256-QAM 8, 1024-QAM 10 and 4096-QAM 12.
• A Gray-coded constellation labels neighbouring points so that they differ in only one bit.

2. PurposeMore bits without more bandwidth

A channel’s bandwidth limits how many symbols per second it can carry. To go faster you can widen the channel, use more antennas, or put more bits in each symbol. QAM is the third option, and it is why each Wi-Fi generation raised the top constellation: 64-QAM (802.11a/g/n), 256-QAM (802.11ac), 1024-QAM (802.11ax) and 4096-QAM (802.11be).

3. MechanismPoints, noise and decisions

Choose a modulation and a signal-to-noise ratio. The small blue dots are the symbols a receiver sees; the receiver decides by picking the nearest point. When noise pushes a dot across the boundary between two points the symbol is wrong. Watch BPSK survive almost any noise while 4096-QAM falls apart.

4. VisualThe ladder of modulations in 802.11

802.11 pairs each modulation with a coding rate (the share of bits that are data rather than error protection). The standard sets two numbers for each pair: how accurate the transmitter must be (relative constellation error, EVM, in dB) and how weak a signal the receiver must still decode. Both get stricter as the constellation gets denser.

From IEEE Std 802.11-2020, clause 21 (VHT), Tables 21-24 and 21-25. The sensitivity figures assume a receiver noise figure of 10 dB and a 5 dB implementation margin. 1024-QAM (802.11ax) and 4096-QAM (802.11be) are defined in the later amendments, which are not in the 2020 edition; they demand tighter accuracy again.

5. MathematicsSpacing, bits and rate

• Points and levels. A square M-QAM constellation has sqrt(M) levels on each axis, at -(sqrt(M) – 1), … -1, +1, … +(sqrt(M) – 1) before scaling. Scaling to unit average power divides by sqrt(2(M – 1) / 3).
• Spacing. The gap between neighbours is then 2 / sqrt(2(M – 1) / 3). For 64-QAM that is 0.309; for 256-QAM 0.153. Halving the gap costs 6 dB of noise margin.
• Symbol errors. For square QAM and Gaussian noise, the symbol error rate is about 4(1 – 1/sqrt(M)) × Q(sqrt(3 × SNR / (M – 1))). The model above prints this value next to the simulated result.
• Rate gain. At the same coding rate, 256-QAM carries 8 / 6 = 1.33 times the bits of 64-QAM, 1024-QAM 10 / 8 = 1.25 times more than 256-QAM, and 4096-QAM 12 / 10 = 1.2 times more than 1024-QAM. The gains shrink while the SNR needed keeps rising.
• Example. 802.11ac on 80 MHz has 234 data subcarriers. With 256-QAM (8 bits), coding rate 5/6 and a 3.6 µs symbol (short guard interval), one stream carries 234 × 8 × 5/6 / 3.6 µs = 433.3 Mbit/s.

6. Real-world behaviourWhy high QAM is only for short range

• The top rates need a very clean signal. The standard’s 20 MHz sensitivity for 256-QAM 5/6 is -57 dBm against -82 dBm for BPSK 1/2: a 25 dB difference. In practice that means high modulations only near the access point and with little interference.
• Transmitter quality sets a ceiling. Even with a perfect channel, a radio whose own error (EVM) is too large cannot use a dense constellation. That is why 1024-QAM and 4096-QAM demand better radios.
• Rate adaptation. The sender keeps testing and chooses the densest constellation that still works. A client reporting a low rate is usually seeing a low SNR rather than a broken radio.
• Wider channels need more signal. Doubling the channel width doubles the noise power, so every rate needs about 3 dB more signal (the standard’s table drops by 3 dB at each doubling).

Practical validationProve it in a capture and on a spectrum analyser

Reading about a band is one thing; seeing it in your own evidence is the skill. These checks work with any monitor-mode capture:

• In a capture, filter on data frames from one client and watch the data rate the radio information reports (the Wireshark field wlan_radio.data_rate) while you walk away from the access point. It steps down through the ladder as the SNR falls.
• Check the modulation and coding scheme (MCS) index reported in the radio information against the table in this topic.
• Question to answer: how much faster is a 1024-QAM link than a 256-QAM link at the same coding rate and width, and what must be true of the signal to get it?

Check your understandingQuick quiz

ReferencesSources and further reading

• IEEE Std 802.11-2020 (IEEE Xplore)
• IEEE 802.11 Working Group: standards timelines (approval and publication dates)
• Wi-Fi Alliance: specifications

Constellation, EVM and sensitivity figures were checked against IEEE Std 802.11-2020 (clause 17 for BPSK to 64-QAM and clause 21 for 256-QAM). The symbol error approximation is standard communications theory. IEEE 802.11ax and 802.11be (1024-QAM and 4096-QAM) are later amendments.