QAM

Quadrature amplitude modulation varies both amplitude and phase to pack many bits per symbol. Learn I/Q representation, square constellations (16-, 64-, 256-, 1024-QAM), spectral efficiency, symbol error rate and required SNR, EVM, adaptive modulation, and OFDM with QAM in Wi-Fi, LTE/5G and cable.

Wi-Fi 6 uses up to 1024-QAM (10 bits per symbol), 5G up to 256-QAM, and cable DOCSIS up to 4096-QAM. Higher orders deliver more throughput in the same bandwidth — if the signal is clean enough.

An analogy

QAM is like a chessboard of points: each square represents a bit pattern. More squares carry more bits, but noise can make you land on the wrong square.

I/Q

Two carriers 90° apart (cosine and sine) are independently amplitude-modulated and added. Each symbol is a point (I, Q) in the constellation.

Higher orders

Each doubling of M adds one bit per symbol but needs ≈ 3 dB more SNR (≈ 6 dB per extra bit on each axis). 16-QAM ≈ 17 dB, 64-QAM ≈ 23 dB, 256-QAM ≈ 29 dB SNR for low error rates (uncoded).

Adaptive modulation

Links measure channel quality and switch modulation and coding (MCS) on the fly — QPSK at cell edge, 256-QAM near the tower — maximising throughput.

OFDM and impairments

OFDM splits a wide channel into thousands of QAM subcarriers, making multipath manageable with a cyclic prefix. Phase noise, PA non-linearity, IQ imbalance and quantisation limit achievable EVM for high-order QAM.

Formulas

• QAM signal: s(t) = I(t) cos ω_c t − Q(t) sin ω_c t
• Bits per symbol: k = log₂ M
• Spectral efficiency: η = log₂ M / (1 + α)
• SER (square M-QAM): P_s ≈ 4(1 − 1/√M) Q(√(3 SNR/(M − 1)))
• EVM ↔ SNR: SNR ≈ −20 log₁₀(EVM_rms)

Worked example: Symbol rate for 100 Mbps

Given: 64-QAM

Find: Symbol rate.

• k = 6
• R_s = 100/6 = 16.7 Mbaud

Answer: 16.7 Mbaud

Worked example: SNR needed

Given: Shannon limit for 6 bit/s/Hz

Find: Minimum SNR.

• SNR = 2⁶ − 1 = 63 → 18 dB

Answer: 18 dB theoretical minimum (real 64-QAM ≈ 22–25 dB)

Common mistakes

• Wrong: Choosing the highest QAM regardless of SNR. — Right: Match MCS to channel quality.
• Wrong: Ignoring transmitter EVM. — Right: EVM limits achievable QAM order.

Applications

• Wi-Fi 6/7: 1024/4096-QAM OFDM.
• 4G/5G: Adaptive QPSK–256-QAM.
• Cable & microwave backhaul: Very high-order QAM.

Key takeaways

• QAM = amplitude + phase (I/Q).
• k = log₂ M bits per symbol.
• ≈ 3 dB more SNR per doubling of M.
• Adaptive MCS and OFDM in modern systems.

Going further

• Probabilistic shaping: Non-uniform constellations approaching Shannon.
• MIMO: Spatial streams multiply throughput.
• DPD: Digital predistortion for PA linearity.