QPSK constellation at 20 dB SNR. Four tight clusters, each representing a 2-bit symbol.
The Core Idea
Before a radio signal reaches your phone, someone had to map data bits onto a physical waveform. Digital modulation does this by choosing points on a 2D plane — the constellation diagram — where each point represents a unique group of bits. QPSK uses 4 points (2 bits/symbol), 16-QAM uses 16 (4 bits/symbol), 64-QAM uses 64 (6 bits/symbol). More points = faster data rate, but points are closer together = more vulnerable to noise.
The Mathematics
A modulated symbol is:
s(t) = I·cos(2πfct) − Q·sin(2πfct)
where (I, Q) is the constellation point. Through an AWGN channel:
(I', Q') = (I + nI, Q + nQ) where nI, nQ ~ N(0, σ²)
and σ² = 1/(2·SNR_linear).
16-QAM at 20 dB SNR. Sixteen clusters, 4 bits each. Points are packed tighter than QPSK.
Switch between modulation orders and watch the clusters multiply. Each step up in order doubles the bits per symbol — but also halves the noise margin between adjacent points.
Bit error rate
The probability of decoding incorrectly depends on the minimum distance between points and noise level:
- QPSK at 20 dB SNR: BER ≈ 10⁻⁵ (one error per 100,000 bits).
- 64-QAM at 20 dB SNR: BER ≈ 10⁻³ — two orders of magnitude worse.
This is the fundamental trade-off: spectral efficiency vs robustness. Wi-Fi and LTE switch between modulation orders in real time — high-order QAM when signal is strong, falling back to QPSK when conditions degrade.
64-QAM at 10 dB SNR. The noise clouds overlap — many symbols will be decoded incorrectly.
Error Vector Magnitude (EVM)
EVM measures the average distance between received and ideal constellation points. A good transmitter has EVM < −30 dB (received points within 3% of ideal). EVM degrades with phase noise, amplifier distortion, and channel fading.
Further reading
- QAM (Wikipedia)
- Constellation diagram
- Proakis, Digital Communications