- 2077 Chaitra · 2+6 marks
M-ary QAM; 16-QAM vs 16-PSK
Short answer
M-ary QAM varies amplitude and phase, giving larger minimum distance than M-PSK at the same average energy. For 16-QAM, d_min is 0.632 sqrt(Es); for 16-PSK, it is 0.390 sqrt(Es), so 16-QAM has about 4.2 dB better noise performance. Both carry 4 bits per symbol.
Why do we need M-ary QAM? Compare 16-QAM and 16-PSK using its constellation diagram.
Need for M-ary QAM
In M-ary PSK all points lie on one circle, so as M increases the points crowd together and the noise margin falls quickly. M-ary QAM varies both amplitude and phase, spreading the points over the I–Q plane. This gives:
- High bandwidth efficiency: log₂M bits per symbol (16-QAM: 4 bits, 64-QAM: 6 bits) in the same bandwidth.
- Better noise performance than M-PSK for the same M and same average power, because the minimum distance is larger.
- Support for high data rates in limited spectrum (LTE, Wi-Fi, DVB, cable modems) and adaptive modulation.
Constellation diagrams
16-QAM (square) 16-PSK (circle)
Q Q
• • | • • • • •
• • | • • • | •
---------+--------- I • | •
• • | • • •-------+-------• I
• • | • • • | •
• | •
• • •
levels ±1, ±3 on I and Q 16 points, 22.5° apart
Minimum distance (same average symbol energy E_s)
16-PSK: d_min = 2√E_s sin(π/16) = 0.390 √E_s
16-QAM: d_min = 2√(E_s/10) = 0.632 √E_s
Ratio = 20 log(0.632/0.390) ≈ 4.2 dB
So 16-QAM needs about 4.2 dB less power than 16-PSK for the same error rate.
Comparison
| Point | 16-QAM | 16-PSK |
|---|---|---|
| Varies | Amplitude and phase | Phase only |
| Constellation | Square grid (4 × 4) | Single circle |
| Amplitude levels | 3 different radii | 1 (constant) |
| d_min (same E_s) | 0.632√E_s | 0.390√E_s |
| Noise immunity | Better (~4.2 dB gain) | Poorer |
| Amplifier needed | Linear (envelope varies) | Can be less linear |
| Bandwidth efficiency | 4 bits/symbol | 4 bits/symbol |
| Sensitivity | Amplitude fading, non-linearity | Phase noise |
Both carry 4 bits per symbol, but 16-QAM uses the signal space more efficiently, which is why QAM is preferred for M ≥ 16.
✓ Answer checked by Claude Opus 5.5 (high effort)
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