--- title: "M-ary QAM; 16-QAM vs 16-PSK" subject: "Wireless Communication" chapter: 4 key: "semester_7/wireless_communication:mary-qam-vs-psk" source: https://www.bctengineer.com/q/semester_7/wireless_communication/mary-qam-vs-psk site: BCT Engineering --- # M-ary QAM; 16-QAM vs 16-PSK Wireless Communication · Chapter 4: Modulation and Demodulation in Mobile Communication - Asked in: 2077 Chaitra, 2+6 marks - Video: [What is QAM modulation?](https://www.youtube.com/watch?v=9_478TsTNPw) — Wireless Explained - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_7/wireless_communication/mary-qam-vs-psk - Whole chapter: https://www.bctengineer.com/md/semester_7/wireless_communication/chapter-4 ## Question Why do we need M-ary QAM? Compare 16-QAM and 16-PSK using its constellation diagram. ## 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. ## Answer #### 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 ```text 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) ```text 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. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. Why is M-ary QAM needed instead of M-ary PSK for large M? A. QAM has a constant envelope unlike PSK B. PSK points crowd on one circle, whereas QAM varies amplitude and phase to spread points over the I-Q plane giving larger spacing C. QAM uses fewer bits per symbol D. QAM needs no linear amplifier Answer: B. Using both amplitude and phase increases the minimum distance for the same average power, improving noise performance. (Key point: Need for QAM) 2. For the same average symbol energy, which d_min is correct? A. 16-QAM 0.390 sqrt(E_s) versus 16-PSK 0.632 sqrt(E_s) B. Both are 0.632 sqrt(E_s) C. 16-QAM 0.632 sqrt(E_s) versus 16-PSK 0.390 sqrt(E_s) D. 16-QAM 0.316 sqrt(E_s) versus 16-PSK 0.632 sqrt(E_s) Answer: C. 16-QAM d_min = 2 sqrt(E_s/10) = 0.632 sqrt(E_s); 16-PSK d_min = 2 sqrt(E_s) sin(pi/16) = 0.390 sqrt(E_s). (Key point: Minimum distance) 3. About how much less power does 16-QAM need than 16-PSK for the same error rate? A. About 1 dB B. About 10 dB C. None, they are the same D. About 4.2 dB Answer: D. 20 log(0.632/0.390) is about 4.2 dB. (Key point: Power advantage) 4. What is a disadvantage of 16-QAM relative to 16-PSK? A. Its envelope varies, so a linear amplifier is needed and it is sensitive to amplitude fading and non-linearity B. It carries fewer bits per symbol C. It has smaller minimum distance D. It has a constant envelope so wastes power Answer: A. Both carry 4 bits per symbol, but QAM has three amplitude levels, which demands linear amplification. (Key point: Drawback of QAM) ## Related in Wireless Communication - [Need for speech coding; vocoder concept](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Aspeech-coding-need-vocoder) — Wireless Communication, chapter 6, asked 2× - [Need for equalization and basic technique](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Aequalization-need-basic) — Wireless Communication, chapter 5 - [Digital vs analog modulation; GMSK](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Adigital-modulation-gmsk) — Wireless Communication, chapter 4 - [Proper vs improper handoff; cellular concept N = 7](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Ahandoff-situation-cellular-n7) — Wireless Communication, chapter 2 - [Okumura vs Hata; delay spread numerical](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Aokumura-hata-delay-spread) — Wireless Communication, chapter 3 - [Feedback vs maximum ratio combining diversity](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Afeedback-vs-mrc-diversity) — Wireless Communication, chapter 5 ## Related in other subjects - [QAM modulation, demodulation and constellation](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Aqam-mod-demod-constellation) — Communication Systems, chapter 7 - [SSB figure of merit and 32-QAM constellation](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Assb-figure-of-merit-32qam) — Communication Systems, chapter 9 - [Constellation diagram significance; E1 vs T1](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Aconstellation-significance-e1-t1) — Communication Systems, chapter 5 - [Need for shift keying; ASK vs FSK vs PSK](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Ashift-keying-ask-fsk-psk) — Communication Systems, chapter 7