--- title: "QAM modulation and demodulation" subject: "Communication Systems" chapter: 7 key: "semester_6/communication_systems:qam-mod-demod" source: https://www.bctengineer.com/q/semester_6/communication_systems/qam-mod-demod site: BCT Engineering --- # QAM modulation and demodulation Communication Systems · Chapter 7: Digital Modulation Techniques - Asked in: 2078 Chaitra, 5 marks - Video: [QAM Quadrature Amplitude Modulation | QAM Transmitter | QAM Receiver | Constellation Diagram of QAM](https://www.youtube.com/watch?v=MAZHck0oWZA) — Engineering Funda - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_6/communication_systems/qam-mod-demod - Whole chapter: https://www.bctengineer.com/md/semester_6/communication_systems/chapter-7 ## Question Explain QAM modulation and demodulation with its required diagram. ## Short answer QAM varies amplitude and phase using I and Q carriers, sending multiple bits per symbol. The modulator splits bits into multilevel I and Q streams multiplied by carriers. The coherent demodulator correlates and makes multilevel decisions. QAM has larger symbol distances than M-PSK for same average power. ## Answer **Quadrature Amplitude Modulation (QAM)** is an M-ary scheme in which both the amplitude and the phase of the carrier change. Two independent amplitude-modulated carriers, $\cos 2\pi f_ct$ (in-phase, I) and $\sin 2\pi f_ct$ (quadrature, Q), are added so that each symbol carries $\log_2 M$ bits. $$ s_k(t)=\sqrt{\frac{2E_0}{T}}\,a_k\cos 2\pi f_ct-\sqrt{\frac{2E_0}{T}}\,b_k\sin 2\pi f_ct,\qquad 0\le t\le T $$ where $(a_k,b_k)$ are integer levels, e.g. $\pm1,\pm3$ for 16-QAM, and $E_0$ is the energy of the lowest-amplitude signal. #### Modulator ```text +-> [2-to-L level] -> a_k -->(X)<- cos wc t binary | | data -->[S/P] (+)--> QAM | | +-> [2-to-L level] -> b_k -->(X)<- -sin wc t ``` 1. The serial data is split into two streams (half the bits each). 2. Each stream is grouped into $\log_2\sqrt{M}$ bits and converted to one of $L=\sqrt{M}$ levels. 3. The levels multiply the I and Q carriers and the products are added. #### Demodulator (coherent) ```text +->(X)->[int 0..T]->[L-level decision]-+ | ^ cos wc t | r(t) ----+ [P/S]-> data | v -sin wc t | +->(X)->[int 0..T]->[L-level decision]-+ ``` 1. Two correlators (multiply and integrate) recover the I and Q amplitudes; the orthogonality of cos and sin removes cross-talk. 2. Each output is compared with $L-1$ thresholds to decide the level. 3. Level-to-bits conversion and a parallel-to-serial converter give the data back. A carrier recovery circuit is needed because detection is coherent. #### 16-QAM constellation ```text Q * * | * * +3 | * * | * * +1 -----------+-----------> I * * | * * -1 | * * | * * -3 -3 -1 +1 +3 ``` 16 points, 4 bits per symbol; with Gray coding, neighbours differ by one bit. For the same $M$, QAM has the same bandwidth efficiency as M-ary PSK ($\log_2 M$ bits per symbol), but because its points are spread over the whole plane rather than on one circle, they are farther apart for the same average power, so QAM gives a lower error probability. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. What is varied in M-ary QAM? A. Only the phase of the carrier B. Both the amplitude and the phase of the carrier, using quadrature carriers C. Only the frequency of the carrier D. Only the amplitude of a single carrier Answer: B. Two amplitude-modulated carriers, cos and sin, are added, so both amplitude and phase change. (Key point: QAM idea) 2. How many bits does each branch of a 16-QAM modulator carry per symbol? A. 4 bits, converted to one of 16 levels B. 1 bit, converted to one of 2 levels C. 2 bits, converted to one of 4 levels D. 8 bits, converted to one of 4 levels Answer: C. The serial data is split into two streams; each uses log2(sqrt(M)) = 2 bits and L = sqrt(M) = 4 levels. (Key point: Bits per symbol) 3. How does the QAM demodulator separate the I and Q data? A. A single envelope detector followed by an ADC B. Band-pass filters at two different frequencies C. A zero-threshold comparator on the sum of both branches D. Correlators with cos and sin carriers; orthogonality removes cross-talk, then L-1 thresholds decide the level Answer: D. Multiply-and-integrate with the two orthogonal carriers recovers each amplitude, and each is compared with L-1 thresholds. (Key point: Demodulator) 4. Why is carrier recovery needed in QAM detection? A. Detection is coherent, so the local carriers must match the transmitted phase B. To amplify the received signal C. To generate the Gray code D. To remove the envelope of the signal Answer: A. Without correct phase, the I and Q channels leak into each other. (Key point: Coherence) ## Related in Communication Systems - [QAM modulation, demodulation and constellation](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Aqam-mod-demod-constellation) — Communication Systems, chapter 7 - [QPSK modulation and demodulation](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Aqpsk-mod-demod) — Communication Systems, chapter 7 - [Analog communication block diagram; modulation and its reasons](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Aanalog-comm-modulation-reasons) — Communication Systems, chapter 1, asked 3× - [Modulation; analog communication system block diagram](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Amodulation-analog-block-diagram) — Communication Systems, chapter 1, asked 3× - [Reasons for modulation; digital communication block diagram](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Amodulation-reasons-digital-adv-duplex) — Communication Systems, chapter 1 - [Communication system block diagram; need for modulation](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Acomm-block-diagram-needs-modulation) — Communication Systems, chapter 1 ## Related in other subjects - [Quadrature amplitude modulation (QAM)](https://www.bctengineer.com/question.md?key=semester_5%2Fdata_communication%3Aqam-explanation) — Data Communication, chapter 5, asked 4× - [M-ary QAM; 16-QAM vs 16-PSK](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Amary-qam-vs-psk) — Wireless Communication, chapter 4