---
title: "QAM: need, generation and detection"
subject: "Communication Systems"
chapter: 7
key: "semester_6/communication_systems:qam-need-generation-detection"
source: https://www.bctengineer.com/q/semester_6/communication_systems/qam-need-generation-detection
site: BCT Engineering
---

# QAM: need, generation and detection

Communication Systems · Chapter 7: Digital Modulation Techniques

- Asked in: 2074 Bhadra (CS I), 3+4 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-need-generation-detection
- Whole chapter: https://www.bctengineer.com/md/semester_6/communication_systems/chapter-7

## Question

What is QAM modulation, why is it necessary? Explain generation and detection of QAM wave.

## Short answer

Quadrature Amplitude Modulation (QAM) sends two messages on the same carrier frequency using carriers 90° apart, saving bandwidth (two signals in one DSB-SC bandwidth) and boosting data rate. Generation uses two product modulators with a phase-shifted carrier; detection coherently multiplies with local quadrature carriers and low-pass filters to recover m1 and m2.

## Answer

**Quadrature Amplitude Modulation (QAM)** sends two independent message signals on the same carrier frequency, using two carriers of the same frequency that are $90^\circ$ apart (cos and sin). It is also called quadrature-carrier multiplexing. In digital form (M-ary QAM) both amplitude and phase change from symbol to symbol.

$$
s(t)=A_c\,m_1(t)\cos 2\pi f_ct+A_c\,m_2(t)\sin 2\pi f_ct
$$

#### Why QAM is necessary

- **Bandwidth saving:** two DSB-SC signals occupy the bandwidth of one, i.e. $2W$ for two messages. Its spectral efficiency equals SSB without needing sharp sideband filters.
- **Higher data rate:** in digital form, M-ary QAM carries $\log_2 M$ bits per symbol (16-QAM: 4 bits), so more data fits a band-limited channel.
- **Better noise performance than M-ary PSK** for the same $M$, because points are spread over the whole plane, not only a circle.
- Used in colour TV (chrominance), telephone modems, Wi-Fi, cable TV, LTE.

#### Generation

```text
 m1(t) ---------->(X)<--- Ac cos wc t
                   |
                  (+)-------> s(t) QAM
                   |
 m2(t) ---------->(X)<--- Ac sin wc t
                        (-90 deg shift of
                         the same oscillator)
```

Two product modulators share one oscillator; one gets the carrier directly and the other through a $-90^\circ$ phase shifter. Their outputs are added. In digital QAM, $m_1$ and $m_2$ are multi-level signals $a_k$, $b_k$ produced by splitting the bit stream (serial-to-parallel) and converting groups of bits to levels.

#### Detection (coherent)

```text
        +->(X)->[LPF]-> (Ac/2) m1(t)
        |   ^ cos wc t
 s(t) --+
        |   v sin wc t
        +->(X)->[LPF]-> (Ac/2) m2(t)
```

In-phase branch:

$$
\begin{aligned}
s(t)\cos\omega_ct &= A_cm_1\cos^2\omega_ct+A_cm_2\sin\omega_ct\cos\omega_ct\\
&=\frac{A_c}{2}m_1(t)+\frac{A_c}{2}m_1\cos 2\omega_ct+\frac{A_c}{2}m_2\sin 2\omega_ct
\end{aligned}
$$

The LPF removes the $2\omega_c$ terms, leaving $\tfrac{A_c}{2}m_1(t)$. Similarly the quadrature branch gives $\tfrac{A_c}{2}m_2(t)$.

The local carrier must have exactly the right phase and frequency. A phase error $\phi$ gives $\tfrac{A_c}{2}[m_1\cos\phi - m_2\sin\phi]$, i.e. **cross-talk** between channels. So a pilot or carrier recovery circuit (e.g. Costas loop) is used. In digital QAM the LPFs are replaced by integrate-and-dump correlators followed by multi-level decision devices.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. What does QAM do?
   A. Sends one message on two different carrier frequencies
   B. Sends two independent messages on the same carrier frequency using cos and sin carriers 90 degrees apart
   C. Sends two messages using amplitude levels on one cosine
   D. Sends one message with two phases
   Answer: B. It is quadrature-carrier multiplexing: two DSB-SC signals in the bandwidth of one. (Key point: QAM concept)

2. Why is QAM better than M-ary PSK for the same M?
   A. It has a constant envelope
   B. It uses less carrier frequency
   C. Points are spread over the whole plane, not only a circle, giving larger distances
   D. It needs no carrier recovery
   Answer: C. Spreading points over the plane increases minimum distance for the same average power. (Key point: Why needed)

3. In the in-phase branch of the detector, s(t)cos(wc t) is passed through an LPF. The output is
   A. Ac m1(t)
   B. (Ac/2)m2(t)
   C. (Ac/2)m1(t)cos(2wc t)
   D. (Ac/2)m1(t)
   Answer: D. The product gives Ac/2 m1 plus 2wc terms, which the LPF removes. (Key point: Detection)

4. What happens if the local carrier has a phase error phi?
   A. Cross-talk: output is (Ac/2)[m1 cos(phi) - m2 sin(phi)]
   B. Only a reduced amplitude, no cross-talk
   C. The frequency of the output doubles
   D. The output becomes zero
   Answer: A. Part of m2 leaks into the m1 channel, so a pilot or Costas loop is used. (Key point: Phase error)

## Related in Communication Systems

- [QAM modulation and demodulation](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Aqam-mod-demod) — Communication Systems, chapter 7
- [QAM modulation, demodulation and constellation](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Aqam-mod-demod-constellation) — Communication Systems, chapter 7
- [PSK generation and detection; GMSK](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Apsk-generation-detection-gmsk) — Communication Systems, chapter 7
- [Why modulation is necessary](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Amodulation-necessary-channel) — Communication Systems, chapter 1
- [BFSK generation, non-coherent detection and signal space](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Abfsk-noncoherent-signal-space) — Communication Systems, chapter 7
- [Differential coding; DPSK modulation and detection](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Adifferential-coding-dpsk) — Communication Systems, chapter 7

## 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×
- [Astable multivibrator for square wave generation](https://www.bctengineer.com/question.md?key=semester_3%2Felectronics_devices_and_circuit%3Aastable-multivibrator-square-wave) — Electronics Devices and Circuit, chapter 5
- [DAC square wave generation at 1 kHz](https://www.bctengineer.com/question.md?key=semester_5%2Finstrumentation_ii%3Adac-square-wave-1khz) — Instrumentation II, chapter 4
- [Need of modulation; antenna parameters](https://www.bctengineer.com/question.md?key=semester_2%2Fbasic_electronics_engineering%3Amodulation-need-antenna-parameters) — Basic Electronics Engineering, chapter 5