Question E8C01:
What is Quadrature Amplitude Modulation or QAM?  

Choices:  
A: A technique for digital data compression used in digital television which removes redundancy in the data by comparing bit amplitudes  
B: Transmission of data by modulating the amplitude of two carriers of the same frequency but 90 degrees out of phase  
C: A method of performing single sideband modulation by shifting the phase of the carrier and modulation components of the signal  
D: A technique for analog modulation of television video signals using phase modulation and compression    

Correct Answer is  B: Transmission of data by modulating the amplitude of two carriers of the same frequency but 90 degrees out of phase  

Correct answer: B

1) Why B is correct
- Quadrature Amplitude Modulation (QAM) sends data by controlling the amplitudes of two sinusoidal carriers that share the same frequency but are 90 degrees out of phase (in-phase I and quadrature Q).
- The transmitted RF signal can be written as:
  $$s(t) = I(t)\cos(2\pi f_c t) - Q(t)\sin(2\pi f_c t)$$
- Here, the data is mapped to the amplitudes of the I and Q components. When combined, this produces a single carrier whose instantaneous amplitude and phase both change to represent symbols.

Useful equivalent form:
- Let the complex baseband be $I(t) + jQ(t) = A(t)e^{j\phi(t)}$.
- Then:
  $$s(t) = A(t)\cos\big(2\pi f_c t + \phi(t)\big)$$
- Where:
  $$A(t) = \sqrt{I^2(t) + Q^2(t)}, \quad \phi(t) = \operatorname{atan2}(Q(t),\, I(t))$$

2) Why the other choices are incorrect
- A: Describes digital data compression (e.g., MPEG in digital TV), not a modulation method. QAM is a modulation scheme, not a compression technique.
- C: Describes the phasing method of generating SSB, where phase shifting cancels one sideband. That is single sideband generation, not QAM.
- D: Analog TV video used vestigial-sideband AM for video (and FM for audio), not “phase modulation and compression.” This does not describe QAM.

3) Useful formulas and rules of thumb
- Signal expression:
  $$s(t) = I(t)\cos(2\pi f_c t) - Q(t)\sin(2\pi f_c t)$$
- Amplitude and phase from I/Q:
  $$A = \sqrt{I^2 + Q^2}, \quad \phi = \operatorname{atan2}(Q, I)$$
- Constellation size and bit rate:
  - For $M$-QAM, bits per symbol: $k = \log_2 M$
  - Data rate: $R_b = k \, R_s$, where $R_s$ is the symbol rate
- Bandwidth (rule of thumb): With raised-cosine filtering, occupied bandwidth is approximately $R_s(1+\alpha)$, where $\alpha$ is the roll-off factor.

Key contrast:
- QPSK changes phase only (constant envelope).
- QAM varies both amplitude and phase via the I and Q amplitudes.