Question E8B08:
What describes orthogonal frequency-division multiplexing (OFDM)?  

Choices:  
A: A frequency modulation technique that uses non-harmonically related frequencies  
B: A bandwidth compression technique using Fourier transforms  
C: A digital mode for narrow-band, slow-speed transmissions  
D: A digital modulation technique using subcarriers at frequencies chosen to avoid intersymbol interference    

Correct Answer is  D: A digital modulation technique using subcarriers at frequencies chosen to avoid intersymbol interference  

Correct answer: D — A digital modulation technique using subcarriers at frequencies chosen to avoid intersymbol interference

1) Why D is correct
- OFDM transmits data in parallel over many closely spaced subcarriers that are mathematically orthogonal.  
- Orthogonality is achieved by choosing the subcarrier spacing so that each subcarrier’s spectrum has zeros at the sampling instants of all the others, preventing mutual interference and mitigating intersymbol interference (ISI) when combined with a guard interval (cyclic prefix).
- Key spacing rule:
  $$\Delta f = \frac{1}{T_u}$$
  where $T_u$ is the useful symbol duration (excludes the cyclic prefix). This makes different subcarriers orthogonal over $T_u$.

2) Why the other choices are incorrect
- A: “A frequency modulation technique…”  
  OFDM is not FM of a single carrier. It is multicarrier digital modulation; each subcarrier is typically PSK/QAM, not FM. Also, subcarriers are placed at specific, harmonically related spacings to maintain orthogonality.
- B: “A bandwidth compression technique using Fourier transforms”  
  While OFDM is efficiently implemented with IFFT/FFT, it is not “bandwidth compression.” FFTs are a computational tool; OFDM’s spectrum efficiency comes from overlapping orthogonal subcarriers, not compression.
- C: “A digital mode for narrow-band, slow-speed transmissions”  
  OFDM is commonly wideband and high data rate (e.g., Wi‑Fi, LTE, DAB). Although each subcarrier has a low symbol rate, the aggregate is wideband and high throughput.

3) Useful formulas and rules of thumb
- Subcarrier spacing for orthogonality:
  $$\Delta f = \frac{1}{T_u}$$
- Time-domain OFDM symbol (useful part):
  $$s(t) = \sum_{k=0}^{N-1} a_k e^{j2\pi (f_0 + k\Delta f)t},\quad 0 \le t < T_u$$
  where $a_k$ are constellation symbols (e.g., QPSK/QAM).
- Cyclic prefix (guard interval) to prevent ISI:
  $$T_s = T_u + T_{cp}, \quad \text{choose } T_{cp} > \tau_{\max}$$
  where $\tau_{\max}$ is the channel’s maximum delay spread. This ensures delayed multipath from the previous symbol does not interfere with the current symbol.