Question E8D03:
Which describes spread spectrum frequency hopping?  

Choices:  
A: If interference is detected by the receiver, it will signal the transmitter to change frequencies  
B: RF signals are clipped to generate a wide band of harmonics which provides redundancy to correct errors  
C: A binary bit stream is used to shift the phase of an RF carrier very rapidly in a pseudorandom sequence  
D: Rapidly varying the frequency of a transmitted signal according to a pseudorandom sequence    

Correct Answer is  D: Rapidly varying the frequency of a transmitted signal according to a pseudorandom sequence  

To understand spread spectrum frequency hopping:

1) Why D is correct
- Frequency-Hopping Spread Spectrum (FHSS) works by rapidly changing, or “hopping,” the transmitter’s carrier frequency among many narrow channels according to a pseudorandom sequence known to both the transmitter and receiver.  
- This exactly matches choice D: “Rapidly varying the frequency of a transmitted signal according to a pseudorandom sequence.”

2) Why the other choices are incorrect
- A: “If interference is detected by the receiver, it will signal the transmitter to change frequencies.”  
  - FHSS does not require a feedback channel to command hops. The hop pattern is predetermined and synchronized; it does not depend on real-time interference detection.
- B: “RF signals are clipped to generate a wide band of harmonics…”  
  - Clipping creates spectral splatter and spurious emissions, not controlled spreading. It’s not a spread-spectrum technique and does not provide error-correcting redundancy.
- C: “A binary bit stream is used to shift the phase of an RF carrier very rapidly in a pseudorandom sequence.”  
  - This describes Direct-Sequence Spread Spectrum (DSSS), where a high-rate pseudonoise (PN) code modulates the phase (e.g., BPSK/QPSK) to spread the signal. It is not frequency hopping.

3) Useful formulas and rules of thumb
- FHSS hopping rate and dwell time:
  $$R_h = \frac{1}{T_d}$$
  where:
  - $R_h$ = hop rate (hops per second)
  - $T_d$ = dwell time per frequency

- Processing gain (rule of thumb):
  - FHSS:
    $$G_p \approx 10 \log_{10}(N) \text{ dB}$$
    where $N$ is the number of hop channels.
  - DSSS (for contrast):
    $$G_p = 10 \log_{10}\!\left(\frac{R_c}{R_b}\right) = 10 \log_{10}\!\left(\frac{B_{\text{spread}}}{B_{\text{data}}}\right) \text{ dB}$$
    where $R_c$ is chip rate and $R_b$ is data rate.

Key idea: FHSS spreads energy over many frequencies by hopping in a pseudorandom pattern; DSSS spreads by rapidly changing phase with a PN code.