A terminal receiving a 2 GHz radio wave is approaching the base station at 30 m/s (108 km/h). Taking the speed of light as 3×10⁸ m/s, which is closest to the magnitude of the frequency shift (Doppler shift) of the wave received by the terminal?

Answer: A. 200 Hz

When the source and receiver approach each other, the received frequency shifts up; when they move apart, it shifts down. The size of the shift is f_d = v·f/c, which is 30 × 2×10⁹ ÷ (3×10⁸) = 200 Hz. The shift grows with higher frequency and faster motion, and the receiver must track it to demodulate. In OFDM, interference between subcarriers increases when the Doppler shift becomes large compared with the subcarrier spacing.

• A. Correct. f_d = v·f/c = 30 × 2×10⁹ ÷ (3×10⁸) = 200 Hz.
• B. This is the shift (2v·f/c) when receiving a wave that has been reflected back, as in radar. One-way communication does not double it.
• C. This uses the speed in km/h, 108, directly. The formula uses 30 m/s.