How does PRF determine range and velocity unambiguity?

How does PRF determine range and velocity unambiguity?

• A. Range unambiguous limit R_amb = c / (2 PRF). Velocity unambiguous limit v_max = PRF λ / 4
• B. Range unambiguous yields PRF/(2c). Velocity unambiguous yields 4/(PRF λ)
• C. Range unambiguous limit R_amb = 2 PRF / c. Velocity unambiguous limit v_max = 4/(PRF λ)
• D. Range unambiguous equals c PRF; Velocity unambiguous equals λ /(4 PRF)

Answer: (A)

PRF, the rate at which pulses are sent, sets how often echoes can be distinctly matched to pulses in time. For range unambiguity, the echo from a target must return before the next pulse is transmitted. The round-trip time is 2R/c, so to avoid mixing echoes from different pulses we require 2R/c < 1/PRF. Solving gives the range unambiguous limit R_amb = c / (2 PRF). For velocity unambiguity, the Doppler shift produced by a moving target is f_D = 2v/λ. The Doppler measurement is obtained from signals sampled at the PRF, so the unambiguous Doppler frequency range is ±PRF/2 (Nyquist limit). Imposing |f_D| ≤ PRF/2 leads to 2|v|/λ ≤ PRF/2, which gives |v| ≤ λ PRF / 4. Hence the velocity unambiguous limit is v_max = λ PRF / 4. So increasing PRF raises the velocity unambiguity limit but lowers the range unambiguity limit, illustrating the trade-off between unambiguous range and unambiguous velocity.

PRF, the rate at which pulses are sent, sets how often echoes can be distinctly matched to pulses in time. For range unambiguity, the echo from a target must return before the next pulse is transmitted. The round-trip time is 2R/c, so to avoid mixing echoes from different pulses we require 2R/c < 1/PRF. Solving gives the range unambiguous limit R_amb = c / (2 PRF).

For velocity unambiguity, the Doppler shift produced by a moving target is f_D = 2v/λ. The Doppler measurement is obtained from signals sampled at the PRF, so the unambiguous Doppler frequency range is ±PRF/2 (Nyquist limit). Imposing |f_D| ≤ PRF/2 leads to 2|v|/λ ≤ PRF/2, which gives |v| ≤ λ PRF / 4. Hence the velocity unambiguous limit is v_max = λ PRF / 4.

So increasing PRF raises the velocity unambiguity limit but lowers the range unambiguity limit, illustrating the trade-off between unambiguous range and unambiguous velocity.