What radar problem links maximum unambiguous range with maximum unambiguous velocity?

The radar problem linking maximum unambiguous range with maximum unambiguous velocity is the Doppler dilemma. It arises because pulse-repetition frequency choices that improve range measurement tend to reduce the unambiguous velocity interval, and vice versa.

A pulse radar determines range from the time between transmission and echo. To avoid confusing an echo from a later pulse with one from an earlier pulse, pulses must be spaced far enough apart. That favours a lower pulse-repetition frequency and gives a larger unambiguous range.

Velocity is inferred from Doppler frequency or pulse-to-pulse phase changes. Sampling those changes without aliasing favours a higher pulse-repetition frequency, which increases the measurable unambiguous velocity range. But closely spaced pulses make distant echoes overlap successive transmissions, creating range ambiguity.

Radar designers manage the conflict with techniques including multiple or staggered pulse-repetition frequencies, frequency agility, and ambiguity-resolution processing. The competing limits are not the same as pulse compression, which changes range resolution, or a range gate, which selects a time interval for returns.