The blind speed formula
In an MTI or pulse-Doppler radar, a target whose radial velocity causes exactly one full phase rotation between pulses (360°) has the same phase as stationary clutter. It cancels perfectly. The blind speeds are v = nλ·PRF/2, where n is any integer. A 3 GHz radar with 1,000 Hz PRF has blind speeds at 50 m/s, 100 m/s, 150 m/s — a jet at exactly 180 knots (93 m/s) would vanish.
Staggered PRF
The fix is simple in theory: change the PRF so the blind speeds shift. A two-stagger PRF (e.g. 1,000 Hz and 1,200 Hz) makes a target blind at one PRF visible at the other. Military radars use multiple stagger patterns, sometimes changing every pulse. Digital processing then unscrambles the pattern and recovers the true velocity.
Range ambiguity
High PRF for velocity means short unambiguous range: R_unambiguous = c/(2·PRF). At 100 kHz PRF, the maximum unambiguous range is 1.5 km. An echo arriving after 2 µs could be a target at 300 km on the current pulse, or a target at 150 km from the previous pulse — ambiguous. Multiple PRFs and phase coding resolve which is which.
Modern solutions
Digital signal processing and variable PRF have essentially solved blind speeds and range ambiguity in modern systems. But the physics remains: a pulsed radar is a sampled system, and sampling creates aliasing. Understanding these ambiguities is still core to radar engineering education — and to interpreting why a target sometimes 'jumps' on screen.