Blind Speed
Understanding Blind Speed
Blind speed is one of radar's most dangerous limitations: a perfectly detectable target becomes completely invisible to MTI processing because its velocity creates a Doppler shift that aliases to zero frequency. At a blind speed, the target moves exactly an integer number of half-wavelengths between consecutive pulses, so every echo arrives with the same phase as the previous one. The MTI canceller, which subtracts consecutive returns, produces zero output; the target is cancelled along with the stationary clutter it was designed to reject.
The practical significance is severe. At X-band with a typical 1 kHz PRF, the first blind speed is only 57.6 km/h, right in the middle of highway traffic and military vehicle speeds. Without mitigation, an MTI radar would lose visibility of targets at this velocity and at every multiple of it. Modern radars use staggered PRF patterns (alternating pulse intervals) to shift the blind speed nulls of each PRI to different velocities, or employ full pulse-Doppler processing with multiple PRFs and Chinese Remainder Theorem ambiguity resolution to achieve velocity coverage without gaps.
Blind Speed Equations
vblind(n) = n × λ × PRF / 2
Inter-Pulse Phase Change:
Δφ = 4πv / (λ × PRF)
At blind speed: Δφ = 2πn → sin(Δφ/2) = 0
MTI Filter Response:
H(fd) = |1 − e−j2πfd/PRF|²
H = 0 when fd = n × PRF
Staggered PRF Combined Blind Speed:
vcombined = kλ / (2 × LCM(T1, T2))
First Blind Speed by Band and PRF
| Band | Freq (GHz) | λ (mm) | PRF (Hz) | v1 (m/s) | v1 (km/h) |
|---|---|---|---|---|---|
| L | 1.3 | 231 | 300 | 34.6 | 124.6 |
| S | 3.0 | 100 | 500 | 25.0 | 90.0 |
| C | 5.6 | 54 | 800 | 21.4 | 77.0 |
| X | 9.4 | 32 | 1000 | 16.0 | 57.6 |
| Ku | 15 | 20 | 2000 | 20.0 | 72.0 |
| Ka | 35 | 8.6 | 5000 | 21.4 | 77.0 |
Mitigation Comparison
| Method | Mechanism | Blind Speed Removed? | Trade-off |
|---|---|---|---|
| Single PRF MTI | Cancellation | No | Simple, fast |
| Staggered PRF | Different nulls per PRI | Mostly (residuals) | −5 dB clutter attn. |
| Pulse-Doppler (single) | FFT Doppler bins | Folding, not null | Velocity ambiguity |
| Multi-PRF PD | CRT ambiguity resolution | Yes (to LCM limit) | Complex processing |
Frequently Asked Questions
Why do they occur?
Doppler sampled at PRF rate. At v = nλPRF/2: target moves n×λ/2 per PRI, phase change = 2πn. MTI sees zero inter-pulse difference. X-band first blind speed is 57.6 km/h; highway traffic and military vehicles fall right in this range.
Staggered PRF?
Alternate PRIs (T1, T2) with coprime ratios. Combined blind speed at LCM(T1,T2). Ratio 25/24: first combined blind speed at 25×v1. 3-PRI stagger pushes it to >900×v1. Trade-off: −5 dB clutter attenuation, complex range processing.
Pulse-Doppler solution?
FFT separates all Doppler bins; targets visible at any velocity but with folding ambiguity. Multi-PRF (2–3 PRFs) + Chinese Remainder Theorem resolves true velocity to LCM range. High PRF at X-band (100 kHz): v1 = 1600 m/s (Mach 4.7).