\(f_d = 2 v_r / \lambda\). The factor of 2 is the two-way path; \(v_r\) is the radial velocity.
\(f_d = 2(300)/0.03 = 20\) kHz. At 30 m/s it is 2 kHz.
Ground clutter has an enormous RCS — far stronger than the target — so the aircraft return is buried on amplitude alone. Clutter must be rejected by Doppler instead.
At \(f_d \approx 0\), because stationary terrain has no radial velocity. Movers sit away from zero Doppler, which is what lets them be separated.
\(y[n] = x[n] - x[n-1]\). Stationary returns cancel; movers, whose phase advanced between pulses, survive.
\(|H(f)| = 2|\sin(\pi f T)|\) with \(T = \text{PRI}\). It has notches at \(f = 0, \text{PRF}, 2\,\text{PRF}, \dots\)
Target velocities whose Doppler lands on an MTI notch, so the target is cancelled with the clutter: \(v_{\text{blind},n} = n\lambda\,\text{PRF}/2\).
Raising PRF raises the blind speeds. At X-band, 1 kHz gives a first blind speed of 15 m/s; 10 kHz pushes it to 150 m/s, usually out of the clutter band — at the cost of range ambiguity.
Collect \(N\) pulses in a coherent dwell and take an \(N\)-point FFT across pulses at each range bin, giving a Doppler spectrum per range bin with bin width \(\text{PRF}/N\).
A 2D image of range vs. Doppler. Clutter forms a vertical ridge at zero Doppler across all ranges; movers land off the ridge in their own cells, easy to threshold.
Match the platform's own ground-clutter Doppler line so the false return sits on the zero-Doppler ridge and is cancelled with the clutter. EP counters include geometry checks and inverse-cancellation logic.
Integrating \(N\) pulses coherently gives an SNR gain proportional to \(N\), while finer Doppler resolution comes from the larger dwell.