Lesson 5 Flashcards

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1. Write the Doppler shift formula.

\(f_d = 2 v_r / \lambda\). The factor of 2 is the two-way path; \(v_r\) is the radial velocity.

2. At X-band, what Doppler shift does 300 m/s produce?

\(f_d = 2(300)/0.03 = 20\) kHz. At 30 m/s it is 2 kHz.

3. Why can't a radar reject clutter by amplitude?

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.

4. Where does clutter sit in Doppler, and why?

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.

5. Write the single delay-line MTI canceller.

\(y[n] = x[n] - x[n-1]\). Stationary returns cancel; movers, whose phase advanced between pulses, survive.

6. What is the MTI frequency response?

\(|H(f)| = 2|\sin(\pi f T)|\) with \(T = \text{PRI}\). It has notches at \(f = 0, \text{PRF}, 2\,\text{PRF}, \dots\)

7. What are blind speeds?

Target velocities whose Doppler lands on an MTI notch, so the target is cancelled with the clutter: \(v_{\text{blind},n} = n\lambda\,\text{PRF}/2\).

8. How does PRF move the blind speeds?

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.

9. What is pulse-Doppler processing?

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 \(\text{PRF}/N\).

10. What does a range-Doppler map look like?

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.

11. How could a jammer make a target hide on the R-D map?

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.

12. What SNR benefit does coherent integration give?

Integrating \(N\) pulses coherently gives an SNR gain proportional to \(N\), while finer Doppler resolution comes from the larger dwell.