MTI Radar Quiz — ECE 521E Radar & Satellite Engineering

Instructions to Candidates

This quiz contains 20 multiple-choice questions covering the first four levels of Bloom's taxonomy.
Select the best answer for each question, then press "Check Answers" to mark your script instantly, or attempt all questions first and consult the Post-Test Answer Key at the end.
Where calculations are required, take c = 3×10⁸ m/s.
Total time: 45 minutes (indicative).

Level 1
Remember (Q1–5)

Level 2
Understand (Q6–10)

Level 3
Apply (Q11–15)

Level 4
Analyse (Q16–20)

Level 1 — Remember (Q1–Q5)

The primary purpose of an MTI radar is to:Remember

(a) Measure the exact radial velocity of a target (b) Reject fixed clutter echoes while passing moving-target echoes (c) Increase the transmitted peak power of the radar (d) Extend the unambiguous range of the radar

Explanation: MTI processing cancels echoes that are identical from pulse to pulse (stationary clutter) and passes echoes whose phase rotates pulse-to-pulse (moving targets). It indicates motion — it does not measure velocity (pulse-Doppler does that).

The Doppler frequency shift of a radar echo is given by:Remember

(a) f_d = v_r/λ (b) f_d = v_rλ/2 (c) f_d = 2v_r/λ (d) f_d = λc/2v_r

Explanation: The factor 2 arises from the two-way propagation: range (and hence echo phase) accumulates at twice the radial velocity, so f_d = 2v_r/λ = 2f₀v_r/c.

The output equation of a single delay-line canceller is:Remember

(a) y(n) = x(n) + x(n−1) (b) y(n) = x(n) − x(n−1) (c) y(n) = x(n) − 2x(n−1) + x(n−2) (d) y(n) = x(n) · x(n−1)

Explanation: The single (first-order) canceller subtracts the previous pulse's sample from the current one. Option (c) is the double canceller; addition would reinforce clutter rather than cancel it.

A "blind speed" of an MTI radar is a target velocity at which:Remember

(a) The MTI response is zero — the moving target cancels exactly like clutter (b) The target echo is strongest (c) The unambiguous range becomes infinite (d) The radar receiver becomes saturated

Explanation: At blind speeds v_n = nλf_r/2 the target moves exactly n half-wavelengths per PRI, so successive echoes are identical and cancel — the target becomes invisible to the MTI.

Ground clutter observed by a stationary radar has a Doppler frequency of approximately:Remember

(a) f_r/2 (b) 2v_r/λ (c) Equal to the transmitter frequency (d) Zero

Explanation: Stationary clutter has no radial motion relative to a stationary radar, so v_r = 0 and f_d = 0 — which is precisely why the MTI notch is placed at zero Doppler. (Wind-blown vegetation gives a small non-zero spread.)

Level 2 — Understand (Q6–Q10)

Why does a double delay-line canceller reject weather clutter better than a single canceller?Understand

(a) It doubles the transmitted pulse width (b) It eliminates blind speeds entirely (c) Its power response falls as f⁴ near zero Doppler, giving a wider and deeper notch for finite-width clutter spectra (d) It doubles the PRF and therefore the unambiguous range

Explanation: Rain/chaff clutter has a broad spectrum. The single canceller's |H|² ∝ sin² (f² near DC) leaks much of that energy, while the double canceller's |H|² ∝ sin⁴ (f⁴ near DC) suppresses far more spectral spill-over. Blind speeds, however, remain at nλf_r/2.

Physically, a target at the first blind speed moves between successive pulses by:Understand

(a) One full wavelength λ (b) Exactly one half-wavelength λ/2 toward or away from the radar (c) One quarter-wavelength λ/4 (d) A distance equal to the range resolution cell

Explanation: v₁T_r = (λf_r/2)(1/f_r) = λ/2. The two-way phase change is then 4π(λ/2)/λ = 2π — the echo is identical on every pulse and cancels, exactly like stationary clutter.

Coherent MTI is preferred over non-coherent MTI mainly because:Understand

(a) It requires no transmitter stability (b) It works even when there is no clutter in the cell (c) It has blind phases instead of blind speeds (d) A stable COHO phase reference preserves full I/Q phase information, giving deep, stable cancellation

Explanation: Non-coherent MTI borrows its phase reference from the clutter itself, so performance collapses when clutter is weak or patchy. Coherent MTI uses a COHO/STALO locked to the transmitter, preserving phase for deep cancellation; its coherent I/Q processing also eliminates blind-phase problems.

Staggered PRF raises the first blind speed because:Understand

(a) The blind speeds of the individual PRIs no longer coincide — the first common null moves to 1/|T₁−T₂| (b) It increases the carrier frequency (c) It shortens the pulse width (d) It increases the antenna gain

Explanation: With unequal pulse intervals T₁, T₂ the canceller nulls of each interval occur at different Doppler frequencies. A target blind in one interval is visible in the other; the first velocity blind in both is v_b = λ/[2|T₁−T₂|], which is much higher than λf_r/2 since |T₁−T₂| ≪ T.

The MTI improvement factor I is defined as:Understand

(a) The ratio of output to input clutter power (b) The PRF divided by the clutter spectral width (c) The ratio of output to input signal-to-clutter ratio: I = (S_out/C_out)/(S_in/C_in) (d) The product of blind speed and unambiguous range

Explanation: I measures how much the MTI filter improves S/C, combining clutter attenuation with any signal gain/loss through the filter. Typical practical values are 40–60 dB. Option (a) describes only clutter attenuation (CA); option (d) is the constant λc/4, unrelated to I.

Level 3 — Apply (Q11–Q15)

An X-band radar (f₀ = 10 GHz) tracks a target approaching at 150 m/s. The Doppler shift is:Apply

(a) +750 Hz (b) +10,000 Hz (c) −10,000 Hz (d) +5,000 Hz

Explanation: λ = c/f₀ = 0.03 m. f_d = 2v_r/λ = 2(150)/0.03 = +10 kHz. The sign is positive because the target approaches. Option (d) forgets the factor of 2.

An S-band radar (λ = 0.1 m) operates at PRF = 800 Hz. The second blind speed is:Apply

(a) 20 m/s (b) 40 m/s (c) 80 m/s (d) 160 m/s

Explanation: v_n = nλf_r/2 → v₂ = 2(0.1)(800)/2 = 80 m/s (v₁ = 40 m/s, v₂ = 80 m/s, v₃ = 120 m/s).

A radar with f_r = 1 kHz uses a double canceller. The magnitude response at f_d = 250 Hz is:Apply

(a) 2.0 (b) 1.414 (c) 4.0 (d) 0.0

Explanation: |H| = 4 sin²(πf_d/f_r) = 4 sin²(π/4) = 4(0.5) = 2.0. Option (b) is the single-canceller value 2sin(π/4); option (d) would require f_d = n·f_r (a blind speed).

A two-PRF stagger uses f₁ = 1000 Hz and f₂ = 1250 Hz at λ = 0.1 m. The first blind speed of the staggered waveform is:Apply

(a) 50 m/s (b) 112.5 m/s (c) 125 m/s (d) 250 m/s

Explanation: v_b = λf₁f₂/[2(f₂−f₁)] = (0.1)(1000)(1250)/[2(250)] = 125000/500 = 250 m/s — five times the uniform-PRF blind speed of 50 m/s, because |T₁−T₂| = 0.2 ms versus T = 1 ms.

An MTI filter achieves clutter attenuation of 50 dB, but moving targets lose 6 dB of signal passing through it. The improvement factor is:Apply

(a) 50 dB (b) 56 dB (c) 44 dB (d) 300 dB

Explanation: I = CA × S_out/S_in = 50 dB − 6 dB = 44 dB in dB arithmetic. The filter's ripple/scalloping loss at the target's Doppler reduces the net S/C improvement.

Level 4 — Analyse (Q16–Q20)

Analysis of a coastal surveillance radar reveals strong residual detections after MTI, occurring only in range cells containing heavy rain showers. The most likely cause and cure are:Analyse

(a) Rain clutter has a broad Doppler spectrum that leaks through the canceller's narrow notch — use a higher-order (N = 3) canceller or adaptive notch widening (b) The transmitter peak power is too low — increase peak power (c) The antenna sidelobes are too high — reduce PRF (d) The radar is operating at its blind speed — halve the carrier frequency

Explanation: Raindrops move with wind, giving clutter spectral widths of tens of Hz — far wider than ground clutter. The f²/f⁴ notch cannot suppress it all, so the clutter crosses the detection threshold and appears as false "detections" (actually clutter breakthrough). Higher-order binomial weights or an adaptive wider notch directly attack the spectral leakage; the other options do not address Doppler spread at all.

An MTI radar displays a periodic loss of a fast aircraft echo roughly every 12 seconds as it flies toward the radar. A coherent analysis would conclude:Analyse

(a) The receiver AGC is oscillating (b) The aircraft's radial velocity periodically passes through a blind speed v_n = nλf_r/2 (c) The aircraft is beyond the unambiguous range once per cycle (d) The COHO has lost lock

Explanation: As the aircraft's radial velocity changes, it sweeps through the discrete blind speeds, and at each crossing the MTI response falls to zero. Because blind speeds are uniformly spaced in velocity (nλf_r/2), a smoothly accelerating target crosses them periodically — matching the observed periodic fading. The cure is staggered PRF or PRF diversity.

Two radars, A (PRF 300 Hz, λ = 0.25 m) and B (PRF 1200 Hz, λ = 0.25 m), both use single cancellers. Compare their first blind speeds (v₁) and unambiguous ranges (R_u):Analyse

(a) A: v₁ = 37.5 m/s, R_u = 500 km; B: v₁ = 150 m/s, R_u = 125 km — quadrupling the PRF quadruples blind speeds but quarters unambiguous range (b) A: v₁ = 150 m/s, R_u = 125 km; B: v₁ = 37.5 m/s, R_u = 500 km (c) Both have identical v₁ and R_u since λ is the same (d) A: v₁ = 37.5 m/s, R_u = 250 km; B: v₁ = 150 m/s, R_u = 62.5 km

Explanation: Using v₁ = λf_r/2 and R_u = c/(2f_r): Radar A → v₁ = 0.25×300/2 = 37.5 m/s, R_u = 3×10⁸/600 = 500 km. Radar B → v₁ = 0.25×1200/2 = 150 m/s, R_u = 3×10⁸/2400 = 125 km. Quadrupling the PRF quadruples blind speeds but quarters unambiguous range — the v₁R_u = λc/4 trade-off that motivates staggered PRF.

A staggered-PRF MTI radar suffers degraded cancellation depth (I drops from 50 dB to 38 dB) after a firmware change that stores raw echo samples without interpolating them to a common time base. The analysis is:Analyse

(a) Staggered PRF fundamentally cannot achieve more than 38 dB (b) The transmitter phase noise increased with the firmware change (c) With unequal PRIs the echo samples are taken at slightly different times per interval; without interpolation the differencing is misregistered, so clutter does not cancel exactly (d) Staggering shifts the clutter spectrum away from the notch

Explanation: This is the classic range-gate misregistration problem of staggered MTI. Successive PRI changes move the sampling instant of a given range cell by fractions of a microsecond; subtracting misaligned samples leaves a residue proportional to the clutter gradient × timing error. Digital interpolation to a common time base before cancellation restores the cancellation depth. Option (b) is unrelated to the firmware change described; (d) confuses stagger with platform-motion clutter shift.

Comparing three processing options for an airborne early-warning radar that must detect slow vehicles over land, the best-supported analysis is:Analyse

(a) A fixed zero-Doppler notch fails because platform motion shifts all ground clutter by f_d = 2v_platformcosθ/λ — clutter-locked MTI (TACCAR) or STAP is required (b) A fixed zero-Doppler notch works best because airborne clutter is always stationary (c) Non-coherent MTI is ideal because it needs no reference oscillator (d) Blind speeds are the only relevant limitation for airborne MTI

Explanation: An aircraft moving at 250 m/s at λ = 0.03 m imparts up to ~16.7 kHz of Doppler on ground clutter (2v/λ). A notch fixed at 0 Hz would sit far outside the clutter spectrum → total clutter breakthrough. TACCAR/clutter-locking centres the notch on the measured clutter mean Doppler, and STAP adaptively shapes the space-time response to null both mainlobe and sidelobe clutter — the only approaches that work for slow ground targets whose Doppler must be separated from mainlobe clutter spread.

Post-Test Answer Key & Summary

Q	Key	Bloom Level	Concept Tested
1	b	Remember	Purpose of MTI
2	c	Remember	Doppler equation (2v_r/λ)
3	b	Remember	Single canceller equation
4	a	Remember	Definition of blind speed
5	d	Remember	Ground clutter Doppler = 0
6	c	Understand	Double canceller vs wide clutter
7	b	Understand	λ/2 movement per PRI at v₁
8	d	Understand	Coherent vs non-coherent MTI
9	a	Understand	Staggered PRF mechanism
10	c	Understand	Improvement factor definition
11	b	Apply	Doppler computation (10 kHz)
12	c	Apply	Blind speeds 40/80 m/s
13	a	Apply	Double-canceller response \|H\| = 2
14	d	Apply	Staggered blind speed 250 m/s
15	c	Apply	I = CA − signal loss = 44 dB
16	a	Analyse	Rain-clutter breakthrough diagnosis
17	b	Analyse	Periodic fading via blind-speed crossing
18	a	Analyse	PRF trade-off v₁ vs R_u
19	c	Analyse	Stagger misregistration loss
20	a	Analyse	Airborne platform motion → clutter lock/STAP

Grading guide: 18–20 = Excellent (mastery of MTI concepts); 14–17 = Good; 10–13 = Fair — revisit blind speeds and improvement factor; <10 = Review the study guide sections on cancellers and staggered PRF before re-attempting.