ECE 495 — Electromagnetic Warfare and Survivability

Block 1: Radar Fundamentals
Lesson 5: Doppler, MTI, and Pulse-Doppler

Juan Jurado, Col, USAF, Ph.D.
Permanent Professor and Head
Electrical and Computer Engineering
Fall 2026

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Block 1 · Lesson 5 · Where We Left Off

Where We Left Off

L4 gave us the pulse train — a sampler in time.

Each pulse carries a phase. Across pulses, that phase moves whenever the target does.

Today

The Doppler shift, MTI filtering, and pulse-Doppler processing — the tools that separate the “movers” from clutter.

Block 1 · Lesson 5 · Objectives

Lesson Objectives

By the end of this lesson, you will be able to:

Compute the Doppler shift from a radial velocity
Explain how a single delay-line MTI rejects ground clutter
Identify blind speeds and how PRF moves them around
Describe pulse-Doppler processing as an FFT across pulses

Clutter is stationary. You are not.

Block 1 · Lesson 5 · Part One

The Second Observable

Range tells the radar where something is. The phase that walks across the pulse train tells it what that something is doing — and that is what pulls a target out of the whole Earth behind it.

Block 1 · Lesson 5 · Doppler Shift

The Doppler Effect on Radar Returns

A target moving radially at $v_r$ shifts the carrier by:

Doppler shift

\[ f_d = \frac{2 \, v_r}{\lambda} \]

The factor of 2 is the two-way path. X-band ($\lambda = 3$ cm) examples:

$v_r = 300$ m/s $\;\Rightarrow\; f_d = 20$ kHz
$v_r = 30$ m/s $\;\Rightarrow\; f_d = 2.0$ kHz

Range tells you where; Doppler tells you what.

Block 1 · Lesson 5 · Clutter

Clutter vs Targets

A radar looking down sees everything, not just the threat.

Ground clutter — huge RCS, $f_d \approx 0$
Weather, sea, foliage — distributed, small $f_d$
Aircraft — modest RCS, $f_d$ from hundreds of Hz to tens of kHz

The aircraft return is buried in clutter on the basis of amplitude alone. Doppler separates the two.

Clutter is a confidently stationary signal the radar must learn to ignore.

Block 1 · Lesson 5 · Part Two

MTI and Its Price

One subtraction removes the clutter. The same subtraction removes anything unlucky enough to share its Doppler — and the PRF decides who that is.

Block 1 · Lesson 5 · MTI Canceller

Single Delay-Line MTI Canceller

Subtract one pulse return from the next — whatever did not change cancels.

The canceller

\[ y[n] = x[n] - x[n-1] \]

Response, $T = $ PRI

\[ |H(f)| = 2 \, |\sin(\pi f T)| \]

Notches at $f = 0, \, \text{PRF}, \, 2\,\text{PRF}, \ldots$ — stationary clutter is killed
Passes Doppler shifts away from those notches — movers survive
Cheap to implement: one PRI of memory and a subtractor

Higher-order cancellers and adaptive MTI go deeper.

Block 1 · Lesson 5 · The Notch

What the Antenna Hears

One range bin at X-band, PRF $= 1$ kHz, sorted by Doppler. Three returns, one axis.

return power

ground clutter0 m/s

convoy22 m/s

helo30 m/s

radial velocity (m/s)

The clutter dwarfs both movers on amplitude. What can you subtract that takes the ridge and leaves the rest?

Block 1 · Lesson 5 · The Notch

The Notch Giveth and Taketh

Drop $|H(f)| = 2|\sin(\pi f T)|$ on top: it is zero at $0, \text{PRF}, 2\,\text{PRF},\ldots$ — every 15 m/s at this PRF.

return power

|H(f)|

cancelled0 m/s

convoy22 m/s · survives

helo30 m/s · blind speed

radial velocity (m/s)

The helo was never detected and never reported. It was filtered.

Block 1 · Lesson 5 · Blind Speeds

Blind Speeds

A target whose Doppler shift lands on any MTI notch looks stationary.

Blind speeds

\[ v_{\text{blind},\, n} = \frac{n \cdot \lambda \cdot \text{PRF}}{2} \]

X-band, PRF $= 1$ kHz: $v_{\text{blind},1} = 15$ m/s, $v_{\text{blind},2} = 30$ m/s, $v_{\text{blind},3} = 45$ m/s, …
Ground vehicles and helicopters live right in this band
Raising PRF to 10 kHz pushes $v_{\text{blind},1}$ to 150 m/s — usually outside the clutter band

That is why pulse-Doppler radars use medium-to-high PRF.

Block 1 · Lesson 5 · Part Three

Reading the Map

Stop thinking about one filter. Collect a whole dwell, transform across the pulses, and every target claims its own cell in range and velocity.

Block 1 · Lesson 5 · Pulse-Doppler

Pulse-Doppler Processing

Collect $N$ pulses in a coherent dwell. Take an $N$-point FFT across pulses at each range bin:

Output is a Doppler spectrum per range bin
Doppler bin width $=$ PRF $/ N$ — finer with more pulses
Each target lands in its own range-Doppler cell
Coherent integration gives an SNR gain proportional to $N$

This is what modern AESA fire control radars are doing under the hood.

Block 1 · Lesson 5 · R-D Map

The Range-Doppler Map

The output of pulse-Doppler processing is a 2D matrix:

Clutter forms a vertical ridge at zero Doppler
Movers land away from the ridge — easy to threshold
EW implication: your Doppler signature is hard to hide

Block 1 · Lesson 5 · Look-Down

Look-Down and Modern Clutter Rejection

A look-down radar competes with the entire Earth in its main beam.

Main-beam clutter Doppler shifts with platform velocity and look angle
Modern radars track and cancel the main-beam clutter line adaptively
Side-lobe clutter is treated separately — this is where good antenna design pays off

EW relevance

Stealth aims to push your return into the clutter band
Standoff jammers raise the noise floor across all Doppler bins

Today's Interactive Demo: Range-Doppler Map

Companion script: L5_DopplerMTI.m
In L6 we look at antennas as patterns — where the clutter actually enters

Live demo

Range-Doppler Map

usafa-ece.github.io/ece-495-ew

Demo hand-off; drive it from here. Read the map first: a bright ridge at zero Doppler is the clutter, and the single cell off the ridge is the mover. Slide the target velocity and watch the cell pull away while the ridge stays put. Toggle the MTI filter and the ridge is nulled. The stat tiles carry Doppler shift, first blind speed, unambiguous velocity and apparent velocity, plus the attenuation MTI is applying to the target. It opens at X band with a ten kilohertz PRF, so the blind-speed readout reads one hundred fifty metres per second; set the target there and the cell folds onto the clutter column and goes. Raise the PRF to move the notches, or step the band chips to rescale Doppler against velocity. Companion script runs on their own.

Block 1 · Lesson 5 · Quick Exercise

Quick Exercise / Type-along: Land on the Notch

Type this with me — X-band, and the PRF from L4's exercise.

lambda = 0.03;                  % X-band, 3 cm
PRF    = 2e3;                   % L4's radar
v      = [20 30 60 250];        % closure velocities, m/s
fd     = 2*v/lambda;            % Doppler shift, Hz
vu     = lambda*PRF/4;          % L4 unambiguous velocity
vapp   = mod(v + vu, 2*vu) - vu;
vblind = (1:3)*lambda*PRF/2;
fprintf('  v(m/s)   fd(kHz)  v_app(m/s)\n');
fprintf('%8.0f %9.2f %11.1f\n', [v; fd/1e3; vapp]);
fprintf('\nv_u = %.1f m/s   blind = %s m/s\n', vu, mat2str(vblind));

Two of the four report 0 m/s. Which two, and why?

Then: a standoff jammer wants the B-21 to appear stationary in the R-D map. What waveform property would it try to spoof?

Block 1 · Lesson 5 · Wrap-Up

Wrap-Up

Key ideas

Doppler shift $f_d = 2 v_r / \lambda$ — the second observable after range
MTI kills zero-Doppler clutter; PRF picks where the blind speeds live
Pulse-Doppler $=$ FFT across pulses $\to$ R-D map with movers in their own bins

Next lesson

L6: Antennas, patterns, beamforming, ESA basics
Work the L6 pre-flight before class — you could be the one up front