ECE 495 — Electromagnetic Warfare and Survivability

Block 1: Radar Fundamentals
Lesson 6: Antenna Patterns and Beamforming

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

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Block 1 · Lesson 6 · Where We Left Off

Where We Left Off

L5 gave us the range-Doppler map.

But the radar only sees energy that comes through its antenna. The antenna's pattern decides what enters the receiver and from where.

Today

Pattern anatomy, the polar plot convention, beamforming, and ESAs — and why side lobes are the back door for EW.

Two radars with identical transmitters behave differently because their patterns differ.

Block 1 · Lesson 6 · Objectives

Lesson Objectives

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

Identify the main lobe, side lobes, and back lobes in a pattern
Read a polar plot and extract HPBW and SLL
Use the gain / aperture / beamwidth rule of thumb to size an antenna
Explain how an ESA steers a beam and what that buys an EW operator

The pattern is the map of where a radar is strong, where it is weak, and where it can be fooled.

Block 1 · Lesson 6 · Part One

Reading the Pattern

Three features, two numbers, and one rule of thumb that sizes any antenna on the back of an envelope.

Block 1 · Lesson 6 · Anatomy

Anatomy of an Antenna Pattern

Main lobe — where the radar wants to look
Side lobes — unintended sensitivity off boresight; the EW back door
Back lobe — look the other way; rarely big but always there

Block 1 · Lesson 6 · The Polar Plot

The Polar Plot

Patterns are drawn in polar coordinates with gain (dB) versus angle.

HPBW — half-power beamwidth, where gain drops 3 dB below peak
SLL — side-lobe level, peak side lobe relative to the main lobe (dB, negative)
Uniform illumination $\Rightarrow$ first SLL $\approx -13.2$ dB; tapering trades SLL for HPBW
Two cuts (azimuth and elevation) describe a 3D pattern

The pattern is where the radar lives — and where it leaks.

Block 1 · Lesson 6 · Sizing an Antenna

Gain, Aperture, Beamwidth Revisited

For an aperture of size $D$:

Rules of thumb

\[ \theta_{\text{HPBW}} \approx \frac{70 \, \lambda}{D} \text{ (deg)}, \qquad G \approx \frac{30{,}000}{\theta_{\text{az}} \cdot \theta_{\text{el}}} \]

X-band example ($\lambda = 3$ cm), $0.5 \times 0.5$ m antenna:

$\theta_{\text{HPBW}} \approx 4.2^\circ$ in each plane
$G \approx 30000 / (4.2 \cdot 4.2) \approx 1700 \Rightarrow 32$ dBi
Tighter beam means more gain — and less coverage per scan position

Block 1 · Lesson 6 · Part Two

Steering Without Moving

Replace one dish with many small radiators, and the beam is pointed by arithmetic instead of by a motor.

Block 1 · Lesson 6 · Beamforming

Beamforming Basics

Replace the dish with $N$ small radiators (an array). Each element transmits the same signal with a programmed phase $\phi_n$.

Progressive phase

\[ \Delta \phi = \frac{2\pi}{\lambda} \, d \, \sin\theta_s \]

Constructive interference at the steering angle $\theta_s$ $\Rightarrow$ main lobe points there
Beam steered electronically — no moving parts
More elements $\Rightarrow$ narrower beam and lower side lobes (with tapering)
Space them too far apart and the pattern aliases — grating lobes, full-strength copies pointing where you did not ask: $d \le \lambda / (1 + |\sin\theta_0|)$

Block 1 · Lesson 6 · Scan Loss

Pointed at Boresight, the Array Is at Its Best

Load a flat phase across the elements and the beam sits at $\theta_0 = 0$ — the array shows the target its full aperture.

$\theta_0 = 0^\circ$full aperture · beamwidth $\theta_B$

−90°

−60°

−30°

0°

30°

60°

90°

Every element is broadside to the target, so the projected aperture is the whole array.

Block 1 · Lesson 6 · Scan Loss

Steer It to 60°, and Physics Sends a Bill

Nothing moved. But the target now sees the array edge-on, so the effective aperture shrinks as $\cos\theta_0$ — and a smaller aperture makes a wider beam.

was here$\theta_0 = 0^\circ$

$\theta_0 = 60^\circ$beamwidth $2\theta_B$ · about $-3$ dB

−90°

−60°

−30°

0°

30°

60°

90°

HPBW broadens as $1/\cos\theta_0$ — at $60^\circ$ that is twice as wide
Effective aperture drops by $\cos 60^\circ = 0.5$, costing about 3 dB of gain

An ESA is worst exactly where it is scanning hardest.

Block 1 · Lesson 6 · ESA / AESA

Electronically Scanned Arrays (ESA / AESA)

ESA $=$ beam steered by phase shifters. AESA $=$ active ESA, each element has its own Tx/Rx module.

What it does	What it buys the threat
Microsecond beam pointing	Track many targets; interleave search and track in one dwell
Graceful degradation	A few failed modules cost a few percent gain, not the radar
Multi-beam	Different waveforms in different directions at the same time

HPBW still broadens as $1/\cos\theta_s$ off boresight — physics does not care how modern the array is
Modern fire control radars and most new IADS surveillance are AESA

Block 1 · Lesson 6 · Why It Matters

Why Patterns Matter for EW

Side-lobe leak — a jammer not on boresight still enters through side lobes
- EP response: side-lobe cancellation, side-lobe blanker, low-SLL antennas
Main-beam pointing — knowing where the threat is looking tells you what it is doing
ESA agility — compresses the threat's kill chain; harder to deceive with classical techniques
Polarization purity — cross-pol leakage shows up in patterns and matters for LO

Side lobes are the back door for EW.

Today's Interactive Demo: Phased Array Simulator

Companion script: L6_ArrayFactorAndSteering.m
In L7 we put these patterns inside an IADS and watch each radar do its job

Live demo

Phased Array Simulator

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

Demo hand-off; drive it from here. Start on the Pattern tab at the defaults — eight elements, half-wavelength spacing, pointed at boresight — and read the Status panel out loud: it reports beamwidth and peak side-lobe level live, measured off the curve on screen. Drag the element count up and let the class watch two numbers move together, the beam narrowing while the side-lobe level settles toward the uniform-illumination constant from the polar-plot slide. Then push the steer angle out and let them see the beam both swing and fatten, which is the scan-loss pair we just walked. The Polar Cut tab draws the same beam round, the way a radar handbook would print it. The Planar toggle adds a second axis so the beam becomes a cone you can steer in azimuth and elevation, and the 3D Hemisphere tab lets you rotate it. The element-factor toggle multiplies in a real element's own pattern. Leave the spacing slider alone for now — they meet it themselves in a minute. Companion script runs on their own.

Block 1 · Lesson 6 · Type-along

Your Turn

Laptops open, MATLAB up. Ten lines that add up phasors, one parameter changed, and a claim from the last slide put to the test.

Block 1 · Lesson 6 · Quick Exercise

Quick Exercise / Type-along: Walk the Grating Lobe

Eight elements, wide spacing. Type it, run it — then change th0 to 30 and run it again.

N = 8;  dlam = 0.9;  th0 = 0;          % elements, d/lambda, steer (deg)
th = -90:0.25:90;                      % look angles (deg)
n  = (0:N-1).';                        % element index, as a column
beta = -2*pi*dlam*sind(th0);           % programmed phase per element
AF = sum(exp(1j*n*(2*pi*dlam*sind(th) + beta)), 1)/N;
plot(th, 20*log10(max(abs(AF),1e-3)), 'LineWidth',1.5);
hold on;  grid on;  ylim([-40 0]);
xlabel('theta (deg)');  ylabel('|AF| (dB)');
fprintf('theta0=%2d | beta=%7.1f deg/elem | limit %.2f | used %.2f\n', ...
        th0, rad2deg(beta), 1/(1+abs(sind(th0))), dlam);

Full-strength lobes at $\theta_0 = 0$? At $\theta_0 = 30^\circ$?

The spacing never changed. What did?

Block 1 · Lesson 6 · Wrap-Up

Wrap-Up

Key ideas

Patterns have main, side, and back lobes; side lobes are the EW back door
HPBW $\propto \lambda / D$; gain $\propto$ aperture $/ \lambda^2$
ESA / AESA $=$ microsecond beam steering, multi-beam, graceful degradation

Next lesson

L7: Threat radar taxonomy in an IADS — EW, ACQ, HF, GCI, TTR, AI, TIR
Work the L7 pre-flight before class — you could be the one up front