Project 3 — Radar Design Lab

Project 3 — Radar Design Lab#

Buy the radar: choose a band, a transmitter, a dish, a receiver, a mast and a pulse width from a priced catalog, so that one ground radar sees a jamming bomber pair and a low-flying cruise missile far enough out, tells the two bombers apart, and stays inside the budget, at the lowest cost your team can find.

At a glance

Teams of two. Worth 3 project points: 2 group points, autograded from the design file your team uploads, and 1 individual point, the Project 3 Individual Questions.

  • Lesson 37 introduces the project. This page and the simulator are open from then on.

  • The Gradescope assignment Project 3 opens on 27 Nov, over Thanksgiving break.

  • Lesson 38 is your team workday.

  • Your team’s design is due Friday 4 December at 2359 (the T-day of Lesson 39).

  • Lesson 40 is the Project 3 Discussion, in our classroom: the debrief, then the individual questions, worked in class.

  • The individual questions are due Thursday 10 December at 2359 (the T-day of Lesson 41).

Each part is due at 2359 on the T-day of its lesson, and Gradescope is authoritative for every deadline. There are no extensions on any part of Project 3.

GenAI is not authorized for any part of Project 3: not the team design, not the individual questions. That is stricter than Project 2, which allowed Level 4.

The Mission#

An adversary is sending two threats against a site you defend. Your team buys one ground-based radar to see them coming:

  • Threat 1: two H-20 bombers in trail, one directly behind the other, each carrying a self-screening jammer.

  • Threat 2: a CJ-10 cruise missile, flying low, with no jammer.

You build the radar from a priced catalog, one pick in each of six categories. It must meet three requirements and stay within a budget. A design that meets them all earns one point; the lowest-cost design that meets them all earns the second. Hence the project’s nickname, Buy the Radar: a radar that works is the start, and the cheapest one that works is the goal.

Educational exercise

This scenario does not represent actual aircraft, missiles, radars, jammers or their prices. The adversary, the threats and the catalog exist for this exercise only.

Start in the Simulator#

Open the EW Simulator and choose ECE 215:

https://usafa-ece.org/apps/ew-simulator/choose.html

The ECE 215 page is this project’s scenario: the same threats, catalog, prices and equations as the handout, and the same model the grader uses. Make your six choices and the page shows, live, each requirement’s verdict and your design’s total cost. It never tells you whether a cheaper design exists. Finding that out is your team’s job, and it is the second point.

The same page is where you submit from: you type your documentation statement there, then Export design saves the file you upload to Gradescope (see Submitting, below).

Use the simulator to check your design, not to find it

Design on paper first, then let the simulator check you.

  • For each requirement, which equation decides it? Write it down, and circle the choices that appear in it.

  • For each threat, which limit is the smallest? A threat’s detection range is the smallest of the limits that apply to it, so work out every one before you decide which choice to spend money on.

  • What does each choice buy? Before you pay for an upgrade, ask which limit it moves, and by how much. The band and the pulse width are free; check what they change too.

  • Then price it, and ask whether a cheaper combination would still pass.

When your hand numbers and the simulator disagree, find out why before you submit.

Requirements#

Requirement

Your radar must…

REQ 1

detect an H-20 at a range of 235 km or more (either aircraft counts: they are identical and fly at the same altitude)

REQ 2

have a range resolution of 6.0 km or less, so that it resolves the two H-20s, which fly 6.0 km apart in trail

REQ 3

detect the CJ-10 at a range of 30 km or more

Budget

cost $1,200,000 or less in total: transmitter + dish + receiver + mast

Every comparison is inclusive: a detection range equal to the requirement passes, a resolution equal to the spacing passes, and a cost equal to the budget passes.

Your Six Choices#

Choice

What it sets

Cost

Band

the frequency \(f\)

free

Transmitter

the peak power \(P_T\)

priced

Dish

the diameter \(D\), and through it the gain \(G_T\)

priced

Receiver

the system noise temperature \(T_{sys}\)

priced

Mast

the height of the radar antenna, in feet

priced

Pulse width

\(\tau\)

free

The catalog, every option with its price, is in the handout and on the simulator page, together with the threat data: each threat’s altitude, its RCS in each band, and the bands, power and gain of the H-20’s jammer.

The Model#

This is the whole model, the same one the grader and the simulator use. Every gain and every ratio is a plain (linear) ratio: no decibels anywhere. There are no losses, no clutter and no multipath, and the radar decides on one pulse.

Wavelength and dish gain. With \(c = 3\times10^8\) m/s and dish efficiency \(\eta = 0.6\),

\[ \lambda = \frac{c}{f}, \qquad G_{dish} = \left(\frac{2\pi r_{dish}}{\lambda}\right)^2 \eta, \qquad r_{dish} = \frac{D}{2}. \]

The catalog lists the dish’s diameter \(D\); the equation sheet’s row takes the radius. The same dish transmits and receives, so in the radar range equation \(G_T = G_{dish}\).

Sensitivity. In this project the receiver bandwidth is matched to the pulse, \(BW = 1/\tau\) (Lessons 35 and 36 say \(BW \approx 1/\tau\)). With \(k = 1.38\times10^{-23}\) J/K and \(SNR_{min} = 15\) (a plain ratio), the Sensitivity \(P_{R,min}\) is

\[ P_{R,min} = SNR_{min}\, k\, T_{sys}\, BW . \]

Noise-limited range. The equation sheet’s radar range equation with \(P_R = P_{R,min}\):

\[ R_{noise} = \left(\frac{P_T G_T^2 (RCS) \lambda^2}{(4\pi)^3 P_{R,min}}\right)^{1/4}. \]

Line of sight. The equation sheet’s row, with both heights in feet (the radar’s mast and the threat’s altitude) and the result in miles:

\[ R_{LOS,mi} = \sqrt{2 h_{ft,1}} + \sqrt{2 h_{ft,2}}, \qquad 1 \text{ mi} = 1.61 \text{ km}. \]

Burn-through range. Only when the radar’s band lies inside one of the H-20 jammer’s bands (edges included); the CJ-10 carries no jammer. The jammer flies with its target (self-screening), which is the case the formula covers (Lesson 37):

\[ R_{BT} = \sqrt{\frac{P_T G_T (RCS)}{P_{T,jam} G_{T,jam}\, 4\pi\, SNR_{min}}} \quad \text{(meters)}. \]

Each H-20 carries its own jammer, but one jammer counts against one echo: the two jammers do not add.

\(R_{BT}\) often comes out in meters, not kilometers. That is not a units error: compare it with how close the jammer can ever come (Lesson 37).

Detection range. A threat’s detection range is the smallest of the limits that apply to it: \(R_{noise}\) and \(R_{LOS}\) always, and \(R_{BT}\) too when that threat’s jammer covers your band. Use that threat’s own RCS (it depends on the band) and its own altitude.

Range resolution and cost.

\[ \Delta R = \frac{c\,\tau}{2}, \qquad \text{total cost} = \text{transmitter} + \text{dish} + \text{receiver} + \text{mast}. \]

Carry at least three significant figures in hand work. A rounded gain can flip a verdict on paper. The grader recomputes everything from your choices, so rounding never changes your grade, but it can change your decision.

How It Is Graded#

Your team uploads one design file to the Gradescope assignment Project 3. The grader grades your six choices: it recomputes every number from them with the model above, and any number the simulator wrote into the file is ignored. It also checks that the file is a current export and carries your documentation statement. It runs two tests, one point each:

Test

You see it

It passes when

Design meets every requirement

as soon as you submit, with each requirement’s PASS or FAIL and your total cost

REQ 1, REQ 2, REQ 3 and the budget all pass

Lowest-cost design

only after the due date

your design meets every requirement and no design that meets them all costs less

Until the due date, the second test and your total score stay hidden. The grader never prints the lowest cost, the lowest-cost design or how far you are from it.

  • Resubmit as often as you like until the deadline.

  • Late submissions are off. After the deadline Gradescope takes no more submissions.

  • A file with no documentation statement is not graded (0 of 2).

  • Upload exactly one .json file. None, or more than one, also scores 0 of 2; the result tells you what it found.

Submitting#

  1. Type your documentation statement in the simulator page, before you export. Begin it with “Documentation:” and state any help you received; if there was none, write “Documentation: None.”

  2. Export design. The simulator saves ece215_project3_design.json, which holds your six choices and your statement.

  3. Upload that .json file to the Gradescope assignment Project 3, once per team, and add your teammate to the submission. Any file name that ends in .json works.

  4. Read the result. The “Design meets every requirement” test lists each requirement’s PASS or FAIL and your total cost. Fix what fails, export again and resubmit.

Common Pitfalls#

  • Heights in feet. The line-of-sight row takes both heights in feet and returns miles; only then convert with 1 mi = 1.61 km. Converting the heights to meters first breaks the equation.

  • An \(R_{BT}\) in meters. It is not a units error. Compare it with how close the jammer can ever come (Lesson 37).

  • Two jammers, one echo. Each H-20 jams for itself; the jammers do not add.

  • Burn-through only in a jammed band. Check the radar’s band against the jammer’s bands (edges included) before you compute \(R_{BT}\), and leave it out when it does not apply.

  • Roots. \(R_{noise}\) is a fourth root and \(R_{BT}\) a square root, so the same upgrade moves them by different factors. Work out what a choice buys before you pay for it.

  • \(BW = 1/\tau\). A shorter pulse sharpens the range resolution, and it also widens the bandwidth, which raises the noise floor: a larger \(P_{R,min}\).

  • Each threat’s own numbers. The RCS depends on the band and on the threat; the altitude depends on the threat. Do not reuse the H-20’s numbers for the CJ-10.

  • Radius, not diameter. The dish-gain row takes \(r_{dish} = D/2\).

  • Rounding. Carry three significant figures or more.

  • No decibels. Every gain and ratio is linear.

  • No documentation statement. The file is not graded.

The Individual Questions#

The third project point is yours alone: the Gradescope Online Assignment Project 3 Individual Questions, auto-graded.

  • It opens after the design is due. You start it in class at Lesson 40, after the debrief, and it is due Thursday 10 December at 2359 (the T-day of Lesson 41).

  • Gradescope grades the 10 parts automatically; each is worth one tenth of this point, so 8 of 10 earns 0.8, and your score is final at the deadline.

  • The questions are about this project and the lowest-cost design your instructor shows at Lesson 40, so they are not posted on this page.

  • Individual work: no collaboration, and no GenAI. You may use the resources listed below.

Authorized Resources#

For the team design:

  • Calculator

  • The ECE 215/S equation sheet

  • Slides, class notes, the readings and the practice problems

  • The EW Simulator

  • Spreadsheets, and code you write yourself (MATLAB, Python, etc.), with every AI assistant and AI autocomplete turned off

  • Collaboration with the cadets in your team only

  • Extra instruction (EI) from ECE 215/S instructors

For the individual questions: the same, minus any collaboration. EI from ECE 215/S instructors is still allowed.

GenAI is not authorized for any part of Project 3. Document all help you received in your documentation statement.

No extensions on any part of Project 3: not the design, not the individual questions. No corrections: both are final at their deadlines, an exception to the syllabus’s one-week correction, because the lowest-cost design is revealed after the design deadline.

Submission Checklist#

  • Design worked on paper: each threat’s limits computed, the smallest one found

  • Design checked on the EW Simulator’s ECE 215 page: REQ 1, REQ 2, REQ 3 and the budget all PASS

  • Cheaper combinations checked: does a less expensive design still pass?

  • Documentation statement typed in the simulator

  • Design exported: ece215_project3_design.json

  • Team submission to Project 3 on Gradescope, teammate added, by Friday 4 December at 2359 (the T-day of Lesson 39); the result read

  • Individual submission to Project 3 Individual Questions on Gradescope, by Thursday 10 December at 2359 (the T-day of Lesson 41)

Files#

Contents