Practice Problems (KEY)

Problem 1

You and your wingman are flying over hostile territory in your advanced F-169 Next Generation Stealth Fighters. An SA-20 SAM site knows you are in the area and is actively searching the skies. The SAM site’s fire control RADAR has the following characteristics: \(80\ \text{kW}\) transmit power, operating frequency of \(5\ \text{GHz}\), and a transmit/receive antenna gain of \(5000\). The RADAR has a PRF of \(10\ \text{kHz}\) and a pulse width of \(75\ \text{ns}\). The RADAR receiver requires a minimum received power of \(1\ \text{pW}\) to detect and process the signal. The F-169s have an RCS of \(0.5\ \text{m}^2\) and are equipped with a RADAR jamming system. This system has an antenna gain of \(7\) but requires \(10\ \mu\text{W}\) of received power to accurately identify the emitter location. The fighters are \(48\ \text{km}\) from the SAM site and flying at a speed of \(223.85\ \text{m/s}\). The F-169s are \(10\ \text{m}\) apart.

a. Can the RADAR detect the F-169s? (assume no LOS issues)

\[ \lambda = \frac{c}{f} = \frac{3 \times 10^{8}\ \text{m/s}}{5 \times 10^{9}\ \text{Hz}} = 0.06\ \text{m} = 60\ \text{mm} \]

\[ R = \sqrt[4]{\frac{P_T G^2 \sigma \lambda^2}{(4\pi)^3 P_R}} = \sqrt[4]{\frac{(80{,}000\ \text{W})(5000)^2 (0.5\ \text{m}^2)(0.06\ \text{m})^2}{(4\pi)^3 (1 \times 10^{-12}\ \text{W})}} = 36.7\ \text{km} \]

No — maximum RADAR range is \(36.7\ \text{km}\) and the fighters are \(48\ \text{km}\) away.

b. At what range (in km) can the fighter’s RADAR jamming system detect the RADAR? (assume no LOS issues)

\[ R_{RWR} = \frac{\lambda}{4\pi} \sqrt{\frac{P_T G_T G_R}{P_R}} = \frac{0.06\ \text{m}}{4\pi} \sqrt{\frac{(80{,}000\ \text{W})(5000)(7)}{10 \times 10^{-6}\ \text{W}}} = 79.9\ \text{km} \]

c. Will the RADAR be able to distinguish both F-169s?

\[ \Delta R = \frac{c \tau}{2} = \frac{(3 \times 10^{8}\ \text{m/s})(75 \times 10^{-9}\ \text{s})}{2} = 11.25\ \text{m} \]

No, the range resolution is not below \(10\ \text{m}\).

d. What is the maximum distance that the RADAR can determine the F-169s range with certainty?

\[ R_{\max} = \frac{c \cdot PRI}{2} = \frac{c}{2 \cdot PRF} = \frac{3 \times 10^{8}\ \text{m/s}}{2 (10{,}000\ \text{Hz})} = 15\ \text{km} \]

Problem 2

A convoy in Iraq employs a jammer system to prevent the remote detonation of improvised explosive devices (IEDs). As the convoy approaches an IED, according to the Friis equation, is the jammer becoming more or less effective?

The jammer is becoming more effective because the range between the jammer and the IED decreases, which increases the received jamming power at the IED.

Problem 3

In order for an attack to be successful, the planners determine a SAM site must be destroyed. What kind of electronic warfare is this?

(a) SEAD

(b) DEAD

(c) Jamming

(d) Chaff

Problem 4

Both RADAR jamming and communications jamming become more effective as the jamming platform moves toward the site being jammed.

(a) True

(b) False

Only communications jamming is more effective as distance decreases. RADAR jamming becomes less effective as the jammer gets closer.

Problem 5

Which of these techniques is not used to counter jamming?

(a) Chirp signals

(b) Chaff and flares

(c) Direct-sequence spread spectrum

(d) Frequency hopping

Chaff and flares are not counter-jamming techniques; they act as decoys.

Problem 6

Chaff creates a false RADAR target that is brighter than the actual target.

(a) True

(b) False

The purpose of chaff is to redirect the missile toward a false target.

Problem 7

A UAS under your control is jamming communications for a command and control site. The communications signal is transmitted from a distance of \(50\ \text{km}\) at a frequency of \(1.8\ \text{GHz}\) with a transmit power of \(1.4\ \text{kW}\). The transmit and receive antennas both have a gain of \(3.0\). The jammer on your UAS has an antenna gain of \(20\) with a transmit power of \(2.4\ \text{kW}\). Your UAS is \(35\ \text{km}\) from the command and control site. If the communications system requires an SNR of \(0.1\), is your jamming effective?

Step 1: Find wavelength

\[ \lambda = \frac{c}{f} = \frac{3 \times 10^{8}\ \text{m/s}}{1.8 \times 10^{9}\ \text{Hz}} = 0.1667\ \text{m} = 166.7\ \text{mm} \]

Step 2: Desired received power

\[ P_R = P_T G_T G_R \left( \frac{\lambda}{4\pi R} \right)^2 = (1400\ \text{W})(3)(3)\left( \frac{0.1667}{4\pi (50{,}000)} \right)^2 = 887\ \text{pW} \]

Step 3: Jamming power

\[ P_R = (2400\ \text{W})(20)(3)\left( \frac{0.1667}{4\pi (35{,}000)} \right)^2 = 20.7\ \text{nW} \]

Step 4: SNR

\[ SNR = \frac{P_{signal}}{P_{jam}} = \frac{887 \times 10^{-12}}{20.7 \times 10^{-9}} = 0.0428 \]

Since \(SNR < 0.1\), jamming is effective.

Problem 8

A targeting RADAR has a pulse width of \(50\ \text{ns}\). If you wish to mask the number of aircraft in your formation, how close must your aircraft fly?

\[ \Delta R = \frac{c \tau}{2} = \frac{(3 \times 10^{8})(50 \times 10^{-9})}{2} = 7.5\ \text{m} \]

Problem 9

A search RADAR transmits at \(800\ \text{MHz}\). What length of chaff is required?

\[ \lambda = \frac{c}{f} = \frac{3 \times 10^{8}}{800 \times 10^{6}} = 0.375\ \text{m} = 375\ \text{mm} \]

\[ \text{Chaff length} = \frac{\lambda}{2} = 187.5\ \text{mm} \]

Problem 10

If attacked by a fighter with Doppler RADAR, why turn to \(3\) or \(9\) o’clock?

\[ f = f_0 \left(1 + \frac{2 v \cos 90^\circ}{c} \right) = f_0 \]

No Doppler shift → appears stationary → RADAR ignores target.

Problem 11

Given the following information about an enemy SAM site and the capabilities of your jammer, at what distance does your jamming pod become ineffective?

Enemy RADAR	Your jamming equipment
\(P_T = 1\ \text{kW}\)	\(P_{jam} = 20\ \text{W}\)
\(G_T = 3000\)	\(G_{jam} = 3.5\)
\(f = 7\ \text{GHz}\)	\(f = 7\ \text{GHz}\)
\(SNR_{\min} = 0.02\)	\(\sigma = 25\ \text{m}^2\)

\[ SNR = \frac{P_{RADAR} G_{RADAR} \sigma}{4\pi P_{jam} G_{jam} R^2} \]

\[ R = \sqrt{\frac{(1000\ \text{W})(3000)(25\ \text{m}^2)}{(20\ \text{W})(3.5)(4\pi)(0.02)}} = 2.06\ \text{km} \]

Jamming becomes ineffective at \(2.06\ \text{km}\).