# null null

```N=5+, Ave, JA Sa |
Problem 1 (4 parts, 40 points)
A radar operates at a 10.5 GHz center frequency, and transmits 100 watts peak power. The system
has an antenna gain of 8 dB, a pulsewidth of 1 usec, and a 10 kHz prf. The radar is capable only
of post-detection integration.
(a) If the radar observes a target of (non-fluctuating) RCS 10 square meters at range 0.5 km, find
bed
N= —
Sw 7 Ah an Pez [06 ww
GC=2 = La T= age CE mae
To= lo kW
№ YE 4.0483 7 „е
Чт me » lo on ) = Son”, m= № +
- V4 S
\ = + a _ Udo) (6.3054 (Wo A 154 D |?
Cy; 2 y S" ¡wo
NT C.304b X 4,0488
VD « wur > ALT A
Tema, У
Lx d8
(b) If the radar has a noise figure of 18 dB, find the single pulse signal to noise ratio achievéd by
the radar for the target of part (a). (10 points)
Nos gown = € kT, К
— \,
= y Oli 15% (2497 ( A»
S\ уе dl US
Sn
Noun a SI? 110344 = 0.Log A8
SE
(c) Estimate the number of pulses that must be integrated by this radar to achieve a probability of
detection of 90% at a false alarm number of 10°. (10 points)
“e Pza a Poo Lo
| fa” 1315 10 J Yoo, Fix 2. ve mad
a E Le UIC IG
his weas ve MED do te Pod <n SHQ gr ut À
LAS - 0.0608 2 Sq 5g, 4.43
So hp L. (
So Cs Co
= № at, hy 1) Sood 5, (p
“
A 25-3,
^) = \\ 41.
A= À 7, es DI
(d) The target is now modeled as a Swerling type 2 target (same average RCS as in parts (a)-(c))
and the same number of pulses as in part (c) is integrated. Estimate the additional signal to noise
ratio required to maintain the performance specified in part (c). (10 points)
fom Tr 23, ANA san Cave Tos Sw, Yo dO
\ = 457, vá = Leí.
Ne o Vaca La VIC arp.
ez pda,
Integados y 4 Tore à tuner De
Problem 2 (4 parts, 36 points)
A 3 GHz radar system with unambiguous range 20 km uses a parabolic dish antenna of aperture
efficiency 0.55 and diameter 5 m. The system achieves a range resolution of 10 m.
(a) Find the gain of the radar’s antenna.
Apeczus area = md. + _
TG A “A= 0, |
С = Weg Yr Sw
x Y a
SÓ - > lb? AC (1.55
гс
| +41.
(b) Find the average power transmitted by the radar if a 1 kW peak power is transmitted.
Ru. > 20 ka = cla
>
Voz > (1-7
Cc
DE = \Dm = с ©
a
C= Alva)
any
<
(©) The radar uses an envelope detector and has an average receiver voltage variance of 2%, = 1
square volt. What is the voltage threshold required to achieve a false alarm time of 1 hour?
PE ma
R- == ma Pz —|
aD - = =z — pl Ay il)
ta Ve Q (3600 | | <x к? 3 \ LS AD
_ +
Cin = © a — RS AI"
Nt = EA ESA -~
(d) If a target is detected at time delay 100 usec, find the range to the target.
C=
== k= Kk.
Problem 3 (6 parts, 4 points each): Circle the answer which is always true.
(1) A 10 GHZ radar wave propagates through 1 km of rain having a rain rate of 40 mm/hr. Which
of the following is a reasonable estimate of the amount of attenuation that would occur?
(a) <0.01 dB (b) 0.05-0.08 dB (c) 0.2-0.4 dB ( (d) 1-2 dB Y (e) none of the above
(2) When using the FFT command of Matlab to transform from the time to the frequency domain:
e first element of the output array contains the value for zero frequency
(b) the last element of the output array contains the value for zero frequency
(c) all elements of the output array will contain only real numbers
(d) the output array must always be phase shifted in order to approximate a Fourier transform
(e) none of the above
(3) Which of the following is true (targets mentioned are Swerling case 5)?
(a) the envelope of received fields when no target is present has a Rician distribution
(b) the envelope of received fields when a target is present has a Rayleigh distribution
(с) Фе envelope of received fields when a target is present has an exponential distribution
d) the standard deviation of any Rayleigh random variable is infinite
O of the above
(4) Which of the following is true?
(a) the RCS of a metal sphere increases as the fourth power of the radar frequency
the RCS of a metal plate increases as the fourth power of the radar frequency
(e RCS of a complex target can vary rapidly as the observation angle is varied
) the RCS of a metal plate is smallest when the plate is observed in its specular orientation
(e) none of the above
(5) Arreceiver operating characteristic curve is
(ay a plot of the probability of detection versus the probability of false alarm for a detector
(b) a plot of the probability of detection versus the threshold voltage for a detector
(c) a plot of the probability of false alarm versus the threshold voltage for a detector
(d) a plot of the probability of detection versus the signal to noise ratio for a detector
(e) none of the above
(6) À radar system with prf 1 kHz has azimuth beamwidth 30 degrees. If the radar is required to
complete an azimuthal rotation in 1 second, the number of pulses than can be integrated for a sin-
gle target is closest to
(a) 1
360°
(c) 100 T ‘ - wm 30 À
ou > See INC Y Bra кол 300? 12, Stand
(e) none of the above |
+ Xr edo Va TE = Va due nm
TV == 83
CT — 12. > -
La pois
```