$(20$ points$)$ In this problem, we're trying to determine the performance of two nearby radars. We will need to generate antenna patterns $($uniform illumination, $\frac{\text{I}}{2}$ spacing$)$ for both radars and determine power densities and SNRs$.$

Radar $1$

i$.$ Frequency $=3GHz$

ii$.$ Peak power $=100kW$

iii. Uniform Linear Array $-$

length $=2$ meters

iv$.$ Transmit Loss $=2dB$

Radar $2$

v$.$ Frequency $=3GHz$

vi$.$ Peak power $=1000W$

vii. Circular array $-$ diameter $=0\mathrm{.}5$ meters

viii. Duty $10\%$

ix$.$ Dwell time $=1ms$

x$.$ Noise Figure $=4\mathrm{.}5dB$

xi$.$ Total System Losses $=10dB$

xii. Bandwidth $=1MHz$

a$.(10$ points$)$ Radar $2$ is turned on$.$ Calculate the Radar $2$ SNR on a $0$ dBsm target $10$ km from Radar $2($at broadside$).$ Answer should be in dBs$.$

b$.(10$ points$)$ Radar $1$ is turned on and Radar $2$ is turned off.

i$.$ Calculate the Radar $1$ power density $(\frac{W}{m^2})$ arriving at the antenna face of Radar $2$ as illustrated below.

ii$.$ If Radar $1$ is rotated $45$ and is pointing directly at Radar $2,$ does that impact the power density arriving at Radar $2\text{'}$s antenna face? If so$,$ how?