$1.$a$.$A radar operates at $2$GHz$.$ its max range is $300$ Km for the detection of a target with radar cross section of $1$ square meter. Its antenna is $6-$meter$-$wide and $3-$meter$-$high and the aperture efficiency is $0\mathrm{.}6.$ The min detectable signal is $10-12$ watts. Determine: i$)$ duty cycle, ii$)$ peak transmitter power, iii$)$ average transmitter power if pulse width is $2$ sec$,$ iv$)$ PRF to achieve max unambiguous range of $300$ Km$,$ v$)$ effective aperture and vi$)$ gain in dB$.$

$1.$b$.$An MTI radar operates at a frequency of $6$GHz with a pulse repetion frewuquency of $1$khz$.$find the first,sex second,third blind speeds of this radar.