A radar has the following parameters: peak power \(P_{t}=65 \mathrm{~kW}\); total losses \(L=5 \mathrm{~dB}\); operating frequency \(f_{0}=8 \mathrm{GHz} ; \mathrm{PRF} f_{r}=4 \mathrm{kHz}\); duty cycle \(d_{t}=0.3\); circular antenna with diameter \(D=1 \mathrm{~m}\); effective aperture is 0.7 of physical aperture; noise figure \(F=8 d B\). (a) Derive the various parameters needed in the radar equation. (b) What is the unambiguous range? (c) Plot the SNR versus range ( \(1 \mathrm{~km}\) to the radar unambiguous range) for a \(5 \mathrm{dBsm}\) target. (d) If the minimum \(S N R\) required for detection is \(14 d B\), what is the detection range for a \(6 \mathrm{dBsm}\) target? What is the detection range if the SNR threshold requirement is raised to \(18 \mathrm{~dB}\) ?