(a) Show how you can use the radar equation to determine the \(\operatorname{PRF} f_{1}\) the pulse width \(\tau\), the peak power \(P_{t}\), the probability of false alarm \(P_{f a}\) and the minimum detectable signal level \(S_{\min }\). Assume the following specifications: operating frequency \(f_{0}=1.5 \mathrm{MHz}\), operating bandwidth \(B=1 \mathrm{MHz}\), noise figure \(F=10 \mathrm{~dB}\), system losses \(L=5 d B\), time of false alarm \(T_{f a}=20 \mathrm{~min}\), detection range \(R=12 \mathrm{~km}\), probability of detection \(P_{D}=0.5\) (three pulses). 

(b) If post-detection integration is assumed, determine the SNR.