An L-band radar has the following specifications: operating frequency \(f_{0}=1.5\) \(G H z\), operating bandwidth \(B=2 \mathrm{MHz}\), noise figure \(F=8 d B\), system losses \(L=4 d B\), time of false alarm \(T_{f a}=12\) minutes, detection range \(R=12 \mathrm{~km}\), probability of detection \(P_{D}=0.5\), antenna gain \(G=5000\), and target RCS \(\sigma=1 \mathrm{~m}^{2}\). (a) Determine the \(\operatorname{PRF} f_{r}\), the pulse width \(\tau\), the peak power \(P_{t}\), the probability of false alarm \(P_{f a}\) and the minimum detectable signal level \(S_{\text {min }}\). (b) How can you reduce the transmitter power to achieve the same performance when 10 pulses are integrated noncoherently? (c) If the radar operates at a shorter range in the single pulse mode, find the new probability of detection when the range decreases to \(9 \mathrm{~km}\).