Consider a low PRF C-band radar operating at \(f_{0}=5000 \mathrm{MHz}\). The antenna has a circular aperture with radius \(2 \mathrm{~m}\). The peak power is \(P_{t}=1 \mathrm{MW}\) and the pulse width is \(\tau=2 \mu \mathrm{s}\). The PRF is \(f_{r}=250 \mathrm{~Hz}\), and the effective temperature is \(T_{0}=600 \mathrm{Kelvin}\). Assume radar losses \(L=15 \mathrm{~dB}\) and target RCS \(\sigma=10 \mathrm{~m}^{2}\). 

(a) Calculate the radar's unambiguous range. 

(b) Calculate the range \(R_{0}\) that corresponds to \(S N R=0 d B\). 

(c) Calculate the \(S N R\) at \(R=0.75 R_{0}\).