Compute (as a function of \(B_{J} / B\) ) the cross-over range for the radar in Problem 3.11. Assume \(P_{J}=200 \mathrm{~W}, G_{J}=15 \mathrm{~dB}\), and \(L_{J}=2 \mathrm{~dB}\). Assume \(G^{\prime}=12 \mathrm{~dB}\), and \(R_{J}=25 \mathrm{~dB}\).

Data From Problem 3.11

A millimeter wave (MMW) radar has the following specifications: operating frequency \(f_{0}=94 \mathrm{GHz}, \mathrm{PRF} f_{r}=15 \mathrm{kHz}\), pulse width \(\tau=0.05 \mathrm{~ms}\), peak power \(P_{t}=10 \mathrm{MW}\), noise figure \(F=5 d B\), circular antenna with diameter \(D=0.254 \mathrm{~m}\), antenna gain \(\mathrm{G}=30 \mathrm{~dB}\), target \(\mathrm{RCS} \sigma=1 \mathrm{~m}^{2}\), system losses \(\mathrm{L}=8 \mathrm{~dB}\), radar scan time \(T_{s c}=3 \mathrm{~s}\), radar angular coverage \(200^{\circ}\), and atmospheric attenuation \(3 \mathrm{~dB} / \mathrm{km}\). Compute the following: (a) wavelength \(\lambda\); (b) range resolution \(\Delta R\); (c) bandwidth \(B\); (d) the \(S N R\) as a function of range; (e) the range for which \(S N R=15 d B\); (f) antenna beam width; (g) antenna scan rate; (h) time on target; (i) the effective maximum range when atmospheric attenuation is considered.