A circularly scanning, fan beam radar has a rotation rate of 2 seconds per revolution. The azimuth beam width is 1.5 degrees and the radar uses a PRF of $12.5kHz$. The radar uses an unmodulated pulse with a width of $1.2\mu$ s and searches a range window that extends from $15km$ to $100km$. The range cells used during search are separated by one pulse width. It is desired that the false alarm probability be set so that the radar experiences only one false alarm every $2min$. What is the required $P_{fa}$ for each range cell? What is the threshold-to-noise ratio, in $dB$, needed to maintain that $P_{fa}$ ?

Data From Problem 10

A circularly scanning, fan beam radar has a rotation rate of 2 seconds per revolution. The azimuth beam width is 1.5 degrees and the radar uses a PRF of \(12.5 \mathrm{kHz}\). The radar uses an unmodulated pulse with a width of \(1.2 \mu\) s and searches a range window that extends from \(15 \mathrm{~km}\) to \(100 \mathrm{~km}\). The range cells used during search are separated by one pulse width. It is desired that the false alarm probability be set so that the radar experiences only one false alarm every \(2 \mathrm{~min}\). What is the required \(P_{f a}\) for each range cell? What is the threshold-to-noise ratio, in \(d B\), needed to maintain that \(P_{f a}\) ?