1) You are designing an air search radar system for a (insert country of your choice) Navy Frigate with a 25 meter mast.
    -At what range will an aircraft flying at an altitude of 300 meters enter radio (radar) line-of-sight?
    -Suppose the aircraft dips to an altitude of 10 meters. What range will it enter radio line-of-sight?

2) Design specifications call for a .5 µ second pulse and detection out to 100.8 kilometers.
    -Calculate the maximum allowable Pulse Repetition Frequency.

3) Systems Engineers have decreed that the maximum allowable false alarm rate is 3.5 false alarms per minute. Calculate the necessary P(False Alarm) to achieve this given that P(F.A.) is a function of the P.R.F. calculated in (2).

4) Calculate the received peak power necessary to detect a target with probability = .95 given a system temperature of 2000K.

5) Calculate the transmitter peak power necessary to yield the received power of (4) for a target at maximum range, with a radar cross section of  100 square meters, carrier frequency = 15 GHz, and antenna gain of 30 dB.

6) Given an antenna with beam width equal to .3 degrees, calculate the maximum allowable antenna rotation rate using the PRF of (3).

7) While on patrol, an aircraft which is being tracked by this system launches a 1000 Km/hr Exocet Missile ( with a radar cross section of .1 square meters) while 35 Km away. This missile immediately drops down to an altitude of 4 meters.
    -At what range will this missile enter radio line-of-sight?
    -How many seconds will you have to detect the target (based on the range just calculated)?
    -Calculate P(detection) at the range just calculated.

This problem set 'inspired' by the Iraqi Exocet missile attack on the USS Stark in the Persian Gulf, 17 May 1987.
To probe further, read Missile Inbound by Jeffrey Levinson and Randy Edwards, Naval Institute Press, 1997.