3-31 DETECTION PROBABILITY FOR A PULSE RADAR 151 



To fix ideas, we consider an example of an AI (airborne intercept) radar. 

 The idealized range Ro has been determined in Paragraph 3-3 to be 20.4 

 n.mi. The radar parameters of interest are assumed as follows: 



Pulse length = 1 jusec Beamwidth = 4.15° 



Azimuth scan = 120° Scan time = 3 sec 



Elevation scan = 17° 



PRF = 500 pps 



The scan area is approximately 17° X 120° = 2040° squared. The beam 

 area is approximately (■7r/4) 4.15^ = 13.6° squared. The number of beam 

 areas within a scan area is 2040/13.6 = 150. With a scan time of 3 seconds 

 and a PRF of 500 pps, the number of pulses received in a scan over the 

 target is 3 X 500/150 = 10. We suppose that a false-alarm time of 100 

 seconds is chosen. With the IF bandwidth matched to the pulse width 

 (approximately equal to its reciprocal) there will be 10^ independent noise 

 samples per second, and the false-alarm nuniber will be 100 X 10^ = 10^ 

 Referring to Fig. 3-4, the relative range at which Pd = 0.9 for « = 10 

 and 7] = 10^ is determined to be 0.72. The actual range giving 90 per cent 

 probability of detection is thus 0.72 X 20.4 = 14.7 n.mi. A similar 

 calculation gives the range corresponding to a detection probability of 

 10 per cent as 17.5 n.mi. The complete probability of detection curve for 

 this example is shown in Fig. 3-5 along with the single scan and cumulative 



10 15 



TARGET RANGE (n.mi.) 



20 25 



Fig. 3-5 Single-Scan and Cumulative Probability of Detection for Text Example. 



probability of detection curves for a fluctuating target when the same basic 

 radar parameters are used. The derivation of methods for the calculation 

 of these other curves is discussed in the rest of this paragraph and in 

 Paragraph 3-4. 



The Effect of Target Fluctuations. The discussion thus far and the 

 curves in Fig. 3-4 refer only to the case where the magnitude of the received 



