150 



THE CALCULATION OF RADAR DETECTION PROBABILITY 



This integral gives the probability of detection of a nonfluctuating target 

 on a single scan. It has been evaluated numerically for a useful range of 

 the false-alarm number and the number of pulses integrated. The results 

 of this calculation are shown in Fig. 3-4." In this figure Pd is plotted as a 

 function of the relative range RjRa whose reciprocal is equal to the fourth 

 root of the signal-to-noise ratio. 



0.999 

 0.998 

 0.995 

 0.990 

 0.980 



0.950 

 0.900 



0.800 

 0.700 

 0.600 

 0.500 

 0.400 

 0.300 

 0.200 



0.100 

 0.050 



0.020 

 0.010 

 0,005 

 0.002 

 0.001 



n = 10 



n=100 



n=1000 



0.6 0.8 1.0 1.2 1.4 1.6 

 RELATIVE RANGE, R/Rq 

 n=NO. OF PULSES INTEGRATED 

 ^=FALSE ALARM NUMBER 



1.8 2.0 



Fig. 3-4 Single-Scan Probability of Detection of a Nonfluctuating Target. 



We refer to Pd as the single-scan or single-glimpse probability to dis- 

 tinguish it from the probability of detection when multiple looks are 

 considered. Another term which is commonly used in this connection is 

 blip-scan ratio which refers to the fraction of the time that an operator will 

 see a blip in a single scan over the target. 



'^For a wider range of such curves and also a discussion of a method for calculating them, 

 see J. I. Marcum, op. cit. 



