3-3] 



DETECTION PROBABILITY FOR A PULSE RADAR 



149 



will exceed a threshold ^, is given by the integral of the probability density 

 function of the sum voltage u of noise alone. 



False alarm probability = - = / P]s[{u)du. (3-23) 



V Jb 



This integral has been evaluated, and the result is shown in Fig. 3-3 for a 

 useful range of parameters. 



1000 



500 



100 



50 



20 



10 



10 20 50 100 200 500 1000 



RELATIVE BIAS LEVEL, b/2 N 



Fig. 3-3 



Relation Between False Alarm Number and Bias Level with a Square- 

 Law Detector. 



Single-Scan Probability of Detection. Having chosen the threshold 

 level on the basis of a required false-alarm time, the probability of detecting 

 a target Pd is found by integrating the probability density function of the 

 signal-plus-noise sum voltage 



Probability of detection = Pa 



i: 



S+N 



{u)du. 



(3-24) 



