03, 



1.0 



0.8 



0.6 



0.4 



0.2 



^ 





^ 



S = 2dB,'puls 



e 



^ 



3 





V 





^ 



4 





^ 



\ 





\ 





/ 



// 









5 - 





// 







^ 



6 . 





y 



7 



10 



12 



Threshold K 



Figure 2. These curves for a binomial fixed-sample-size test typical of those 

 employed in stage B indicate that using the same threshold for all range bins 

 would result in little or no loss in optimality. 



False-Alarm Rate (FAR) 



For a fair comparison of the detection capabilities of various testing 

 procedures, all should have the same FAR. The FAR of the fixed-sample single- 

 stage system is proportional to the number m of range bins per beam position and 

 to the false-alarm probability a of an individual test and is inversely proportional 

 to the number N of pulses per beam position. 



FAR = (3600 sec/hr) x PRF x m a/N 



The FAR of the two-stage system (sequential or fixed stages) has no simple 

 exact formulation but is closely approximated by 



FAR = 3600 X PRF x M . Me 



VN 



13 



