164 



THE CALCULATION OF RADAR DETECTION PROBABILITY 



channel. Of course, there will be two chances to detect the target. If the 

 probability of detecting the target in the first channel is denoted by Pi and 

 that for the second channel by P2, the probability of detecting the target 

 in at least one of the channels will be 



Pd2 = 1 - (1 - Pi)(l - P,) = P,^ p,- p,p,. (3-48) 



The straddling factor will be periodic in range, with a period equal to the 

 pulse length in range units. In the example illustrated in Fig. 3-14, the 



Ro=25 n. mi. 

 AR = 0.67 n. mi. 



10 15 



RANGE (n. mi.) 



Fig. 3-14 Sifigle Scan and Cumulative Probabilities of Detection for a Pulsed 

 Doppler Radar. 



oscillations of the detection probability with a period of about 1 /12 n.mi., 

 which are shown in the expanded view, represent the eflfects of straddling. 

 When the received pulse straddles the transmitted pulse, eclipsing is 

 produced because the receiver is gated off when the transmitter is on to 

 prevent feed-through. The effect of eclipsing is much more severe than that 

 •of gate straddling. When the received pulse is centered on the transmitted 

 pulse, the signal received and the resulting probability of detection become 

 zero and produce a blind range at which the system is completely insen- 

 sitive. These blind ranges are periodically spaced at intervals equal to the 

 repetition period measured in range units. The nulls in the curve in Fig. 

 3-14 at intervals of slightly less than a nautical mile represent the effects of 

 eclipsing. 



