166 THE CALCULATION OF RADAR DETECTION PROBABILITY 



An approach similar to that taken in this paragraph should be applicable 

 to many similar problems. For instance, a multiple-PRF method of 

 determining range in a high-PRF pulse doppler system is described in 

 Paragraph 6-G. In order to determine range on a given scan over the target, 

 it must be detected in all PRF's, and the return must not be eclipsed nor 

 can there be interference with a return from another target with the same 

 doppler shift but at a different range. Calculating the probability of 

 measuring range in such a situation is quite complicated, but should be 

 possible with the methods indicated. 



An Example. The following system parameters of a gated pulsed 

 doppler radar are assumed to provide an illustration of the methods under 

 discussion. 



Rq = idealized range = 25 n. mi. 



77 = false-alarm number = 10^ 



T = pulse width = l^sec 



fr = pulse repetition rate = 100 kc/sec 



d = duty ratio = 0.1 



n = pulses integrated = 1 



R = closing rate = 0.33 n. mi. /sec 



/sc = scan time = 2 sec 



AR = range decrement = 0.67 n.mi. 



For 7] = 10^ and n = I, the value of K is found from Fig. 3-7 to be 6 db, 

 or i^ = 4. The basic single-scan probability of detection of a fluctuating 

 target is thus 



p, = ,,-4(ff/25)^^ /^ in n.mi. (3-54) 



This probability has been plotted in Fig. 3-14 as the maximum value o( Pd2- 

 Also plotted in that figure are Pd'^ and Pd^ corresponding to the minimum 

 and average values of Pd2- The shaded area between the minimum and 

 maximum values of Pdi is composed of many oscillations with a period of 

 about 1 /12 n.mi. This is illustrated in the expanded view. At intervals 

 of slightly less than a mile, one of these oscillations deepens into a complete 

 null due to the eclipsing to give a narrow blind region. 



When the effect of the eclipsing is neglected, the cumulative probability 

 is easily determined from Fig. 3-8. Remembering that straddling has the 

 effect of doubling the effective value of A', the normalized range corre- 

 sponding to Pd~ is defined by 



