Radar Detection - MATLAB Simulations for Radar Systems Design - page 105

R 0
R

----  

( SNR ) dB = 40 log

(2.98)

Also, define the range R 50 as the range at which P D = 0.5 = P 50 . Normally,

the radar unambiguous range R u is set equal to 2 R 50 .

The cumulative probability of detection refers to detecting the target at least
once by the time it is at range . More precisely, consider a target closing on a
scanning radar, where the target is illuminated only during a scan (frame). As
the target gets closer to the radar, its probability of detection increases since the
SNR is increased. Suppose that the probability of detection during the

R

nth

frame is ; then, the cumulative probability of detecting the target at least
once during the

P D n

nth frame (see Fig. 2.16 ) is given by

n
∏

P C n = 1 – ( 1 – P D i )

(2.99)

i = 1

is usually selected to be very small. Clearly, the probability of not detect-
ing the target during the

P D 1

nth frame is 1 – P C n . The probability of detection for

the ith frame, P D i , is computed as discussed in the previous section.

nt h frame

fra m e 1

…

P D n P D n P D 1

+ 1

(n+ 1 )th frame

Figure 2.16. Detecting a target in many frames.

2.8.1. Mini Design Case Study 2.2
A radar detects a closing target at , with probability of detection
equal to . Assume . Compute and sketch the single look
probability of detection as a function of normalized range (with respect to
), over the interval

R = 10 Km

– 7

P D 0.5 P fa = 10

R = 10 Km ( 2 0 – ) Km . If the range between two succes-

sive frames is 1 Km , what is the cumulative probability of detection at

R = 8 Km ?