172 



THE CALCULATION OF RADAR DETECTION PROBABILITY 



the ratio of their reflected powers, which is 4-to-l or 6 db. The minimum 

 separating the two targets in Fig. 3-17 is 0.707 of the smallest maximum, so 

 that these targets are just barely resolved. The target separation required 

 to achieve this resolution is 1.21 beamwidths. Thus, with a 4-to-l size ratio 

 for targets, the resolution is 21 per cent greater than for targets of equal 

 size. This can become important when the target's size fluctuates randomly. 

 Fig. 3-18 shows how the effective resolution angle varies with target power 

 ratio. 



2 4 6 8 10 12 14 16 18 20 

 POWER RATIO OF TARGETS —db 



Fig. 3-18 Resolution as a Function of Target Power Ratio. 



Another factor which can affect resolution is the signal-to-noise ratio. 

 The simplest way to account for this factor is to apply the already adopted 

 definition for resolution to the received signal-plus-noise power envelope. 

 The deterioration of angular resolution with signal-to-noise ratio which 

 can be determined in this manner is shown in Fig. 3-19. 



2 3 4 5 6 7 

 SIGNAL ■ TO ■ NOISE RATIO ~db 



Fig. 3-19 Resolution of Two Equal Targets as a Function of Signal-to-Noise Ratio. 



