168 THE CALCULATION OF RADAR DETECTION PROBABILITY 



Now in general the predetection signal-to-noise ratio is proportional to 

 the reciprocal of the predetection bandwidth: 



S/N'^'^- (3-58) 



Also, the equivalent signal-to-noise ratio of a fluctuating target is 

 proportional to a power of the number of video pulses integrated as in 

 Equation 3-33: 



S/N ~ ny. (3-59) 



The appropriate power y corresponds to the slopes of the curves in 

 Fig. 3-7. 



The equivalent gain in signal-to-noise ratio obtained through postdetec- 

 tion integration can now be expressed either as the ratio of the actual and 

 equivalent predetection bandwidths or simply as w"^: 



D / D \ 7 



Equivalent gain in S/N ~ "m ~ ^^ = ( ^r ) • (3- 



60) 



The equivalent predetection bandwidth thus is given approximately by 



B' = (2^y B'-y. (3-61) 



In Equation 3-33, the value of 7 was found to be 0.6. If this is stretched 

 a point and assumed to be 0.5, the following simple expression is obtained: 



B' = ^|2^f. (3-62) 



This approximation is often used for estimating performance where post- 

 detection filtering is involved. 



3-6 FACTORS AFFECTING ANGULAR RESOLUTION 



In many applications, it is required that a radar system be capable of 

 separating or distinguishing closely spaced targets. This capability is 

 referred to as the resolution of the system. Targets may be resolved on the 

 basis of any of their characteristics. Thus they may be distinguished in 

 range, velocity, or angular position. This paragraph discusses angular 

 resolution. ^^ In ground mapping, the radar's angular resolution provides a 

 primary means of target discrimination. In AEW radar systems, the 

 angular resolution of the system breaks up multiple target complexes into 

 individual components to provide an estimate of the threat. In fire-control 

 radar, the angular resolution must be sufficient to separate desired targets 

 from interfering targets and clutter. 



I'^A similar discussion can be found in J. Freedman, "Resolution in Radar Systems," Proc. 

 IRE 39, 813-1818 (1951), upon which parts of this section are based. 



