290 TECHNIQUES FOR SIGNAL AND NOISE ANALYSIS 



The power density of the video noise is given in Equation 5-149. It was 

 determined in Paragraph 5-10 that the signal-to-noise ratio at the output 

 of a matched filter is equal to the ratio of the signal energy to the noise 

 power density, so we have 



Signal-to-noise ratio at O.S2{lcj^y{S/NYd\Q/4') 

 output of video filter = z^ = {2a'^y2{S/N)d^T 



= 026S{S/N){Q/i^T) 



= 0.1GS{S/N)n. (5-153) 



The number of pulses per beamwidth given by the ratio Q jxpT has been 

 denoted by n in this equation. 



The bandwidth of the signal can be determined from the spectrum of the 

 scan modulation. The Fourier transform of the modulating function in 

 Equation 5-151 is as follows. 



/ ^ e\ / -co^0.099^ \ 



Spectrum of scan modulation = ( -yO.lSTr • I exp I ■ 1 



(5-154) 

 The bandwidth, as defined by Equation 5-143, is easily computed: 



Scan modulation bandwidth = B 



- 2.35,/^/e 5-155) 



The rms error in measuring the target angle can now be estimated from 

 Equation 5-145 as the scan rate divided by the product of the scan modu- 

 lation bandwidth and the voltage signal-to-noise ratio in the video filter 

 output: 



rms angle error = (M^-y^^ = (li^yi'' = i/Bz (5-156) 



= 4^Q/13S4^^026S{S/N)n 



= O.S25e/^|(S/N)n. 



The angular error of a scanning radar has been studied in the technical 

 literature^ for conditions very similar to the assumptions of this example. 

 In that study the minimum possible rms angular error was found to be 

 approximately proportional to an expression of the form of Equation 5-156 



-P. Swerling, "Maximum Angular Accuracy of a Pulsed Search Radar," Proc. IRE 44, 



1140-1155 (1956). 



